Metrics for expq3 (problem 3.4.2)

analyze158.0ms (0.7%)

Memory

6.7MiB live, 261.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25.4%	74.6%	0%	0%	0%	0
0%	0%	25.4%	74.6%	0%	0%	0%	1
0%	0%	25.4%	74.6%	0%	0%	0%	2
0%	0%	25.4%	74.6%	0%	0%	0%	3
0%	0%	22.2%	74.6%	0%	3.2%	0%	4
0%	0%	20.6%	74.6%	0%	4.8%	0%	5
0%	0%	18.3%	74.6%	0%	7.1%	0%	6
0%	0%	10.7%	74.6%	0%	14.7%	0%	7
0%	0%	9.3%	74.6%	0%	16.1%	0%	8
0%	0%	8.2%	74.6%	0%	17.2%	0%	9
0%	0%	5.7%	74.6%	0%	19.7%	0%	10
0%	0%	5%	74.6%	0%	20.4%	0%	11
0%	0%	4.4%	74.6%	0%	21%	0%	12

Compiler

Compiled 52 to 27 computations (48.1% saved)

sample17.8s (75%)

Memory

231.7MiB live, 22 921.9MiB allocated

Samples

12.3s	64 318×	0	invalid
1.6s	8 256×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 10.7s

ival-mult: 3.2s (29.8% of total)

ival-expm1: 1.7s (15.6% of total)

const: 1.6s (14.8% of total)

ival-<=: 1.2s (11.5% of total)

ival-fabs: 1.0s (9.6% of total)

ival-div: 664.0ms (6.2% of total)

ival-add: 601.0ms (5.6% of total)

ival-fmin: 456.0ms (4.3% of total)

ival-and: 202.0ms (1.9% of total)

exact: 47.0ms (0.4% of total)

ival-assert: 27.0ms (0.3% of total)

Bogosity

preprocess321.0ms (1.4%)

Memory

-51.8MiB live, 350.0MiB allocated

Algorithm

2×	egg-herbie

Rules

4 832×	`accelerator-lowering-fma.f32`
4 832×	`accelerator-lowering-fma.f64`
2 736×	`-lowering-.f32`
2 736×	`-lowering-.f64`
1 332×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	257
1	265	253
2	724	251
3	2180	248
4	7098	248
0	17	24
1	43	24
2	96	24
3	161	24
4	312	24
5	641	24
6	1245	24
7	3450	24
8	6179	24
9	7527	24
10	7834	24
11	7910	24
12	7940	24
0	8071	18

Stop Event

1×	iter limit
1×	node limit
1×	node limit

Calls

Call 1

Inputs
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

Outputs

(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

(*.f64 (expm1.f64 (*.f64 eps (+.f64 a b))) (/.f64 (/.f64 eps (expm1.f64 (*.f64 eps a))) (expm1.f64 (*.f64 eps b))))

Call 2

Inputs
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* (+ (neg a) b) eps)) 1)) (* (- (exp (* (neg a) eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* (+ a (neg b)) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* (neg b) eps)) 1)))
(/ (* (neg eps) (- (exp (* (+ a b) (neg eps))) 1)) (* (- (exp (* a (neg eps))) 1) (- (exp (* b (neg eps))) 1)))
(neg (/ (* eps (- (exp (* (+ (neg a) b) eps)) 1)) (* (- (exp (* (neg a) eps)) 1) (- (exp (* b eps)) 1))))
(neg (/ (* eps (- (exp (* (+ a (neg b)) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* (neg b) eps)) 1))))
(neg (/ (* (neg eps) (- (exp (* (+ a b) (neg eps))) 1)) (* (- (exp (* a (neg eps))) 1) (- (exp (* b (neg eps))) 1))))
(/ (* eps (- (exp (* (+ b a) eps)) 1)) (* (- (exp (* b eps)) 1) (- (exp (* a eps)) 1)))
(/ (* a (- (exp (* (+ eps b) a)) 1)) (* (- (exp (* eps a)) 1) (- (exp (* b a)) 1)))
(/ (* b (- (exp (* (+ a eps) b)) 1)) (* (- (exp (* a b)) 1) (- (exp (* eps b)) 1)))

Outputs
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(* (+ (pow (exp eps) (+ a b)) -1) (/ (/ eps (+ (pow (exp eps) b) -1)) (+ (pow (exp a) eps) -1)))
(/ (* eps (- (exp (* (+ (neg a) b) eps)) 1)) (* (- (exp (* (neg a) eps)) 1) (- (exp (* b eps)) 1)))
(* (+ (pow (exp eps) (- b a)) -1) (/ (/ eps (+ (pow (exp eps) b) -1)) (+ (pow (exp a) (neg eps)) -1)))
(/ (* eps (- (exp (* (+ a (neg b)) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* (neg b) eps)) 1)))
(* eps (/ (+ (pow (exp eps) (- a b)) -1) (* (+ (pow (exp a) eps) -1) (+ (pow (exp eps) (neg b)) -1))))
(/ (* (neg eps) (- (exp (* (+ a b) (neg eps))) 1)) (* (- (exp (* a (neg eps))) 1) (- (exp (* b (neg eps))) 1)))
(/ (- eps (/ eps (pow (exp eps) (+ a b)))) (* (+ (pow (exp a) (neg eps)) -1) (+ (pow (exp eps) (neg b)) -1)))
(neg (/ (* eps (- (exp (* (+ (neg a) b) eps)) 1)) (* (- (exp (* (neg a) eps)) 1) (- (exp (* b eps)) 1))))
(* (+ (pow (exp eps) (- b a)) -1) (/ (/ eps (+ (pow (exp eps) b) -1)) (- 1 (pow (exp a) (neg eps)))))
(neg (/ (* eps (- (exp (* (+ a (neg b)) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* (neg b) eps)) 1))))
(* (+ (pow (exp eps) (- a b)) -1) (/ (/ eps (- 1 (pow (exp a) eps))) (+ (pow (exp eps) (neg b)) -1)))
(neg (/ (* (neg eps) (- (exp (* (+ a b) (neg eps))) 1)) (* (- (exp (* a (neg eps))) 1) (- (exp (* b (neg eps))) 1))))
(/ (- eps (/ eps (pow (exp eps) (+ a b)))) (* (+ (pow (exp a) (neg eps)) -1) (- 1 (pow (exp eps) (neg b)))))
(/ (* eps (- (exp (* (+ b a) eps)) 1)) (* (- (exp (* b eps)) 1) (- (exp (* a eps)) 1)))
(* (+ (pow (exp eps) (+ a b)) -1) (/ (/ eps (+ (pow (exp eps) b) -1)) (+ (pow (exp a) eps) -1)))
(/ (* a (- (exp (* (+ eps b) a)) 1)) (* (- (exp (* eps a)) 1) (- (exp (* b a)) 1)))
(/ (- (* a (pow (exp a) (+ eps b))) a) (* (+ (pow (exp a) eps) -1) (+ (pow (exp a) b) -1)))
(/ (* b (- (exp (* (+ a eps) b)) 1)) (* (- (exp (* a b)) 1) (- (exp (* eps b)) 1)))
(/ (- (* b (pow (exp b) (+ eps a))) b) (* (+ (pow (exp eps) b) -1) (+ (pow (exp a) b) -1)))

Symmetry

(sort a b)

explain263.0ms (1.1%)

Memory

11.0MiB live, 324.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
242	0	-	3	(7.566481447026095e-99 6.30556912951083e-17 2.000764706103117e-101)	`(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))`
146	0	-	0	-	`(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))`
116	0	-	0	-	`(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))`
109	1	(-1.9837963419166407e-19 -1.1518507712851906e-161 2.2129558108121056e-162)	0	-	`(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))`
0	0	-	0	-	`(+.f64 a b)`
0	0	-	0	-	`(*.f64 b eps)`
0	0	-	0	-	`(exp.f64 (*.f64 a eps))`
0	0	-	0	-	`a`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(*.f64 a eps)`
0	0	-	0	-	`(exp.f64 (*.f64 (+.f64 a b) eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))`
0	0	-	0	-	`(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64)))`
0	0	-	0	-	`(*.f64 (+.f64 a b) eps)`
0	0	-	0	-	`(exp.f64 (*.f64 b eps))`
0	0	-	0	-	`b`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))`	u/u	212	0
↳	`(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64)))`	underflow	212
↳	`(*.f64 (+.f64 a b) eps)`	underflow	110
↳	`(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))`	underflow	110
↳	`(*.f64 b eps)`	underflow	146
↳	`(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))`	underflow	140
↳	`(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))`	underflow	146
↳	`(.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))`	underflow	239
↳	`(*.f64 a eps)`	underflow	140
`-.f64`	`(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))`	cancellation	146	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))`	cancellation	116	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))`	cancellation	110	0
`/.f64`	`(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))`	n/u	27	0
↳	`(*.f64 b eps)`	underflow	146
↳	`(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))`	underflow	140
↳	`(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))`	underflow	146
↳	`(.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64)))`	underflow	239
↳	`(*.f64 a eps)`	underflow	140

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	110
3	83
4	63

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

62.0ms

512×

valid

Compiler

Compiled 256 to 72 computations (71.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 15.0ms (36.5% of total)

ival-exp: 12.0ms (29.2% of total)

ival-expm1: 7.0ms (17% of total)

ival-div: 3.0ms (7.3% of total)

ival-add: 3.0ms (7.3% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	0.0%	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))

Status

Accuracy

Program

▶

0.0%

(/.f64 (*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))

Compiler

Compiled 27 to 17 computations (37% saved)

simplify233.0ms (1%)

Memory

25.4MiB live, 269.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))
✓	cost-diff	128	(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))
✓	cost-diff	128	(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))
✓	cost-diff	128	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))

Rules

4 832×	`accelerator-lowering-fma.f32`
4 832×	`accelerator-lowering-fma.f64`
2 736×	`-lowering-.f32`
2 736×	`-lowering-.f64`
1 132×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	99
1	43	99
2	96	99
3	161	99
4	312	99
5	641	99
6	1245	99
7	3450	99
8	6179	99
9	7527	99
10	7834	99
11	7910	99
12	7940	99
0	8071	81

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(* eps (- (exp (* (+ a b) eps)) 1))
eps
(- (exp (* (+ a b) eps)) 1)
(exp (* (+ a b) eps))
(* (+ a b) eps)
(+ a b)
a
b
1
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
(- (exp (* a eps)) 1)
(exp (* a eps))
(* a eps)
(- (exp (* b eps)) 1)
(exp (* b eps))
(* b eps)

Outputs
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (/.f64 (/.f64 eps (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))
(* eps (- (exp (* (+ a b) eps)) 1))
(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
eps
(- (exp (* (+ a b) eps)) 1)
(expm1.f64 (*.f64 eps (+.f64 a b)))
(exp (* (+ a b) eps))
(exp.f64 (*.f64 eps (+.f64 a b)))
(* (+ a b) eps)
(*.f64 eps (+.f64 a b))
(+ a b)
(+.f64 a b)
a
b
1
#s(literal 1 binary64)
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
(- (exp (* a eps)) 1)
(expm1.f64 (*.f64 eps a))
(exp (* a eps))
(exp.f64 (*.f64 eps a))
(* a eps)
(*.f64 eps a)
(- (exp (* b eps)) 1)
(expm1.f64 (*.f64 eps b))
(exp (* b eps))
(exp.f64 (*.f64 eps b))
(* b eps)
(*.f64 eps b)

localize55.0ms (0.2%)

Memory

-33.2MiB live, 84.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	61.5%	(-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))
✓	accuracy	60.4%	(-.f64 (exp.f64 (*.f64 a eps)) #s(literal 1 binary64))
✓	accuracy	49.5%	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))
✓	accuracy	9.2%	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))

Samples

35.0ms

256×

valid

Compiler

Compiled 101 to 19 computations (81.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 7.0ms (33.2% of total)

ival-expm1: 6.0ms (28.4% of total)

ival-exp: 5.0ms (23.7% of total)

ival-div: 2.0ms (9.5% of total)

ival-add: 1.0ms (4.7% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series20.0ms (0.1%)

Memory

23.3MiB live, 23.3MiB allocated

Counts

4 → 120

Calls

Call 1

Inputs
#<alt (- (exp (* (+ a b) eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>

Outputs
#<alt (- (exp (* b eps)) 1)>
#<alt (- (+ (exp (* b eps)) (* a (* eps (exp (* b eps))))) 1)>
#<alt (- (+ (exp (* b eps)) (* a (+ (* 1/2 (* a (* (pow eps 2) (exp (* b eps))))) (* eps (exp (* b eps)))))) 1)>
#<alt (- (+ (exp (* b eps)) (* a (+ (* a (+ (* 1/6 (* a (* (pow eps 3) (exp (* b eps))))) (* 1/2 (* (pow eps 2) (exp (* b eps)))))) (* eps (exp (* b eps)))))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (- b (* -1 a)))) 1)>
#<alt (- (exp (* eps (- b (* -1 a)))) 1)>
#<alt (- (exp (* eps (- b (* -1 a)))) 1)>
#<alt (- (exp (* eps (- b (* -1 a)))) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (+ (exp (* a eps)) (* b (* eps (exp (* a eps))))) 1)>
#<alt (- (+ (exp (* a eps)) (* b (+ (* 1/2 (* b (* (pow eps 2) (exp (* a eps))))) (* eps (exp (* a eps)))))) 1)>
#<alt (- (+ (exp (* a eps)) (* b (+ (* b (+ (* 1/6 (* b (* (pow eps 3) (exp (* a eps))))) (* 1/2 (* (pow eps 2) (exp (* a eps)))))) (* eps (exp (* a eps)))))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (- a (* -1 b)))) 1)>
#<alt (- (exp (* eps (- a (* -1 b)))) 1)>
#<alt (- (exp (* eps (- a (* -1 b)))) 1)>
#<alt (- (exp (* eps (- a (* -1 b)))) 1)>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a (+ b (* 1/2 (* eps (pow (+ a b) 2))))))>
#<alt (* eps (+ a (+ b (* eps (+ (* 1/6 (* eps (pow (+ a b) 3))) (* 1/2 (pow (+ a b) 2)))))))>
#<alt (* eps (+ a (+ b (* eps (+ (* 1/2 (pow (+ a b) 2)) (* eps (+ (* 1/24 (* eps (pow (+ a b) 4))) (* 1/6 (pow (+ a b) 3)))))))))>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (* a eps)>
#<alt (* a (+ eps (* 1/2 (* a (pow eps 2)))))>
#<alt (* a (+ eps (* a (+ (* 1/6 (* a (pow eps 3))) (* 1/2 (pow eps 2))))))>
#<alt (* a (+ eps (* a (+ (* 1/2 (pow eps 2)) (* a (+ (* 1/24 (* a (pow eps 4))) (* 1/6 (pow eps 3))))))))>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (* a eps)>
#<alt (* eps (+ a (* 1/2 (* (pow a 2) eps))))>
#<alt (* eps (+ a (* eps (+ (* 1/6 (* (pow a 3) eps)) (* 1/2 (pow a 2))))))>
#<alt (* eps (+ a (* eps (+ (* 1/2 (pow a 2)) (* eps (+ (* 1/24 (* (pow a 4) eps)) (* 1/6 (pow a 3))))))))>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (* b eps)>
#<alt (* b (+ eps (* 1/2 (* b (pow eps 2)))))>
#<alt (* b (+ eps (* b (+ (* 1/6 (* b (pow eps 3))) (* 1/2 (pow eps 2))))))>
#<alt (* b (+ eps (* b (+ (* 1/2 (pow eps 2)) (* b (+ (* 1/24 (* b (pow eps 4))) (* 1/6 (pow eps 3))))))))>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (* b eps)>
#<alt (* eps (+ b (* 1/2 (* (pow b 2) eps))))>
#<alt (* eps (+ b (* eps (+ (* 1/6 (* (pow b 3) eps)) (* 1/2 (pow b 2))))))>
#<alt (* eps (+ b (* eps (+ (* 1/2 (pow b 2)) (* eps (+ (* 1/24 (* (pow b 4) eps)) (* 1/6 (pow b 3))))))))>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (exp (* b eps)) 1)>
#<alt (/ (+ a b) (* a b))>
#<alt (+ (* eps (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (+ (/ 1 a) (/ 1 b)))>
#<alt (+ (* eps (- (+ (* 1/2 (/ (pow (+ a b) 2) (* a b))) (* eps (- (* 1/6 (/ (pow (+ a b) 3) (* a b))) (+ (/ (* (+ a b) (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2)))))) (* (pow a 2) (pow b 2))) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b)))))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (+ (/ 1 a) (/ 1 b)))>
#<alt (+ (* eps (- (+ (* 1/2 (/ (pow (+ a b) 2) (* a b))) (* eps (- (+ (* 1/6 (/ (pow (+ a b) 3) (* a b))) (* eps (- (* 1/24 (/ (pow (+ a b) 4) (* a b))) (+ (/ (* (+ a b) (+ (* 1/24 (* a (pow b 4))) (+ (* 1/24 (* (pow a 4) b)) (+ (* 1/12 (* (pow a 2) (pow b 3))) (* 1/12 (* (pow a 3) (pow b 2))))))) (* (pow a 2) (pow b 2))) (+ (/ (* (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2))))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b)) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/6 (/ (pow (+ a b) 3) (* a b))) (+ (/ (* (+ a b) (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2)))))) (* (pow a 2) (pow b 2))) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b))))) (* a b))))))) (+ (/ (* (+ a b) (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2)))))) (* (pow a 2) (pow b 2))) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b)))))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (+ (/ 1 a) (/ 1 b)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ 1 a)>
#<alt (/ (+ 1 (* a (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps)))) a)>
#<alt (/ (+ 1 (* a (- (+ (* a (- (* 1/2 (/ (* (pow eps 2) (exp (* b eps))) (- (exp (* b eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1))) (* 1/2 eps)))) a)>
#<alt (/ (+ 1 (* a (- (+ (* a (- (+ (* 1/2 (/ (* (pow eps 2) (exp (* b eps))) (- (exp (* b eps)) 1))) (* a (- (* 1/6 (/ (* (pow eps 3) (exp (* b eps))) (- (exp (* b eps)) 1))) (+ (* 1/24 (pow eps 3)) (+ (* 1/6 (* (pow eps 2) (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps)))) (* 1/2 (* eps (- (* 1/2 (/ (* (pow eps 2) (exp (* b eps))) (- (exp (* b eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps))))))))))))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1))) (* 1/2 eps)))) a)>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ 1 b)>
#<alt (/ (+ 1 (* b (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps)))) b)>
#<alt (/ (+ 1 (* b (- (+ (* b (- (* 1/2 (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1))) (* 1/2 eps)))) b)>
#<alt (/ (+ 1 (* b (- (+ (* b (- (+ (* 1/2 (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1))) (* b (- (* 1/6 (/ (* (pow eps 3) (exp (* a eps))) (- (exp (* a eps)) 1))) (+ (* 1/24 (pow eps 3)) (+ (* 1/6 (* (pow eps 2) (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps)))) (* 1/2 (* eps (- (* 1/2 (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps))))))))))))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1))) (* 1/2 eps)))) b)>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>

Calls

30 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
2.0ms	a	@	0	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
2.0ms	eps	@	-inf	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
1.0ms	a	@	inf	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
1.0ms	b	@	inf	(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

rewrite480.0ms (2%)

Memory

-4.5MiB live, 583.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 838×	`-lowering-.f32`
5 838×	`-lowering-.f64`
4 440×	`/-lowering-/.f32`
4 440×	`/-lowering-/.f64`
3 902×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	95	44
2	753	44
0	8473	32

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 364

Calls

Call 1

Inputs
(- (exp (* (+ a b) eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* b eps)) 1)
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

Outputs
(+.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 (*.f64 (+.f64 a b) eps)))
(+.f64 (/.f64 (exp.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))))))))
(+.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64)))))
(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)))))))
(-.f64 (/.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))) (-.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))) #s(literal 1 binary64)) (.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))) #s(literal 1 binary64)) (.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal -1 binary64)))))
(fma.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal -1 binary64))
(fma.f64 (exp.f64 (.f64 a eps)) (exp.f64 (.f64 b eps)) #s(literal -1 binary64))
(fma.f64 (exp.f64 (.f64 b eps)) (exp.f64 (.f64 a eps)) #s(literal -1 binary64))
(fma.f64 (exp.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))))))))
(fma.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64)))))
(fma.f64 (exp.f64 (.f64 (+.f64 a b) (/.f64 eps #s(literal 2 binary64)))) (exp.f64 (.f64 (+.f64 a b) (/.f64 eps #s(literal 2 binary64)))) #s(literal -1 binary64))
(fma.f64 (exp.f64 (.f64 (+.f64 a b) (/.f64 eps #s(literal 2 binary64)))) (.f64 (exp.f64 (*.f64 (+.f64 a b) (/.f64 eps #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 (/.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (/.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64)))))
(fma.f64 (pow.f64 (exp.f64 eps) (/.f64 (+.f64 a b) #s(literal 2 binary64))) (pow.f64 (exp.f64 eps) (/.f64 (+.f64 a b) #s(literal 2 binary64))) #s(literal -1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (exp.f64 (.f64 (+.f64 a b) (/.f64 eps #s(literal 2 binary64))))) (exp.f64 (*.f64 (+.f64 a b) (/.f64 eps #s(literal 2 binary64)))) #s(literal -1 binary64))
(expm1.f64 (*.f64 (+.f64 a b) eps))
(expm1.f64 (*.f64 (log.f64 (exp.f64 eps)) (+.f64 a b)))
(neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 (+.f64 a b) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (+.f64 a b) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (+.f64 a b) eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))) #s(literal 1 binary64)) (.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal -1 binary64))) (expm1.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64)))))
(/.f64 (expm1.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (*.f64 (+.f64 a b) eps))))))
(/.f64 (expm1.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))) (-.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))) #s(literal 1 binary64)) (.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 (+.f64 a b) eps)))))
(/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))) (+.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (*.f64 (+.f64 a b) eps)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64)))) (neg.f64 (-.f64 (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))) #s(literal 1 binary64)) (.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal -1 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)))) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)))) (-.f64 #s(literal -1 binary64) (exp.f64 (*.f64 (+.f64 a b) eps))))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)))))) (.f64 (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))))) #s(literal 1 binary64))) (.f64 (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps))))) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (*.f64 (+.f64 a b) eps)))))))
(/.f64 (-.f64 (+.f64 (exp.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)))) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (pow.f64 (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))))) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (*.f64 (+.f64 a b) eps)))))))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 (.f64 (+.f64 a b) eps) #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (.f64 (+.f64 a b) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 (+.f64 a b) eps)))))))
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(.f64 (.f64 #s(literal 1 binary64) (.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (-.f64 #s(literal 0 binary64) eps))) (/.f64 #s(literal -1 binary64) (.f64 (expm1.f64 (.f64 a eps)) (expm1.f64 (*.f64 b eps)))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 eps (expm1.f64 (.f64 b eps)))) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 a eps))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 a eps)))) (/.f64 eps (expm1.f64 (*.f64 b eps))))
(.f64 (.f64 #s(literal 1 binary64) (/.f64 (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (/.f64 (expm1.f64 (.f64 a eps)) eps)) (expm1.f64 (.f64 b (.f64 eps #s(literal 3 binary64)))))) (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 b eps))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 b eps)))))
(.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b (.f64 eps #s(literal 3 binary64)))))) (+.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 b eps))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 b eps)))))
(.f64 (.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 #s(literal 2 binary64) (.f64 b eps))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 b eps))))
(.f64 (.f64 (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps))) eps) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 a eps))))
(.f64 (.f64 (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps))) (/.f64 eps (expm1.f64 (.f64 a (.f64 eps #s(literal 3 binary64)))))) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 a eps)) (exp.f64 (.f64 #s(literal 2 binary64) (*.f64 a eps))))))
(.f64 (.f64 (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps))) (/.f64 eps (expm1.f64 (.f64 #s(literal 2 binary64) (.f64 a eps))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a eps))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 (.f64 a eps)) (expm1.f64 (.f64 b eps)))) eps) (expm1.f64 (.f64 (+.f64 a b) eps)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 (.f64 a eps)) (expm1.f64 (.f64 b eps)))) (expm1.f64 (.f64 (+.f64 a b) eps))) eps)

simplify511.0ms (2.2%)

Memory

2.4MiB live, 755.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 330×	`accelerator-lowering-fma.f32`
9 330×	`accelerator-lowering-fma.f64`
7 346×	`-lowering-.f32`
7 346×	`-lowering-.f64`
4 214×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	336	2612
1	1079	2564
2	3419	2564
0	8500	2144

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(- (exp (* b eps)) 1)
(- (+ (exp (* b eps)) (* a (* eps (exp (* b eps))))) 1)
(- (+ (exp (* b eps)) (* a (+ (* 1/2 (* a (* (pow eps 2) (exp (* b eps))))) (* eps (exp (* b eps)))))) 1)
(- (+ (exp (* b eps)) (* a (+ (* a (+ (* 1/6 (* a (* (pow eps 3) (exp (* b eps))))) (* 1/2 (* (pow eps 2) (exp (* b eps)))))) (* eps (exp (* b eps)))))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (- b (* -1 a)))) 1)
(- (exp (* eps (- b (* -1 a)))) 1)
(- (exp (* eps (- b (* -1 a)))) 1)
(- (exp (* eps (- b (* -1 a)))) 1)
(- (exp (* a eps)) 1)
(- (+ (exp (* a eps)) (* b (* eps (exp (* a eps))))) 1)
(- (+ (exp (* a eps)) (* b (+ (* 1/2 (* b (* (pow eps 2) (exp (* a eps))))) (* eps (exp (* a eps)))))) 1)
(- (+ (exp (* a eps)) (* b (+ (* b (+ (* 1/6 (* b (* (pow eps 3) (exp (* a eps))))) (* 1/2 (* (pow eps 2) (exp (* a eps)))))) (* eps (exp (* a eps)))))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (- a (* -1 b)))) 1)
(- (exp (* eps (- a (* -1 b)))) 1)
(- (exp (* eps (- a (* -1 b)))) 1)
(- (exp (* eps (- a (* -1 b)))) 1)
(* eps (+ a b))
(* eps (+ a (+ b (* 1/2 (* eps (pow (+ a b) 2))))))
(* eps (+ a (+ b (* eps (+ (* 1/6 (* eps (pow (+ a b) 3))) (* 1/2 (pow (+ a b) 2)))))))
(* eps (+ a (+ b (* eps (+ (* 1/2 (pow (+ a b) 2)) (* eps (+ (* 1/24 (* eps (pow (+ a b) 4))) (* 1/6 (pow (+ a b) 3)))))))))
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(* a eps)
(* a (+ eps (* 1/2 (* a (pow eps 2)))))
(* a (+ eps (* a (+ (* 1/6 (* a (pow eps 3))) (* 1/2 (pow eps 2))))))
(* a (+ eps (* a (+ (* 1/2 (pow eps 2)) (* a (+ (* 1/24 (* a (pow eps 4))) (* 1/6 (pow eps 3))))))))
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(* a eps)
(* eps (+ a (* 1/2 (* (pow a 2) eps))))
(* eps (+ a (* eps (+ (* 1/6 (* (pow a 3) eps)) (* 1/2 (pow a 2))))))
(* eps (+ a (* eps (+ (* 1/2 (pow a 2)) (* eps (+ (* 1/24 (* (pow a 4) eps)) (* 1/6 (pow a 3))))))))
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(- (exp (* a eps)) 1)
(* b eps)
(* b (+ eps (* 1/2 (* b (pow eps 2)))))
(* b (+ eps (* b (+ (* 1/6 (* b (pow eps 3))) (* 1/2 (pow eps 2))))))
(* b (+ eps (* b (+ (* 1/2 (pow eps 2)) (* b (+ (* 1/24 (* b (pow eps 4))) (* 1/6 (pow eps 3))))))))
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(* b eps)
(* eps (+ b (* 1/2 (* (pow b 2) eps))))
(* eps (+ b (* eps (+ (* 1/6 (* (pow b 3) eps)) (* 1/2 (pow b 2))))))
(* eps (+ b (* eps (+ (* 1/2 (pow b 2)) (* eps (+ (* 1/24 (* (pow b 4) eps)) (* 1/6 (pow b 3))))))))
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(- (exp (* b eps)) 1)
(/ (+ a b) (* a b))
(+ (* eps (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (+ (/ 1 a) (/ 1 b)))
(+ (* eps (- (+ (* 1/2 (/ (pow (+ a b) 2) (* a b))) (* eps (- (* 1/6 (/ (pow (+ a b) 3) (* a b))) (+ (/ (* (+ a b) (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2)))))) (* (pow a 2) (pow b 2))) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b)))))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (+ (/ 1 a) (/ 1 b)))
(+ (* eps (- (+ (* 1/2 (/ (pow (+ a b) 2) (* a b))) (* eps (- (+ (* 1/6 (/ (pow (+ a b) 3) (* a b))) (* eps (- (* 1/24 (/ (pow (+ a b) 4) (* a b))) (+ (/ (* (+ a b) (+ (* 1/24 (* a (pow b 4))) (+ (* 1/24 (* (pow a 4) b)) (+ (* 1/12 (* (pow a 2) (pow b 3))) (* 1/12 (* (pow a 3) (pow b 2))))))) (* (pow a 2) (pow b 2))) (+ (/ (* (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2))))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b)) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/6 (/ (pow (+ a b) 3) (* a b))) (+ (/ (* (+ a b) (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2)))))) (* (pow a 2) (pow b 2))) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b))))) (* a b))))))) (+ (/ (* (+ a b) (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2)))))) (* (pow a 2) (pow b 2))) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b)))))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (+ (/ 1 a) (/ 1 b)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ 1 a)
(/ (+ 1 (* a (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps)))) a)
(/ (+ 1 (* a (- (+ (* a (- (* 1/2 (/ (* (pow eps 2) (exp (* b eps))) (- (exp (* b eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1))) (* 1/2 eps)))) a)
(/ (+ 1 (* a (- (+ (* a (- (+ (* 1/2 (/ (* (pow eps 2) (exp (* b eps))) (- (exp (* b eps)) 1))) (* a (- (* 1/6 (/ (* (pow eps 3) (exp (* b eps))) (- (exp (* b eps)) 1))) (+ (* 1/24 (pow eps 3)) (+ (* 1/6 (* (pow eps 2) (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps)))) (* 1/2 (* eps (- (* 1/2 (/ (* (pow eps 2) (exp (* b eps))) (- (exp (* b eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps))))))))))))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* b eps))) (- (exp (* b eps)) 1))) (* 1/2 eps)))) a)
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ 1 b)
(/ (+ 1 (* b (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps)))) b)
(/ (+ 1 (* b (- (+ (* b (- (* 1/2 (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1))) (* 1/2 eps)))) b)
(/ (+ 1 (* b (- (+ (* b (- (+ (* 1/2 (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1))) (* b (- (* 1/6 (/ (* (pow eps 3) (exp (* a eps))) (- (exp (* a eps)) 1))) (+ (* 1/24 (pow eps 3)) (+ (* 1/6 (* (pow eps 2) (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps)))) (* 1/2 (* eps (- (* 1/2 (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps))))))))))))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1))) (* 1/2 eps)))) b)
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

Outputs
(- (exp (* b eps)) 1)
(expm1.f64 (*.f64 b eps))
(- (+ (exp (* b eps)) (* a (* eps (exp (* b eps))))) 1)
(+.f64 (.f64 (+.f64 (.f64 eps a) #s(literal 1 binary64)) (exp.f64 (*.f64 b eps))) #s(literal -1 binary64))
(- (+ (exp (* b eps)) (* a (+ (* 1/2 (* a (* (pow eps 2) (exp (* b eps))))) (* eps (exp (* b eps)))))) 1)
(+.f64 (+.f64 (.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 (exp.f64 (.f64 b eps)) (.f64 eps eps))) (.f64 (+.f64 (.f64 eps a) #s(literal 1 binary64)) (exp.f64 (*.f64 b eps)))) #s(literal -1 binary64))
(- (+ (exp (* b eps)) (* a (+ (* a (+ (* 1/6 (* a (* (pow eps 3) (exp (* b eps))))) (* 1/2 (* (pow eps 2) (exp (* b eps)))))) (* eps (exp (* b eps)))))) 1)
(+.f64 (+.f64 (.f64 (+.f64 (.f64 (.f64 a (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (exp.f64 (.f64 b eps))) (.f64 (exp.f64 (.f64 b eps)) (.f64 eps (.f64 eps #s(literal 1/2 binary64))))) (.f64 a a)) (.f64 (+.f64 (.f64 eps a) #s(literal 1 binary64)) (exp.f64 (*.f64 b eps)))) #s(literal -1 binary64))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (- b (* -1 a)))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (- b (* -1 a)))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (- b (* -1 a)))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (- b (* -1 a)))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* a eps)) 1)
(expm1.f64 (*.f64 eps a))
(- (+ (exp (* a eps)) (* b (* eps (exp (* a eps))))) 1)
(+.f64 #s(literal -1 binary64) (.f64 (+.f64 (.f64 b eps) #s(literal 1 binary64)) (exp.f64 (*.f64 eps a))))
(- (+ (exp (* a eps)) (* b (+ (* 1/2 (* b (* (pow eps 2) (exp (* a eps))))) (* eps (exp (* a eps)))))) 1)
(+.f64 #s(literal -1 binary64) (+.f64 (.f64 (.f64 (exp.f64 (.f64 eps a)) (.f64 b (.f64 eps eps))) (.f64 b #s(literal 1/2 binary64))) (.f64 (+.f64 (.f64 b eps) #s(literal 1 binary64)) (exp.f64 (*.f64 eps a)))))
(- (+ (exp (* a eps)) (* b (+ (* b (+ (* 1/6 (* b (* (pow eps 3) (exp (* a eps))))) (* 1/2 (* (pow eps 2) (exp (* a eps)))))) (* eps (exp (* a eps)))))) 1)
(+.f64 #s(literal -1 binary64) (+.f64 (.f64 (+.f64 (.f64 (.f64 b (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64))))) (exp.f64 (.f64 eps a))) (.f64 (exp.f64 (.f64 eps a)) (.f64 eps (.f64 eps #s(literal 1/2 binary64))))) (.f64 b b)) (.f64 (+.f64 (.f64 b eps) #s(literal 1 binary64)) (exp.f64 (*.f64 eps a)))))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (- a (* -1 b)))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (- a (* -1 b)))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (- a (* -1 b)))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (- a (* -1 b)))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(* eps (+ a b))
(*.f64 eps (+.f64 b a))
(* eps (+ a (+ b (* 1/2 (* eps (pow (+ a b) 2))))))
(.f64 eps (+.f64 (+.f64 b a) (.f64 (.f64 (+.f64 b a) (+.f64 b a)) (.f64 eps #s(literal 1/2 binary64)))))
(* eps (+ a (+ b (* eps (+ (* 1/6 (* eps (pow (+ a b) 3))) (* 1/2 (pow (+ a b) 2)))))))
(.f64 eps (+.f64 b (+.f64 a (.f64 eps (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 b a) (+.f64 b a))) (.f64 (.f64 (+.f64 b a) (.f64 (+.f64 b a) (+.f64 b a))) (.f64 eps #s(literal 1/6 binary64))))))))
(* eps (+ a (+ b (* eps (+ (* 1/2 (pow (+ a b) 2)) (* eps (+ (* 1/24 (* eps (pow (+ a b) 4))) (* 1/6 (pow (+ a b) 3)))))))))
(.f64 eps (+.f64 (+.f64 b a) (.f64 eps (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 b a) (+.f64 b a))) (.f64 eps (+.f64 (.f64 (pow.f64 (+.f64 b a) #s(literal 4 binary64)) (.f64 eps #s(literal 1/24 binary64))) (.f64 (.f64 (+.f64 b a) (+.f64 b a)) (.f64 (+.f64 b a) #s(literal 1/6 binary64)))))))))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(- (exp (* eps (+ a b))) 1)
(expm1.f64 (*.f64 eps (+.f64 b a)))
(* a eps)
(*.f64 eps a)
(* a (+ eps (* 1/2 (* a (pow eps 2)))))
(.f64 eps (+.f64 a (.f64 eps (.f64 a (.f64 a #s(literal 1/2 binary64))))))
(* a (+ eps (* a (+ (* 1/6 (* a (pow eps 3))) (* 1/2 (pow eps 2))))))
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(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ (+ 1 (* b (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps)))) b)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))))) b)
(/ (+ 1 (* b (- (+ (* b (- (* 1/2 (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1))) (* 1/2 eps)))) b)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (+.f64 (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))) (.f64 b (+.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 eps a)) (.f64 eps (.f64 eps #s(literal 1/2 binary64)))) (expm1.f64 (.f64 eps a))) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64)))))))) b)
(/ (+ 1 (* b (- (+ (* b (- (+ (* 1/2 (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1))) (* b (- (* 1/6 (/ (* (pow eps 3) (exp (* a eps))) (- (exp (* a eps)) 1))) (+ (* 1/24 (pow eps 3)) (+ (* 1/6 (* (pow eps 2) (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps)))) (* 1/2 (* eps (- (* 1/2 (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps))))))))))))) (+ (* 1/6 (pow eps 2)) (* 1/2 (* eps (- (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1)) (* 1/2 eps))))))) (/ (* eps (exp (* a eps))) (- (exp (* a eps)) 1))) (* 1/2 eps)))) b)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (+.f64 (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))) (.f64 b (+.f64 (.f64 b (+.f64 (-.f64 (/.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) (exp.f64 (.f64 eps a))) (expm1.f64 (.f64 eps a))) (+.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/24 binary64))) (.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64)))))) (.f64 (+.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 eps a)) (.f64 eps (.f64 eps #s(literal 1/2 binary64)))) (expm1.f64 (.f64 eps a))) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64)))) (.f64 eps #s(literal -1/2 binary64))))) (+.f64 (+.f64 (/.f64 (.f64 (exp.f64 (.f64 eps a)) (.f64 eps (.f64 eps #s(literal 1/2 binary64)))) (expm1.f64 (.f64 eps a))) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))) (*.f64 eps #s(literal -1/2 binary64))))))))) b)
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 b a)))) (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 eps a))))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 b a)))) (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 eps a))))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 b a)))) (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 eps a))))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 b a)))) (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 eps a))))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 b a)))) (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 eps a))))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 b a)))) (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 eps a))))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 b a)))) (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 eps a))))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 b a)))) (.f64 (expm1.f64 (.f64 b eps)) (expm1.f64 (*.f64 eps a))))

eval47.0ms (0.2%)

Memory: 12.8MiB live, 85.3MiB allocated
Compiler: Compiled 17 594 to 1 599 computations (90.9% saved)

prune99.0ms (0.4%)

Memory

23.0MiB live, 145.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	479	5	484
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	480	5	485

Accuracy

100.0%

Counts

485 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f64 (/.f64 (+.f64 b a) a) b)
▶	31.5%	(/.f64 (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (/.f64 (expm1.f64 (.f64 a eps)) eps)) (expm1.f64 (*.f64 b eps)))
▶	43.6%	(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))))) b)
▶	52.8%	(/.f64 #s(literal 1 binary64) b)
▶	47.4%	(/.f64 #s(literal 1 binary64) a)

Compiler

Compiled 130 to 86 computations (33.8% saved)

simplify281.0ms (1.2%)

Memory

-49.4MiB live, 446.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 (+.f64 a b) eps)
✓	cost-diff	(expm1.f64 (*.f64 (+.f64 a b) eps))
✓	cost-diff	(/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (/.f64 (expm1.f64 (.f64 a eps)) eps))
✓	cost-diff	(/.f64 (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (/.f64 (expm1.f64 (.f64 a eps)) eps)) (expm1.f64 (*.f64 b eps)))
✓	cost-diff	(.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps a))) #s(literal -1/2 binary64)))
✓	cost-diff	(.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64)))))
✓	cost-diff	(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))))) b)
✓	cost-diff	(/.f64 #s(literal 1 binary64) b)
✓	cost-diff	(/.f64 #s(literal 1 binary64) a)
✓	cost-diff	(+.f64 b a)
✓	cost-diff	(/.f64 (+.f64 b a) a)
✓	cost-diff	(/.f64 (/.f64 (+.f64 b a) a) b)

Rules

5 916×	`accelerator-lowering-fma.f32`
5 916×	`accelerator-lowering-fma.f64`
2 824×	`-lowering-.f32`
2 824×	`-lowering-.f64`
1 332×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	227
1	76	227
2	147	227
3	290	227
4	531	227
5	1265	227
6	3425	227
7	6630	227
0	8060	193

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (+ b a) a) b)
(/ (+ b a) a)
(+ b a)
b
a
(/ 1 a)
1
a
(/ 1 b)
1
b
(/ (+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))) b)
(+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2))))
1
(* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))
b
(* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2))
eps
(+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)
(/ (exp (* eps a)) (- (exp (* eps a)) 1))
(exp (* eps a))
(* eps a)
a
(- (exp (* eps a)) 1)
-1/2
(/ (/ (- (exp (* (+ a b) eps)) 1) (/ (- (exp (* a eps)) 1) eps)) (- (exp (* b eps)) 1))
(/ (- (exp (* (+ a b) eps)) 1) (/ (- (exp (* a eps)) 1) eps))
(- (exp (* (+ a b) eps)) 1)
(* (+ a b) eps)
(+ a b)
a
b
eps
(/ (- (exp (* a eps)) 1) eps)
(- (exp (* a eps)) 1)
(* a eps)
(- (exp (* b eps)) 1)
(* b eps)

Outputs
(/ (/ (+ b a) a) b)
(/.f64 (+.f64 b a) (*.f64 b a))
(/ (+ b a) a)
(/.f64 (+.f64 b a) a)
(+ b a)
(+.f64 b a)
b
a
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
1
#s(literal 1 binary64)
a
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
1
#s(literal 1 binary64)
b
(/ (+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))) b)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps))) #s(literal -1/2 binary64)) (.f64 b eps))) b)
(+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2))))
(+.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps))) #s(literal -1/2 binary64)) (.f64 b eps)))
1
#s(literal 1 binary64)
(* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))
(.f64 (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps))) #s(literal -1/2 binary64)) (.f64 b eps))
b
(* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2))
(.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (*.f64 a eps))) #s(literal -1/2 binary64)))
eps
(+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)
(+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps))) #s(literal -1/2 binary64))
(/ (exp (* eps a)) (- (exp (* eps a)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(exp (* eps a))
(exp.f64 (*.f64 a eps))
(* eps a)
(*.f64 a eps)
a
(- (exp (* eps a)) 1)
(expm1.f64 (*.f64 a eps))
-1/2
#s(literal -1/2 binary64)
(/ (/ (- (exp (* (+ a b) eps)) 1) (/ (- (exp (* a eps)) 1) eps)) (- (exp (* b eps)) 1))
(/.f64 (/.f64 (expm1.f64 (.f64 (+.f64 b a) eps)) (expm1.f64 (.f64 a eps))) (/.f64 (expm1.f64 (*.f64 b eps)) eps))
(/ (- (exp (* (+ a b) eps)) 1) (/ (- (exp (* a eps)) 1) eps))
(/.f64 (expm1.f64 (.f64 (+.f64 b a) eps)) (/.f64 (expm1.f64 (.f64 a eps)) eps))
(- (exp (* (+ a b) eps)) 1)
(expm1.f64 (*.f64 (+.f64 b a) eps))
(* (+ a b) eps)
(*.f64 (+.f64 b a) eps)
(+ a b)
(+.f64 b a)
a
b
eps
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(- (exp (* a eps)) 1)
(expm1.f64 (*.f64 a eps))
(* a eps)
(*.f64 a eps)
(- (exp (* b eps)) 1)
(expm1.f64 (*.f64 b eps))
(* b eps)
(*.f64 b eps)

localize117.0ms (0.5%)

Memory

31.0MiB live, 181.9MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (+.f64 a b) eps)
✓	accuracy	57.7%	(/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (/.f64 (expm1.f64 (.f64 a eps)) eps))
✓	accuracy	46.5%	(/.f64 (expm1.f64 (*.f64 a eps)) eps)
✓	accuracy	45.6%	(/.f64 (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (/.f64 (expm1.f64 (.f64 a eps)) eps)) (expm1.f64 (*.f64 b eps)))
✓	accuracy	99.8%	(/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a)))
✓	accuracy	99.8%	(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))))) b)
✓	accuracy	99.5%	(.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))))
✓	accuracy	43.6%	(.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps a))) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) b)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) a)
✓	accuracy	100.0%	(+.f64 b a)
✓	accuracy	100.0%	(/.f64 (+.f64 b a) a)
✓	accuracy	99.8%	(/.f64 (/.f64 (+.f64 b a) a) b)

Samples

80.0ms

256×

valid

Compiler

Compiled 197 to 31 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-add: 29.0ms (49.5% of total)

ival-div: 14.0ms (23.9% of total)

ival-mult: 8.0ms (13.7% of total)

ival-expm1: 5.0ms (8.5% of total)

ival-exp: 2.0ms (3.4% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series142.0ms (0.6%)

Memory

-9.5MiB live, 146.3MiB allocated

Counts

15 → 420

Calls

Call 1

Inputs
#<alt (/ (/ (+ b a) a) b)>
#<alt (/ (+ b a) a)>
#<alt (+ b a)>
#<alt (/ 1 a)>
#<alt (/ 1 b)>
#<alt (/ (+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))) b)>
#<alt (+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2))))>
#<alt (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))>
#<alt (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2))>
#<alt (/ (/ (- (exp (* (+ a b) eps)) 1) (/ (- (exp (* a eps)) 1) eps)) (- (exp (* b eps)) 1))>
#<alt (/ (- (exp (* (+ a b) eps)) 1) (/ (- (exp (* a eps)) 1) eps))>
#<alt (- (exp (* (+ a b) eps)) 1)>
#<alt (* (+ a b) eps)>
#<alt (/ (exp (* eps a)) (- (exp (* eps a)) 1))>
#<alt (/ (- (exp (* a eps)) 1) eps)>

Outputs
#<alt (/ 1 b)>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (/ 1 a)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 a)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (/ 1 b)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 b)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt 1>
#<alt (+ 1 (/ b a))>
#<alt (+ 1 (/ b a))>
#<alt (+ 1 (/ b a))>
#<alt (/ b a)>
#<alt (* b (+ (/ 1 a) (/ 1 b)))>
#<alt (* b (+ (/ 1 a) (/ 1 b)))>
#<alt (* b (+ (/ 1 a) (/ 1 b)))>
#<alt (/ b a)>
#<alt (* b (+ (/ 1 a) (/ 1 b)))>
#<alt (* b (+ (/ 1 a) (/ 1 b)))>
#<alt (* b (+ (/ 1 a) (/ 1 b)))>
#<alt (/ b a)>
#<alt (/ (+ a b) a)>
#<alt (/ (+ a b) a)>
#<alt (/ (+ a b) a)>
#<alt 1>
#<alt (+ 1 (/ b a))>
#<alt (+ 1 (/ b a))>
#<alt (+ 1 (/ b a))>
#<alt 1>
#<alt (+ 1 (/ b a))>
#<alt (+ 1 (/ b a))>
#<alt (+ 1 (/ b a))>
#<alt a>
#<alt (+ a b)>
#<alt (+ a b)>
#<alt (+ a b)>
#<alt b>
#<alt (* b (+ 1 (/ a b)))>
#<alt (* b (+ 1 (/ a b)))>
#<alt (* b (+ 1 (/ a b)))>
#<alt b>
#<alt (* -1 (* b (- (* -1 (/ a b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ a b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ a b)) 1)))>
#<alt b>
#<alt (+ a b)>
#<alt (+ a b)>
#<alt (+ a b)>
#<alt a>
#<alt (* a (+ 1 (/ b a)))>
#<alt (* a (+ 1 (/ b a)))>
#<alt (* a (+ 1 (/ b a)))>
#<alt a>
#<alt (* -1 (* a (- (* -1 (/ b a)) 1)))>
#<alt (* -1 (* a (- (* -1 (/ b a)) 1)))>
#<alt (* -1 (* a (- (* -1 (/ b a)) 1)))>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ (+ 1 (* b (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)))) b)>
#<alt (/ (+ 1 (* b (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)))) b)>
#<alt (/ (+ 1 (* b (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)))) b)>
#<alt (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2))>
#<alt (+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))>
#<alt (+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))>
#<alt (+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))>
#<alt (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2))>
#<alt (+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))>
#<alt (+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))>
#<alt (+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (+ (* (pow eps 2) (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))) (+ (/ 1 a) (/ 1 b)))>
#<alt (+ (* (pow eps 2) (- (+ (* 1/2 a) (* eps (- (* 1/6 (pow a 2)) (+ (* 1/24 (pow a 2)) (+ (* 1/12 (pow a 2)) (* 1/2 (* a (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))))))) (+ (* 1/6 a) (* 1/4 a)))) (+ (/ 1 a) (/ 1 b)))>
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#<alt (+ (* eps (- (+ (* 1/2 (/ (pow (+ a b) 2) (* a b))) (* eps (- (+ (* 1/6 (/ (pow (+ a b) 3) (* a b))) (* eps (- (* 1/24 (/ (pow (+ a b) 4) (* a b))) (+ (/ (* (+ a b) (+ (* 1/24 (* a (pow b 4))) (+ (* 1/24 (* (pow a 4) b)) (+ (* 1/12 (* (pow a 2) (pow b 3))) (* 1/12 (* (pow a 3) (pow b 2))))))) (* (pow a 2) (pow b 2))) (+ (/ (* (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2))))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b)) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/6 (/ (pow (+ a b) 3) (* a b))) (+ (/ (* (+ a b) (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2)))))) (* (pow a 2) (pow b 2))) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b))))) (* a b))))))) (+ (/ (* (+ a b) (+ (* 1/6 (* a (pow b 3))) (+ (* 1/6 (* (pow a 3) b)) (* 1/4 (* (pow a 2) (pow b 2)))))) (* (pow a 2) (pow b 2))) (/ (* (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b))) (- (* 1/2 (/ (pow (+ a b) 2) (* a b))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (* a b)))))) (/ (* (+ a b) (+ (* 1/2 (* a (pow b 2))) (* 1/2 (* (pow a 2) b)))) (* (pow a 2) (pow b 2))))) (+ (/ 1 a) (/ 1 b)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))>
#<alt (/ (- (exp (* b eps)) 1) a)>
#<alt (/ (- (+ (exp (* b eps)) (* a (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1)))))) 1) a)>
#<alt (/ (- (+ (exp (* b eps)) (* a (- (+ (* a (- (* 1/2 (* (pow eps 2) (exp (* b eps)))) (+ (* 1/6 (* (pow eps 2) (- (exp (* b eps)) 1))) (* 1/2 (* eps (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1))))))))) (* eps (exp (* b eps)))) (* 1/2 (* eps (- (exp (* b eps)) 1)))))) 1) a)>
#<alt (/ (- (+ (exp (* b eps)) (* a (- (+ (* a (- (+ (* 1/2 (* (pow eps 2) (exp (* b eps)))) (* a (- (* 1/6 (* (pow eps 3) (exp (* b eps)))) (+ (* 1/24 (* (pow eps 3) (- (exp (* b eps)) 1))) (+ (* 1/6 (* (pow eps 2) (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1)))))) (* 1/2 (* eps (- (* 1/2 (* (pow eps 2) (exp (* b eps)))) (+ (* 1/6 (* (pow eps 2) (- (exp (* b eps)) 1))) (* 1/2 (* eps (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1))))))))))))))) (+ (* 1/6 (* (pow eps 2) (- (exp (* b eps)) 1))) (* 1/2 (* eps (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1))))))))) (* eps (exp (* b eps)))) (* 1/2 (* eps (- (exp (* b eps)) 1)))))) 1) a)>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (- (exp (* a eps)) 1))>
#<alt eps>
#<alt (+ eps (/ (* b (* (pow eps 2) (exp (* a eps)))) (- (exp (* a eps)) 1)))>
#<alt (+ eps (* b (+ (* 1/2 (/ (* b (* (pow eps 3) (exp (* a eps)))) (- (exp (* a eps)) 1))) (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1)))))>
#<alt (+ eps (* b (+ (* b (+ (* 1/6 (/ (* b (* (pow eps 4) (exp (* a eps)))) (- (exp (* a eps)) 1))) (* 1/2 (/ (* (pow eps 3) (exp (* a eps))) (- (exp (* a eps)) 1))))) (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1)))))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (+ a b)) a)>
#<alt (* eps (+ 1 (+ (* eps (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b)))) (/ b a))))>
#<alt (* eps (+ 1 (+ (* eps (- (+ (* 1/2 (/ (pow (+ a b) 2) a)) (* eps (- (* 1/6 (/ (pow (+ a b) 3) a)) (+ (* 1/6 (* a (+ a b))) (* 1/2 (* a (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b))))))))) (* 1/2 (+ a b)))) (/ b a))))>
#<alt (* eps (+ 1 (+ (* eps (- (+ (* 1/2 (/ (pow (+ a b) 2) a)) (* eps (- (+ (* 1/6 (/ (pow (+ a b) 3) a)) (* eps (- (* 1/24 (/ (pow (+ a b) 4) a)) (+ (* 1/24 (* (pow a 2) (+ a b))) (+ (* 1/6 (* (pow a 2) (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b))))) (* 1/2 (* a (- (* 1/6 (/ (pow (+ a b) 3) a)) (+ (* 1/6 (* a (+ a b))) (* 1/2 (* a (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b)))))))))))))) (+ (* 1/6 (* a (+ a b))) (* 1/2 (* a (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b))))))))) (* 1/2 (+ a b)))) (/ b a))))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))>
#<alt (- (exp (* b eps)) 1)>
#<alt (- (+ (exp (* b eps)) (* a (* eps (exp (* b eps))))) 1)>
#<alt (- (+ (exp (* b eps)) (* a (+ (* 1/2 (* a (* (pow eps 2) (exp (* b eps))))) (* eps (exp (* b eps)))))) 1)>
#<alt (- (+ (exp (* b eps)) (* a (+ (* a (+ (* 1/6 (* a (* (pow eps 3) (exp (* b eps))))) (* 1/2 (* (pow eps 2) (exp (* b eps)))))) (* eps (exp (* b eps)))))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (- b (* -1 a)))) 1)>
#<alt (- (exp (* eps (- b (* -1 a)))) 1)>
#<alt (- (exp (* eps (- b (* -1 a)))) 1)>
#<alt (- (exp (* eps (- b (* -1 a)))) 1)>
#<alt (- (exp (* a eps)) 1)>
#<alt (- (+ (exp (* a eps)) (* b (* eps (exp (* a eps))))) 1)>
#<alt (- (+ (exp (* a eps)) (* b (+ (* 1/2 (* b (* (pow eps 2) (exp (* a eps))))) (* eps (exp (* a eps)))))) 1)>
#<alt (- (+ (exp (* a eps)) (* b (+ (* b (+ (* 1/6 (* b (* (pow eps 3) (exp (* a eps))))) (* 1/2 (* (pow eps 2) (exp (* a eps)))))) (* eps (exp (* a eps)))))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (- a (* -1 b)))) 1)>
#<alt (- (exp (* eps (- a (* -1 b)))) 1)>
#<alt (- (exp (* eps (- a (* -1 b)))) 1)>
#<alt (- (exp (* eps (- a (* -1 b)))) 1)>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a (+ b (* 1/2 (* eps (pow (+ a b) 2))))))>
#<alt (* eps (+ a (+ b (* eps (+ (* 1/6 (* eps (pow (+ a b) 3))) (* 1/2 (pow (+ a b) 2)))))))>
#<alt (* eps (+ a (+ b (* eps (+ (* 1/2 (pow (+ a b) 2)) (* eps (+ (* 1/24 (* eps (pow (+ a b) 4))) (* 1/6 (pow (+ a b) 3)))))))))>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (- (exp (* eps (+ a b))) 1)>
#<alt (* b eps)>
#<alt (+ (* a eps) (* b eps))>
#<alt (+ (* a eps) (* b eps))>
#<alt (+ (* a eps) (* b eps))>
#<alt (* a eps)>
#<alt (* a (+ eps (/ (* b eps) a)))>
#<alt (* a (+ eps (/ (* b eps) a)))>
#<alt (* a (+ eps (/ (* b eps) a)))>
#<alt (* a eps)>
#<alt (* -1 (* a (+ (* -1 eps) (* -1 (/ (* b eps) a)))))>
#<alt (* -1 (* a (+ (* -1 eps) (* -1 (/ (* b eps) a)))))>
#<alt (* -1 (* a (+ (* -1 eps) (* -1 (/ (* b eps) a)))))>
#<alt (* a eps)>
#<alt (+ (* a eps) (* b eps))>
#<alt (+ (* a eps) (* b eps))>
#<alt (+ (* a eps) (* b eps))>
#<alt (* b eps)>
#<alt (* b (+ eps (/ (* a eps) b)))>
#<alt (* b (+ eps (/ (* a eps) b)))>
#<alt (* b (+ eps (/ (* a eps) b)))>
#<alt (* b eps)>
#<alt (* -1 (* b (+ (* -1 eps) (* -1 (/ (* a eps) b)))))>
#<alt (* -1 (* b (+ (* -1 eps) (* -1 (/ (* a eps) b)))))>
#<alt (* -1 (* b (+ (* -1 eps) (* -1 (/ (* a eps) b)))))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (* eps (+ a b))>
#<alt (/ 1 (* a eps))>
#<alt (/ (+ (* 1/2 eps) (/ 1 a)) eps)>
#<alt (/ (+ (* eps (+ 1/2 (* eps (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))) (/ 1 a)) eps)>
#<alt (/ (+ (* eps (+ 1/2 (* eps (- (+ (* 1/2 a) (* eps (- (* 1/6 (pow a 2)) (+ (* 1/24 (pow a 2)) (+ (* 1/12 (pow a 2)) (* 1/2 (* a (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))))))) (+ (* 1/6 a) (* 1/4 a)))))) (/ 1 a)) eps)>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ 1 (* a eps))>
#<alt (/ (+ (* 1/2 a) (/ 1 eps)) a)>
#<alt (/ (+ (* a (+ 1/2 (* a (- (* 1/2 eps) (+ (* 1/6 eps) (* 1/4 eps)))))) (/ 1 eps)) a)>
#<alt (/ (+ (* a (+ 1/2 (* a (- (+ (* 1/2 eps) (* a (- (* 1/6 (pow eps 2)) (+ (* 1/24 (pow eps 2)) (+ (* 1/12 (pow eps 2)) (* 1/2 (* eps (- (* 1/2 eps) (+ (* 1/6 eps) (* 1/4 eps)))))))))) (+ (* 1/6 eps) (* 1/4 eps)))))) (/ 1 eps)) a)>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt (/ (exp (* a eps)) (- (exp (* a eps)) 1))>
#<alt a>
#<alt (* a (+ 1 (* 1/2 (* a eps))))>
#<alt (* a (+ 1 (* a (+ (* 1/6 (* a (pow eps 2))) (* 1/2 eps)))))>
#<alt (* a (+ 1 (* a (+ (* 1/2 eps) (* a (+ (* 1/24 (* a (pow eps 3))) (* 1/6 (pow eps 2))))))))>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt a>
#<alt (+ a (* 1/2 (* (pow a 2) eps)))>
#<alt (+ a (* eps (+ (* 1/6 (* (pow a 3) eps)) (* 1/2 (pow a 2)))))>
#<alt (+ a (* eps (+ (* 1/2 (pow a 2)) (* eps (+ (* 1/24 (* (pow a 4) eps)) (* 1/6 (pow a 3)))))))>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>
#<alt (/ (- (exp (* a eps)) 1) eps)>

Calls

105 calls:

Time	Variable		Point	Expression
63.0ms	b	@	-inf	(/ (- (exp (* (+ a b) eps)) 1) (/ (- (exp (* a eps)) 1) eps))
3.0ms	a	@	0	(/ (/ (+ b a) a) b)
3.0ms	a	@	inf	(/ (+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))) b)
2.0ms	a	@	inf	(/ (/ (+ b a) a) b)
2.0ms	eps	@	0	(/ (+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))) b)

rewrite444.0ms (1.9%)

Memory

8.7MiB live, 890.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 194×	`/-lowering-/.f32`
5 194×	`/-lowering-/.f64`
4 446×	`-lowering-.f32`
4 446×	`-lowering-.f64`
3 132×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	166
1	222	166
2	1834	166
0	8687	140

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 829

Calls

Call 1

Inputs
(/ (/ (+ b a) a) b)
(/ (+ b a) a)
(+ b a)
(/ 1 a)
(/ 1 b)
(/ (+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))) b)
(+ 1 (* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2))))
(* b (* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2)))
(* eps (+ (/ (exp (* eps a)) (- (exp (* eps a)) 1)) -1/2))
(/ (/ (- (exp (* (+ a b) eps)) 1) (/ (- (exp (* a eps)) 1) eps)) (- (exp (* b eps)) 1))
(/ (- (exp (* (+ a b) eps)) 1) (/ (- (exp (* a eps)) 1) eps))
(- (exp (* (+ a b) eps)) 1)
(* (+ a b) eps)
(/ (exp (* eps a)) (- (exp (* eps a)) 1))
(/ (- (exp (* a eps)) 1) eps)

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 b (/.f64 (+.f64 b a) a))) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 b b) (-.f64 b a)) (.f64 b a)) (/.f64 (/.f64 (.f64 a a) (-.f64 b a)) (.f64 b a)))
(-.f64 (/.f64 (/.f64 (.f64 a a) (-.f64 a b)) (.f64 b a)) (/.f64 (/.f64 (.f64 b b) (-.f64 a b)) (.f64 b a)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) b)) (/.f64 (/.f64 (+.f64 b a) a) (-.f64 #s(literal 0 binary64) b)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (.f64 b a))) (/.f64 (+.f64 b a) (neg.f64 (.f64 b a))))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 b (-.f64 #s(literal 0 binary64) a))) (/.f64 (+.f64 b a) (.f64 b (-.f64 #s(literal 0 binary64) a))))
(-.f64 (/.f64 (.f64 b b) (.f64 (.f64 b a) (-.f64 b a))) (/.f64 (.f64 a a) (.f64 (.f64 b a) (-.f64 b a))))
(-.f64 (/.f64 (.f64 a a) (.f64 (.f64 b a) (-.f64 a b))) (/.f64 (.f64 b b) (.f64 (.f64 b a) (-.f64 a b))))
(neg.f64 (/.f64 (/.f64 (+.f64 b a) a) (-.f64 #s(literal 0 binary64) b)))
(/.f64 (+.f64 b a) (*.f64 b a))
(/.f64 (/.f64 (+.f64 b a) a) b)
(/.f64 (/.f64 (+.f64 b a) a) (neg.f64 (-.f64 #s(literal 0 binary64) b)))
(/.f64 #s(literal 1 binary64) (/.f64 b (/.f64 (+.f64 b a) a)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 a (+.f64 b a)) b))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 b a) (+.f64 b a)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 b (/.f64 (+.f64 b a) a)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (/.f64 a (+.f64 b a)) (-.f64 #s(literal 0 binary64) b))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 b (/.f64 (+.f64 b a) a)))))
(/.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 a (+.f64 b a)))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 a (+.f64 b a)) (-.f64 #s(literal 0 binary64) b)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 b (/.f64 (+.f64 b a) a))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 a (+.f64 b a)) b)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 b a) (+.f64 b a))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 b (/.f64 (+.f64 b a) a)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 b a) a)) (-.f64 #s(literal 0 binary64) b))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 b a) a)) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) b))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 b a)) (neg.f64 (*.f64 b a)))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 b a)) (*.f64 b (-.f64 #s(literal 0 binary64) a)))
(/.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a))) (.f64 (.f64 b a) (+.f64 (.f64 b b) (.f64 a (-.f64 a b)))))
(/.f64 (+.f64 (.f64 b (.f64 b b)) (.f64 a (.f64 a a))) (.f64 (.f64 b a) (+.f64 (.f64 a a) (.f64 b (-.f64 b a)))))
(/.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 (.f64 b a) (-.f64 b a)))
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(.f64 (/.f64 (exp.f64 (.f64 a (/.f64 eps #s(literal 2 binary64)))) (expm1.f64 (.f64 (.f64 a eps) #s(literal 2 binary64)))) (/.f64 (exp.f64 (.f64 a (/.f64 eps #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))))
(.f64 (/.f64 (exp.f64 (.f64 eps (/.f64 a #s(literal 2 binary64)))) (expm1.f64 (.f64 (.f64 a eps) #s(literal 3 binary64)))) (/.f64 (exp.f64 (.f64 eps (/.f64 a #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))))))
(.f64 (/.f64 (exp.f64 (.f64 eps (/.f64 a #s(literal 2 binary64)))) (expm1.f64 (.f64 (.f64 a eps) #s(literal 2 binary64)))) (/.f64 (exp.f64 (.f64 eps (/.f64 a #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))))
(+.f64 (/.f64 (exp.f64 (*.f64 a eps)) eps) (neg.f64 (/.f64 #s(literal 1 binary64) eps)))
(exp.f64 (.f64 (log.f64 (/.f64 eps (expm1.f64 (.f64 a eps)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (exp.f64 (*.f64 a eps)) eps) (/.f64 #s(literal 1 binary64) eps))
(-.f64 (/.f64 (/.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))) eps) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))) eps))
(-.f64 (/.f64 (/.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))) eps) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))) eps))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (expm1.f64 (*.f64 a eps)) (-.f64 #s(literal 0 binary64) eps)))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) (.f64 eps (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))))) (/.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))))))
(-.f64 (/.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (.f64 eps (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))) (/.f64 #s(literal 1 binary64) (.f64 eps (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))))
(-.f64 (/.f64 (.f64 (exp.f64 (.f64 a eps)) eps) (.f64 eps eps)) (/.f64 (.f64 eps #s(literal 1 binary64)) (*.f64 eps eps)))
(-.f64 (/.f64 (.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)))) (+.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) #s(literal 2 binary64)) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) (/.f64 #s(literal 1 binary64) eps))))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps))) (+.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) #s(literal 2 binary64)) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (exp.f64 (*.f64 a eps)) eps) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) #s(literal 2 binary64)) (+.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) (/.f64 #s(literal 1 binary64) eps))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)) (+.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) (/.f64 #s(literal 1 binary64) eps))))
(fma.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (*.f64 a eps)) eps) (neg.f64 (/.f64 #s(literal 1 binary64) eps)))
(fma.f64 (exp.f64 (*.f64 a eps)) (/.f64 #s(literal 1 binary64) eps) (neg.f64 (/.f64 #s(literal 1 binary64) eps)))
(neg.f64 (/.f64 (expm1.f64 (*.f64 a eps)) (-.f64 #s(literal 0 binary64) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 eps (expm1.f64 (*.f64 a eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps (expm1.f64 (*.f64 a eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 eps (expm1.f64 (*.f64 a eps))))))
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 eps (expm1.f64 (*.f64 a eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 eps (expm1.f64 (*.f64 a eps))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a eps))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) (.f64 eps (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))))
(/.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (.f64 eps (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 a eps)) eps) (.f64 eps #s(literal 1 binary64))) (.f64 eps eps))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a eps)))) eps))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a eps))) eps))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 3 binary64)))) (neg.f64 (.f64 eps (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 2 binary64)))) (neg.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a eps)))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)))) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)))) (+.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) #s(literal 2 binary64)) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (exp.f64 (*.f64 a eps)) eps) (/.f64 #s(literal 1 binary64) eps)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps))) (+.f64 (/.f64 (exp.f64 (*.f64 a eps)) eps) (/.f64 #s(literal 1 binary64) eps)))
(/.f64 (.f64 (expm1.f64 (.f64 a eps)) #s(literal 1 binary64)) eps)
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) eps)) (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))
(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (*.f64 a eps))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 eps (exp.f64 (.f64 a eps))) #s(literal 1 binary64))) (.f64 (/.f64 eps (exp.f64 (*.f64 a eps))) eps))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 eps #s(literal 1 binary64))) (.f64 (/.f64 eps (exp.f64 (.f64 a eps))) #s(literal 1 binary64))) (.f64 (/.f64 eps (exp.f64 (*.f64 a eps))) (/.f64 eps #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)) (.f64 (/.f64 eps (exp.f64 (.f64 a eps))) #s(literal -1 binary64))) (.f64 (/.f64 eps (exp.f64 (*.f64 a eps))) (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 a eps)) (/.f64 eps #s(literal 1 binary64))) (.f64 eps #s(literal 1 binary64))) (.f64 eps (/.f64 eps #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 a eps)) (-.f64 #s(literal 0 binary64) eps)) (.f64 eps #s(literal -1 binary64))) (.f64 eps (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (.f64 a eps))) eps) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) eps) eps))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (.f64 a eps))) (/.f64 eps #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 eps #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (.f64 a eps))) (-.f64 #s(literal 0 binary64) eps)) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (neg.f64 (-.f64 (.f64 (exp.f64 (.f64 a eps)) eps) (.f64 eps #s(literal 1 binary64)))) (neg.f64 (.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a eps)))) eps)))
(/.f64 (neg.f64 (.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 a eps))) eps)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 a eps))))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps))))
(/.f64 (neg.f64 (-.f64 (.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)))) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps))))) (neg.f64 (+.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) #s(literal 2 binary64)) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (exp.f64 (*.f64 a eps)) eps) (/.f64 #s(literal 1 binary64) eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)))) (neg.f64 (+.f64 (/.f64 (exp.f64 (*.f64 a eps)) eps) (/.f64 #s(literal 1 binary64) eps))))
(/.f64 (neg.f64 (.f64 (expm1.f64 (.f64 a eps)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) eps))) (neg.f64 (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))))
(/.f64 (neg.f64 (.f64 (expm1.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) eps))) (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))))
(/.f64 (+.f64 (.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 3 binary64))) (.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) eps)))) (pow.f64 (neg.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (exp.f64 (.f64 a eps)) eps) #s(literal 2 binary64)) (-.f64 (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (/.f64 (exp.f64 (*.f64 a eps)) eps) (neg.f64 (/.f64 #s(literal 1 binary64) eps))))))
(pow.f64 (/.f64 (expm1.f64 (*.f64 a eps)) eps) #s(literal 1 binary64))
(pow.f64 (/.f64 eps (expm1.f64 (*.f64 a eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 eps (expm1.f64 (*.f64 a eps))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 (.f64 a eps)) eps))
(.f64 (expm1.f64 (.f64 a eps)) (/.f64 #s(literal 1 binary64) eps))
(.f64 (expm1.f64 (.f64 a eps)) (/.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 a eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)))
(.f64 (/.f64 #s(literal 1 binary64) eps) (expm1.f64 (.f64 a eps)))
(.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (.f64 a eps))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (.f64 a eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) eps))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (expm1.f64 (.f64 a eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)))
(.f64 (pow.f64 (/.f64 eps (expm1.f64 (.f64 (.f64 a eps) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 (.f64 a eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))))))
(.f64 (pow.f64 (/.f64 eps (expm1.f64 (.f64 (.f64 a eps) #s(literal 2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps))) eps) (/.f64 (expm1.f64 (.f64 a eps)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 a eps)))))

simplify652.0ms (2.7%)

Memory

-2.2MiB live, 1 019.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 454×	`accelerator-lowering-fma.f32`
11 454×	`accelerator-lowering-fma.f64`
7 268×	`-lowering-.f32`
7 268×	`-lowering-.f64`
3 816×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	625	7574
1	1915	7124
2	6207	7109
0	8063	6199

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(/ 1 b)
(/ (+ 1 (/ b a)) b)
(/ (+ 1 (/ b a)) b)
(/ (+ 1 (/ b a)) b)
(/ 1 a)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 a)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 a)
(/ (+ 1 (/ a b)) a)
(/ (+ 1 (/ a b)) a)
(/ (+ 1 (/ a b)) a)
(/ 1 b)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 b)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
1
(+ 1 (/ b a))
(+ 1 (/ b a))
(+ 1 (/ b a))
(/ b a)
(* b (+ (/ 1 a) (/ 1 b)))
(* b (+ (/ 1 a) (/ 1 b)))
(* b (+ (/ 1 a) (/ 1 b)))
(/ b a)
(* b (+ (/ 1 a) (/ 1 b)))
(* b (+ (/ 1 a) (/ 1 b)))
(* b (+ (/ 1 a) (/ 1 b)))
(/ b a)
(/ (+ a b) a)
(/ (+ a b) a)
(/ (+ a b) a)
1
(+ 1 (/ b a))
(+ 1 (/ b a))
(+ 1 (/ b a))
1
(+ 1 (/ b a))
(+ 1 (/ b a))
(+ 1 (/ b a))
a
(+ a b)
(+ a b)
(+ a b)
b
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
b
(+ a b)
(+ a b)
(+ a b)
a
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ (+ 1 (* b (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)))) b)
(/ (+ 1 (* b (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)))) b)
(/ (+ 1 (* b (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)))) b)
(* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(/ (+ 1 (/ b a)) b)
(+ (* (pow eps 2) (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))) (+ (/ 1 a) (/ 1 b)))
(+ (* (pow eps 2) (- (+ (* 1/2 a) (* eps (- (* 1/6 (pow a 2)) (+ (* 1/24 (pow a 2)) (+ (* 1/12 (pow a 2)) (* 1/2 (* a (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))))))) (+ (* 1/6 a) (* 1/4 a)))) (+ (/ 1 a) (/ 1 b)))
(+ (* (pow eps 2) (- (+ (* 1/2 a) (* eps (- (+ (* 1/6 (pow a 2)) (* eps (- (* 1/24 (pow a 3)) (+ (* 1/120 (pow a 3)) (+ (* 1/48 (pow a 3)) (+ (* 1/6 (* (pow a 2) (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a))))) (* 1/2 (* a (- (* 1/6 (pow a 2)) (+ (* 1/24 (pow a 2)) (+ (* 1/12 (pow a 2)) (* 1/2 (* a (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))))))))))))) (+ (* 1/24 (pow a 2)) (+ (* 1/12 (pow a 2)) (* 1/2 (* a (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))))))) (+ (* 1/6 a) (* 1/4 a)))) (+ (/ 1 a) (/ 1 b)))
(* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2))
(* eps (- (+ (/ 1 (* b eps)) (/ (exp (* a eps)) (- (exp (* a eps)) 1))) 1/2))
(* eps (- (+ (/ 1 (* b eps)) (/ (exp (* a eps)) (- (exp (* a eps)) 1))) 1/2))
(* eps (- (+ (/ 1 (* b eps)) (/ (exp (* a eps)) (- (exp (* a eps)) 1))) 1/2))
(* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2))
(* -1 (* eps (- (* -1 (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 (* b eps)))))
(* -1 (* eps (- (* -1 (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 (* b eps)))))
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1
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(/ (- (+ (exp (* b eps)) (* a (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1)))))) 1) a)
(/ (- (+ (exp (* b eps)) (* a (- (+ (* a (- (* 1/2 (* (pow eps 2) (exp (* b eps)))) (+ (* 1/6 (* (pow eps 2) (- (exp (* b eps)) 1))) (* 1/2 (* eps (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1))))))))) (* eps (exp (* b eps)))) (* 1/2 (* eps (- (exp (* b eps)) 1)))))) 1) a)
(/ (- (+ (exp (* b eps)) (* a (- (+ (* a (- (+ (* 1/2 (* (pow eps 2) (exp (* b eps)))) (* a (- (* 1/6 (* (pow eps 3) (exp (* b eps)))) (+ (* 1/24 (* (pow eps 3) (- (exp (* b eps)) 1))) (+ (* 1/6 (* (pow eps 2) (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1)))))) (* 1/2 (* eps (- (* 1/2 (* (pow eps 2) (exp (* b eps)))) (+ (* 1/6 (* (pow eps 2) (- (exp (* b eps)) 1))) (* 1/2 (* eps (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1))))))))))))))) (+ (* 1/6 (* (pow eps 2) (- (exp (* b eps)) 1))) (* 1/2 (* eps (- (* eps (exp (* b eps))) (* 1/2 (* eps (- (exp (* b eps)) 1))))))))) (* eps (exp (* b eps)))) (* 1/2 (* eps (- (exp (* b eps)) 1)))))) 1) a)
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (- b (* -1 a)))) 1)) (- (exp (* a eps)) 1))
eps
(+ eps (/ (* b (* (pow eps 2) (exp (* a eps)))) (- (exp (* a eps)) 1)))
(+ eps (* b (+ (* 1/2 (/ (* b (* (pow eps 3) (exp (* a eps)))) (- (exp (* a eps)) 1))) (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1)))))
(+ eps (* b (+ (* b (+ (* 1/6 (/ (* b (* (pow eps 4) (exp (* a eps)))) (- (exp (* a eps)) 1))) (* 1/2 (/ (* (pow eps 3) (exp (* a eps))) (- (exp (* a eps)) 1))))) (/ (* (pow eps 2) (exp (* a eps))) (- (exp (* a eps)) 1)))))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (- a (* -1 b)))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (+ a b)) a)
(* eps (+ 1 (+ (* eps (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b)))) (/ b a))))
(* eps (+ 1 (+ (* eps (- (+ (* 1/2 (/ (pow (+ a b) 2) a)) (* eps (- (* 1/6 (/ (pow (+ a b) 3) a)) (+ (* 1/6 (* a (+ a b))) (* 1/2 (* a (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b))))))))) (* 1/2 (+ a b)))) (/ b a))))
(* eps (+ 1 (+ (* eps (- (+ (* 1/2 (/ (pow (+ a b) 2) a)) (* eps (- (+ (* 1/6 (/ (pow (+ a b) 3) a)) (* eps (- (* 1/24 (/ (pow (+ a b) 4) a)) (+ (* 1/24 (* (pow a 2) (+ a b))) (+ (* 1/6 (* (pow a 2) (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b))))) (* 1/2 (* a (- (* 1/6 (/ (pow (+ a b) 3) a)) (+ (* 1/6 (* a (+ a b))) (* 1/2 (* a (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b)))))))))))))) (+ (* 1/6 (* a (+ a b))) (* 1/2 (* a (- (* 1/2 (/ (pow (+ a b) 2) a)) (* 1/2 (+ a b))))))))) (* 1/2 (+ a b)))) (/ b a))))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(/ (* eps (- (exp (* eps (+ a b))) 1)) (- (exp (* a eps)) 1))
(- (exp (* b eps)) 1)
(- (+ (exp (* b eps)) (* a (* eps (exp (* b eps))))) 1)
(- (+ (exp (* b eps)) (* a (+ (* 1/2 (* a (* (pow eps 2) (exp (* b eps))))) (* eps (exp (* b eps)))))) 1)
(- (+ (exp (* b eps)) (* a (+ (* a (+ (* 1/6 (* a (* (pow eps 3) (exp (* b eps))))) (* 1/2 (* (pow eps 2) (exp (* b eps)))))) (* eps (exp (* b eps)))))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (- b (* -1 a)))) 1)
(- (exp (* eps (- b (* -1 a)))) 1)
(- (exp (* eps (- b (* -1 a)))) 1)
(- (exp (* eps (- b (* -1 a)))) 1)
(- (exp (* a eps)) 1)
(- (+ (exp (* a eps)) (* b (* eps (exp (* a eps))))) 1)
(- (+ (exp (* a eps)) (* b (+ (* 1/2 (* b (* (pow eps 2) (exp (* a eps))))) (* eps (exp (* a eps)))))) 1)
(- (+ (exp (* a eps)) (* b (+ (* b (+ (* 1/6 (* b (* (pow eps 3) (exp (* a eps))))) (* 1/2 (* (pow eps 2) (exp (* a eps)))))) (* eps (exp (* a eps)))))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (- a (* -1 b)))) 1)
(- (exp (* eps (- a (* -1 b)))) 1)
(- (exp (* eps (- a (* -1 b)))) 1)
(- (exp (* eps (- a (* -1 b)))) 1)
(* eps (+ a b))
(* eps (+ a (+ b (* 1/2 (* eps (pow (+ a b) 2))))))
(* eps (+ a (+ b (* eps (+ (* 1/6 (* eps (pow (+ a b) 3))) (* 1/2 (pow (+ a b) 2)))))))
(* eps (+ a (+ b (* eps (+ (* 1/2 (pow (+ a b) 2)) (* eps (+ (* 1/24 (* eps (pow (+ a b) 4))) (* 1/6 (pow (+ a b) 3)))))))))
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(- (exp (* eps (+ a b))) 1)
(* b eps)
(+ (* a eps) (* b eps))
(+ (* a eps) (* b eps))
(+ (* a eps) (* b eps))
(* a eps)
(* a (+ eps (/ (* b eps) a)))
(* a (+ eps (/ (* b eps) a)))
(* a (+ eps (/ (* b eps) a)))
(* a eps)
(* -1 (* a (+ (* -1 eps) (* -1 (/ (* b eps) a)))))
(* -1 (* a (+ (* -1 eps) (* -1 (/ (* b eps) a)))))
(* -1 (* a (+ (* -1 eps) (* -1 (/ (* b eps) a)))))
(* a eps)
(+ (* a eps) (* b eps))
(+ (* a eps) (* b eps))
(+ (* a eps) (* b eps))
(* b eps)
(* b (+ eps (/ (* a eps) b)))
(* b (+ eps (/ (* a eps) b)))
(* b (+ eps (/ (* a eps) b)))
(* b eps)
(* -1 (* b (+ (* -1 eps) (* -1 (/ (* a eps) b)))))
(* -1 (* b (+ (* -1 eps) (* -1 (/ (* a eps) b)))))
(* -1 (* b (+ (* -1 eps) (* -1 (/ (* a eps) b)))))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(* eps (+ a b))
(/ 1 (* a eps))
(/ (+ (* 1/2 eps) (/ 1 a)) eps)
(/ (+ (* eps (+ 1/2 (* eps (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))) (/ 1 a)) eps)
(/ (+ (* eps (+ 1/2 (* eps (- (+ (* 1/2 a) (* eps (- (* 1/6 (pow a 2)) (+ (* 1/24 (pow a 2)) (+ (* 1/12 (pow a 2)) (* 1/2 (* a (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))))))) (+ (* 1/6 a) (* 1/4 a)))))) (/ 1 a)) eps)
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ 1 (* a eps))
(/ (+ (* 1/2 a) (/ 1 eps)) a)
(/ (+ (* a (+ 1/2 (* a (- (* 1/2 eps) (+ (* 1/6 eps) (* 1/4 eps)))))) (/ 1 eps)) a)
(/ (+ (* a (+ 1/2 (* a (- (+ (* 1/2 eps) (* a (- (* 1/6 (pow eps 2)) (+ (* 1/24 (pow eps 2)) (+ (* 1/12 (pow eps 2)) (* 1/2 (* eps (- (* 1/2 eps) (+ (* 1/6 eps) (* 1/4 eps)))))))))) (+ (* 1/6 eps) (* 1/4 eps)))))) (/ 1 eps)) a)
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
a
(* a (+ 1 (* 1/2 (* a eps))))
(* a (+ 1 (* a (+ (* 1/6 (* a (pow eps 2))) (* 1/2 eps)))))
(* a (+ 1 (* a (+ (* 1/2 eps) (* a (+ (* 1/24 (* a (pow eps 3))) (* 1/6 (pow eps 2))))))))
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
a
(+ a (* 1/2 (* (pow a 2) eps)))
(+ a (* eps (+ (* 1/6 (* (pow a 3) eps)) (* 1/2 (pow a 2)))))
(+ a (* eps (+ (* 1/2 (pow a 2)) (* eps (+ (* 1/24 (* (pow a 4) eps)) (* 1/6 (pow a 3)))))))
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)
(/ (- (exp (* a eps)) 1) eps)

Outputs
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ (+ 1 (/ a b)) a)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
(/ (+ 1 (/ a b)) a)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
(/ (+ 1 (/ a b)) a)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
1
#s(literal 1 binary64)
(+ 1 (/ b a))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(+ 1 (/ b a))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(+ 1 (/ b a))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(/ b a)
(/.f64 b a)
(* b (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(* b (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(* b (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(/ b a)
(/.f64 b a)
(* b (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(* b (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(* b (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(/ b a)
(/.f64 b a)
(/ (+ a b) a)
(/.f64 (+.f64 b a) a)
(/ (+ a b) a)
(/.f64 (+.f64 b a) a)
(/ (+ a b) a)
(/.f64 (+.f64 b a) a)
1
#s(literal 1 binary64)
(+ 1 (/ b a))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(+ 1 (/ b a))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(+ 1 (/ b a))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
1
#s(literal 1 binary64)
(+ 1 (/ b a))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(+ 1 (/ b a))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(+ 1 (/ b a))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
a
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
b
(* b (+ 1 (/ a b)))
(+.f64 b (*.f64 #s(literal 1 binary64) (/.f64 a #s(literal 1 binary64))))
(* b (+ 1 (/ a b)))
(+.f64 b (*.f64 #s(literal 1 binary64) (/.f64 a #s(literal 1 binary64))))
(* b (+ 1 (/ a b)))
(+.f64 b (*.f64 #s(literal 1 binary64) (/.f64 a #s(literal 1 binary64))))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 a b)) (-.f64 #s(literal 0 binary64) b))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 a b)) (-.f64 #s(literal 0 binary64) b))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 a b)) (-.f64 #s(literal 0 binary64) b))
b
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
a
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
(* a (+ 1 (/ b a)))
(*.f64 a (+.f64 #s(literal 1 binary64) (/.f64 b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 a (-.f64 #s(literal -1 binary64) (/.f64 b a))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 a (-.f64 #s(literal -1 binary64) (/.f64 b a))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 a (-.f64 #s(literal -1 binary64) (/.f64 b a))))
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ (+ 1 (* b (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)))) b)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps))) #s(literal -1/2 binary64))))) b)
(/ (+ 1 (* b (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)))) b)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps))) #s(literal -1/2 binary64))))) b)
(/ (+ 1 (* b (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)))) b)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps))) #s(literal -1/2 binary64))))) b)
(* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (*.f64 a eps))) #s(literal -1/2 binary64)))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (*.f64 a eps))) #s(literal -1/2 binary64))))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (*.f64 a eps))) #s(literal -1/2 binary64))))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (*.f64 a eps))) #s(literal -1/2 binary64))))
(* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2))
(.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (*.f64 a eps))) #s(literal -1/2 binary64)))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (*.f64 a eps))) #s(literal -1/2 binary64))))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (*.f64 a eps))) #s(literal -1/2 binary64))))
(+ (* eps (- (/ (exp (* a eps)) (- (exp (* a eps)) 1)) 1/2)) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (*.f64 a eps))) #s(literal -1/2 binary64))))
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(+ (* (pow eps 2) (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))) (+ (/ 1 a) (/ 1 b)))
(+.f64 (/.f64 #s(literal 1 binary64) b) (+.f64 (/.f64 #s(literal 1 binary64) a) (.f64 (.f64 eps eps) (*.f64 a #s(literal 1/12 binary64)))))
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(+.f64 (.f64 b eps) (.f64 #s(literal 1 binary64) (/.f64 (*.f64 a eps) #s(literal 1 binary64))))
(* -1 (* b (+ (* -1 eps) (* -1 (/ (* a eps) b)))))
(+.f64 (.f64 b eps) (.f64 #s(literal 1 binary64) (/.f64 (*.f64 a eps) #s(literal 1 binary64))))
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(* eps (+ a b))
(*.f64 (+.f64 b a) eps)
(/ 1 (* a eps))
(/.f64 #s(literal 1 binary64) (*.f64 a eps))
(/ (+ (* 1/2 eps) (/ 1 a)) eps)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) a) (*.f64 eps #s(literal 1/2 binary64))) eps)
(/ (+ (* eps (+ 1/2 (* eps (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))) (/ 1 a)) eps)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) a) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (*.f64 a #s(literal 1/12 binary64)))))) eps)
(/ (+ (* eps (+ 1/2 (* eps (- (+ (* 1/2 a) (* eps (- (* 1/6 (pow a 2)) (+ (* 1/24 (pow a 2)) (+ (* 1/12 (pow a 2)) (* 1/2 (* a (- (* 1/2 a) (+ (* 1/6 a) (* 1/4 a)))))))))) (+ (* 1/6 a) (* 1/4 a)))))) (/ 1 a)) eps)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) a) (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (+.f64 (.f64 a #s(literal 1/12 binary64)) (.f64 eps (-.f64 (.f64 a (.f64 a #s(literal 1/6 binary64))) (+.f64 (.f64 a (.f64 #s(literal 1/2 binary64) (.f64 a #s(literal 1/12 binary64)))) (.f64 (*.f64 a a) #s(literal 1/8 binary64)))))))))) eps)
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ 1 (* a eps))
(/.f64 #s(literal 1 binary64) (*.f64 a eps))
(/ (+ (* 1/2 a) (/ 1 eps)) a)
(/.f64 (+.f64 (*.f64 a #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) eps)) a)
(/ (+ (* a (+ 1/2 (* a (- (* 1/2 eps) (+ (* 1/6 eps) (* 1/4 eps)))))) (/ 1 eps)) a)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 a (+.f64 #s(literal 1/2 binary64) (.f64 a (*.f64 eps #s(literal 1/12 binary64)))))) a)
(/ (+ (* a (+ 1/2 (* a (- (+ (* 1/2 eps) (* a (- (* 1/6 (pow eps 2)) (+ (* 1/24 (pow eps 2)) (+ (* 1/12 (pow eps 2)) (* 1/2 (* eps (- (* 1/2 eps) (+ (* 1/6 eps) (* 1/4 eps)))))))))) (+ (* 1/6 eps) (* 1/4 eps)))))) (/ 1 eps)) a)
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 a (+.f64 #s(literal 1/2 binary64) (.f64 a (+.f64 (.f64 a (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (+.f64 (.f64 eps (.f64 #s(literal 1/2 binary64) (.f64 eps #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))))) (*.f64 eps #s(literal 1/12 binary64))))))) a)
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
(/ (exp (* a eps)) (- (exp (* a eps)) 1))
(/.f64 (exp.f64 (.f64 a eps)) (expm1.f64 (.f64 a eps)))
a
(* a (+ 1 (* 1/2 (* a eps))))
(.f64 a (+.f64 #s(literal 1 binary64) (.f64 a (*.f64 eps #s(literal 1/2 binary64)))))
(* a (+ 1 (* a (+ (* 1/6 (* a (pow eps 2))) (* 1/2 eps)))))
(.f64 a (+.f64 #s(literal 1 binary64) (.f64 a (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 a (.f64 (.f64 eps eps) #s(literal 1/6 binary64)))))))
(* a (+ 1 (* a (+ (* 1/2 eps) (* a (+ (* 1/24 (* a (pow eps 3))) (* 1/6 (pow eps 2))))))))
(.f64 a (+.f64 #s(literal 1 binary64) (.f64 a (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 a (+.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 #s(literal 1/24 binary64) (.f64 a (.f64 eps (.f64 eps eps))))))))))
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
a
(+ a (* 1/2 (* (pow a 2) eps)))
(.f64 a (+.f64 #s(literal 1 binary64) (.f64 a (*.f64 eps #s(literal 1/2 binary64)))))
(+ a (* eps (+ (* 1/6 (* (pow a 3) eps)) (* 1/2 (pow a 2)))))
(+.f64 a (.f64 eps (+.f64 (.f64 eps (.f64 a (.f64 a (.f64 a #s(literal 1/6 binary64))))) (.f64 a (*.f64 a #s(literal 1/2 binary64))))))
(+ a (* eps (+ (* 1/2 (pow a 2)) (* eps (+ (* 1/24 (* (pow a 4) eps)) (* 1/6 (pow a 3)))))))
(+.f64 a (.f64 eps (+.f64 (.f64 a (.f64 a #s(literal 1/2 binary64))) (.f64 eps (+.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (pow.f64 a #s(literal 4 binary64)))) (.f64 a (.f64 a (*.f64 a #s(literal 1/6 binary64)))))))))
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)
(/ (- (exp (* a eps)) 1) eps)
(/.f64 (expm1.f64 (*.f64 a eps)) eps)

eval205.0ms (0.9%)

Memory: 3.1MiB live, 262.2MiB allocated
Compiler: Compiled 32 230 to 3 612 computations (88.8% saved)

prune146.0ms (0.6%)

Memory

-2.6MiB live, 314.1MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1 246	3	1 249
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 248	6	1 254

Accuracy

100.0%

Counts

1 254 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(/.f64 (/.f64 (+.f64 b a) a) b)
▶	47.2%	(/.f64 (/.f64 b a) b)
▶	99.8%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
✓	52.8%	(/.f64 #s(literal 1 binary64) b)
✓	47.4%	(/.f64 #s(literal 1 binary64) a)
▶	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

Compiler

Compiled 50 to 35 computations (30% saved)

simplify4.0ms (0%)

Memory

10.7MiB live, 10.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 b a)
✓	cost-diff	128	(/.f64 (/.f64 b a) b)
✓	cost-diff	0	(/.f64 a b)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 a b))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) a)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) b)
✓	cost-diff	0	(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

Rules

14×	`/-lowering-/.f32`
14×	`/-lowering-/.f64`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
4×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	17	42
2	20	42
3	20	42
0	20	42

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (/ 1 b) (/ 1 a))
(/ 1 b)
1
b
(/ 1 a)
a
(/ (+ 1 (/ a b)) a)
(+ 1 (/ a b))
1
(/ a b)
a
b
(/ (/ b a) b)
(/ b a)
b
a

Outputs
(+ (/ 1 b) (/ 1 a))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
1
#s(literal 1 binary64)
b
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
a
(/ (+ 1 (/ a b)) a)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
1
#s(literal 1 binary64)
(/ a b)
(/.f64 a b)
a
b
(/ (/ b a) b)
(/.f64 #s(literal 1 binary64) a)
(/ b a)
(/.f64 b a)
b
a

localize42.0ms (0.2%)

Memory

-11.8MiB live, 81.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 b a)
✓	accuracy	99.6%	(/.f64 (/.f64 b a) b)
✓	accuracy	100.0%	(/.f64 a b)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 a b))
✓	accuracy	99.8%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) b)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) a)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

Samples

22.0ms

256×

valid

Compiler

Compiled 46 to 14 computations (69.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-div: 10.0ms (78.2% of total)

ival-add: 2.0ms (15.6% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series6.0ms (0%)

Memory

15.1MiB live, 15.1MiB allocated

Counts

8 → 168

Calls

Call 1

Inputs
#<alt (+ (/ 1 b) (/ 1 a))>
#<alt (/ 1 b)>
#<alt (/ 1 a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (+ 1 (/ a b))>
#<alt (/ a b)>
#<alt (/ (/ b a) b)>
#<alt (/ b a)>

Outputs
#<alt (/ 1 b)>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (/ 1 a)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 a)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (/ 1 b)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 b)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (/ (+ 1 (/ a b)) a)>
#<alt (/ 1 b)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 b)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 b)>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (/ (+ 1 (/ b a)) b)>
#<alt (/ 1 a)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (/ 1 a)>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt (+ (/ 1 a) (/ 1 b))>
#<alt 1>
#<alt (+ 1 (/ a b))>
#<alt (+ 1 (/ a b))>
#<alt (+ 1 (/ a b))>
#<alt (/ a b)>
#<alt (* a (+ (/ 1 a) (/ 1 b)))>
#<alt (* a (+ (/ 1 a) (/ 1 b)))>
#<alt (* a (+ (/ 1 a) (/ 1 b)))>
#<alt (/ a b)>
#<alt (* a (+ (/ 1 a) (/ 1 b)))>
#<alt (* a (+ (/ 1 a) (/ 1 b)))>
#<alt (* a (+ (/ 1 a) (/ 1 b)))>
#<alt (/ a b)>
#<alt (/ (+ a b) b)>
#<alt (/ (+ a b) b)>
#<alt (/ (+ a b) b)>
#<alt 1>
#<alt (+ 1 (/ a b))>
#<alt (+ 1 (/ a b))>
#<alt (+ 1 (/ a b))>
#<alt 1>
#<alt (+ 1 (/ a b))>
#<alt (+ 1 (/ a b))>
#<alt (+ 1 (/ a b))>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ 1 a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>
#<alt (/ b a)>

Calls

42 calls:

Time	Variable		Point	Expression
0.0ms	a	@	-inf	(/ (+ 1 (/ a b)) a)
0.0ms	a	@	inf	(/ (+ 1 (/ a b)) a)
0.0ms	b	@	-inf	(/ (+ 1 (/ a b)) a)
0.0ms	a	@	0	(/ (+ 1 (/ a b)) a)
0.0ms	b	@	-inf	(/ b a)

rewrite389.0ms (1.6%)

Memory

10.2MiB live, 509.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 180×	`accelerator-lowering-fma.f32`
5 180×	`accelerator-lowering-fma.f64`
3 562×	`-lowering-.f32`
3 562×	`-lowering-.f64`
3 210×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	76	34
2	762	34
0	8254	34

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 584

Calls

Call 1

Inputs
(+ (/ 1 b) (/ 1 a))
(/ 1 b)
(/ 1 a)
(/ (+ 1 (/ a b)) a)
(+ 1 (/ a b))
(/ a b)
(/ (/ b a) b)
(/ b a)

Outputs
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))
(+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 b b)) (+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal -1 binary64) a))) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) (+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal -1 binary64) a)))))
(-.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal -1 binary64) a))
(-.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal -1 binary64) b))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 b b)) (+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal -1 binary64) a))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) (+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal -1 binary64) a))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) (+.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal -1 binary64) b))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 b b)) (+.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal -1 binary64) b))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a) (/.f64 #s(literal 1 binary64) b))
(fma.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 b b)) (+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal -1 binary64) a))) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 a a)) (+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal -1 binary64) a)))))
(fma.f64 b (/.f64 (/.f64 #s(literal 1 binary64) b) a) (/.f64 #s(literal 1 binary64) b))
(fma.f64 (/.f64 #s(literal 1 binary64) b) #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) a))
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(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) a) (pow.f64 b #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal -1/2 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 b #s(literal -1/2 binary64))) (/.f64 (/.f64 #s(literal -1 binary64) a) (pow.f64 b #s(literal -1/2 binary64))))
(*.f64 (/.f64 (pow.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) b)) (/.f64 (pow.f64 a #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 a #s(literal -1/2 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 a #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) b)))
(*.f64 (/.f64 (pow.f64 a #s(literal -1/2 binary64)) (pow.f64 b #s(literal -1/2 binary64))) (/.f64 (pow.f64 a #s(literal -1/2 binary64)) (pow.f64 b #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (/.f64 a b) #s(literal -1/2 binary64)) (pow.f64 (/.f64 a b) #s(literal -1/2 binary64)))
(.f64 (.f64 b (pow.f64 a #s(literal -1/2 binary64))) (pow.f64 a #s(literal -1/2 binary64)))

simplify339.0ms (1.4%)

Memory

-6.1MiB live, 672.3MiB allocated

Algorithm

1×	egg-herbie

Rules

10 126×	`accelerator-lowering-fma.f32`
10 126×	`accelerator-lowering-fma.f64`
4 848×	`-lowering-.f32`
4 848×	`-lowering-.f64`
2 974×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	678
1	28	678
2	38	678
3	41	678
4	71	678
5	102	678
6	150	678
7	347	678
8	1439	678
9	3905	678
10	4244	678
11	4605	678
12	5114	678
13	5802	678
14	6473	678
0	8218	678

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
(/ 1 b)
(/ (+ 1 (/ b a)) b)
(/ (+ 1 (/ b a)) b)
(/ (+ 1 (/ b a)) b)
(/ 1 a)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 a)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 a)
(/ (+ 1 (/ a b)) a)
(/ (+ 1 (/ a b)) a)
(/ (+ 1 (/ a b)) a)
(/ 1 b)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 b)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ (+ 1 (/ a b)) a)
(/ (+ 1 (/ a b)) a)
(/ (+ 1 (/ a b)) a)
(/ 1 b)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 b)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 b)
(/ (+ 1 (/ b a)) b)
(/ (+ 1 (/ b a)) b)
(/ (+ 1 (/ b a)) b)
(/ 1 a)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(/ 1 a)
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
(+ (/ 1 a) (/ 1 b))
1
(+ 1 (/ a b))
(+ 1 (/ a b))
(+ 1 (/ a b))
(/ a b)
(* a (+ (/ 1 a) (/ 1 b)))
(* a (+ (/ 1 a) (/ 1 b)))
(* a (+ (/ 1 a) (/ 1 b)))
(/ a b)
(* a (+ (/ 1 a) (/ 1 b)))
(* a (+ (/ 1 a) (/ 1 b)))
(* a (+ (/ 1 a) (/ 1 b)))
(/ a b)
(/ (+ a b) b)
(/ (+ a b) b)
(/ (+ a b) b)
1
(+ 1 (/ a b))
(+ 1 (/ a b))
(+ 1 (/ a b))
1
(+ 1 (/ a b))
(+ 1 (/ a b))
(+ 1 (/ a b))
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ 1 a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)
(/ b a)

Outputs
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ (+ 1 (/ a b)) a)
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ (+ 1 (/ a b)) a)
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ (+ 1 (/ a b)) a)
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ (+ 1 (/ a b)) a)
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ (+ 1 (/ a b)) a)
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ (+ 1 (/ a b)) a)
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(/ (+ 1 (/ b a)) b)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 b a)) b)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(+ (/ 1 a) (/ 1 b))
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
1
#s(literal 1 binary64)
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(/ a b)
(/.f64 a b)
(* a (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(* a (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(* a (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(/ a b)
(/.f64 a b)
(* a (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(* a (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(* a (+ (/ 1 a) (/ 1 b)))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(/ a b)
(/.f64 a b)
(/ (+ a b) b)
(/.f64 (+.f64 b a) b)
(/ (+ a b) b)
(/.f64 (+.f64 b a) b)
(/ (+ a b) b)
(/.f64 (+.f64 b a) b)
1
#s(literal 1 binary64)
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
1
#s(literal 1 binary64)
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(+ 1 (/ a b))
(+.f64 #s(literal 1 binary64) (/.f64 a b))
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ 1 a)
(/.f64 #s(literal 1 binary64) a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)
(/ b a)
(/.f64 b a)

eval90.0ms (0.4%)

Memory: 15.0MiB live, 258.8MiB allocated
Compiler: Compiled 11 322 to 1 191 computations (89.5% saved)

prune97.0ms (0.4%)

Memory

-15.2MiB live, 286.4MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	751	1	752
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	751	7	758

Accuracy

100.0%

Counts

758 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(/.f64 (/.f64 (+.f64 b a) a) b)
✓	47.2%	(/.f64 (/.f64 b a) b)
▶	52.7%	(/.f64 (/.f64 a b) a)
✓	99.8%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
✓	52.8%	(/.f64 #s(literal 1 binary64) b)
✓	47.4%	(/.f64 #s(literal 1 binary64) a)
✓	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

Compiler

Compiled 58 to 40 computations (31% saved)

simplify3.0ms (0%)

Memory

10.9MiB live, 10.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 a b)
✓	cost-diff	128	(/.f64 (/.f64 a b) a)

Rules

8×	`/-lowering-/.f32`
8×	`/-lowering-/.f64`
4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-inverses`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	6	10
2	9	8
3	10	8
4	12	8
0	12	8

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (/ a b) a)
(/ a b)
a
b

Outputs
(/ (/ a b) a)
(/.f64 #s(literal 1 binary64) b)
(/ a b)
(/.f64 a b)
a
b

localize16.0ms (0.1%)

Memory

10.7MiB live, 49.1MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 a b)
✓	accuracy	99.6%	(/.f64 (/.f64 a b) a)

Samples

11.0ms

256×

valid

Compiler

Compiled 12 to 7 computations (41.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 4.0ms (104.6% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.7MiB live, 2.6MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (/ (/ a b) a)>
#<alt (/ a b)>

Outputs
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ 1 b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>
#<alt (/ a b)>

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	a	@	0	(/ (/ a b) a)
0.0ms	a	@	inf	(/ (/ a b) a)
0.0ms	b	@	-inf	(/ (/ a b) a)
0.0ms	a	@	-inf	(/ (/ a b) a)
0.0ms	b	@	inf	(/ (/ a b) a)

rewrite165.0ms (0.7%)

Memory

-11.7MiB live, 243.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 518×	`-lowering-.f32`
1 518×	`-lowering-.f64`
1 264×	`/-lowering-/.f32`
1 264×	`/-lowering-/.f64`
464×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	20	8
2	122	6
3	711	6
0	3128	6

Stop Event

1×	iter limit
1×	iter limit
1×	node limit

Counts

2 → 219

Calls

Call 1

Inputs
(/ (/ a b) a)
(/ a b)

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) b))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) a) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) b))
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(/.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (.f64 a (/.f64 a b)) b))) (/.f64 a b))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (-.f64 #s(literal 0 binary64) (.f64 a (.f64 a a)))) (.f64 a a))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) b) (-.f64 #s(literal 0 binary64) (.f64 a a))) a)
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 a (.f64 a a))) (/.f64 #s(literal -1 binary64) b)) (.f64 a a))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 a a)) (/.f64 #s(literal -1 binary64) b)) a)
(/.f64 (/.f64 a (/.f64 #s(literal -1 binary64) a)) (/.f64 a (/.f64 #s(literal -1 binary64) b)))
(/.f64 (/.f64 a (/.f64 b a)) a)
(/.f64 (/.f64 a (-.f64 #s(literal 0 binary64) (/.f64 b a))) (-.f64 #s(literal 0 binary64) a))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) b) (pow.f64 a #s(literal -1/2 binary64))) (pow.f64 a #s(literal -1/2 binary64)))
(pow.f64 (/.f64 a b) #s(literal 1 binary64))
(pow.f64 (/.f64 b a) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 a b) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 b a) (/.f64 b a)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 b a))) #s(literal -1 binary64))
(*.f64 a (/.f64 #s(literal 1 binary64) b))
(*.f64 (/.f64 a b) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) a) (/.f64 #s(literal -1 binary64) b))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 a b)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (/.f64 a b)) (/.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 #s(literal 1 binary64) a)))
(.f64 (-.f64 #s(literal 0 binary64) (/.f64 a b)) (.f64 (/.f64 #s(literal -1 binary64) a) a))
(*.f64 #s(literal 1 binary64) (/.f64 a b))
(*.f64 (/.f64 #s(literal 1 binary64) b) a)
(.f64 (/.f64 #s(literal 1 binary64) a) (.f64 (/.f64 a b) a))
(*.f64 (/.f64 #s(literal 1 binary64) a) (/.f64 (/.f64 a b) (/.f64 #s(literal 1 binary64) a)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 a b)))
(*.f64 (/.f64 #s(literal -1 binary64) b) (-.f64 #s(literal 0 binary64) a))
(*.f64 (/.f64 #s(literal -1 binary64) b) (pow.f64 (/.f64 #s(literal -1 binary64) a) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) a) (.f64 (-.f64 #s(literal 0 binary64) (/.f64 a b)) a))
(*.f64 (/.f64 #s(literal -1 binary64) a) (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 a b)) (/.f64 #s(literal 1 binary64) a)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) a) b) (.f64 a a))
(.f64 (/.f64 (/.f64 #s(literal -1 binary64) a) b) (.f64 (-.f64 #s(literal 0 binary64) a) a))
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) a) b) (/.f64 (-.f64 #s(literal 0 binary64) a) (/.f64 #s(literal 1 binary64) a)))
(.f64 (.f64 a a) (/.f64 (/.f64 #s(literal 1 binary64) a) b))
(*.f64 (pow.f64 (/.f64 a b) #s(literal 1/2 binary64)) (pow.f64 (/.f64 a b) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 a b) #s(literal 1/2 binary64)) (.f64 (pow.f64 (/.f64 a b) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 a b) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (/.f64 a b) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 b #s(literal -1/2 binary64)) (.f64 (pow.f64 b #s(literal -1/2 binary64)) a))
(*.f64 (pow.f64 b #s(literal -1/2 binary64)) (/.f64 (pow.f64 b #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) a)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) a) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) b))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) a) a) (/.f64 (/.f64 #s(literal -1 binary64) a) b))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) a) (/.f64 a b)) (/.f64 #s(literal -1 binary64) a))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) a) (-.f64 #s(literal 0 binary64) (/.f64 a b))) (/.f64 #s(literal 1 binary64) a))
(.f64 (.f64 a (/.f64 a b)) (/.f64 #s(literal 1 binary64) a))
(.f64 (.f64 a (-.f64 #s(literal 0 binary64) a)) (/.f64 (/.f64 #s(literal -1 binary64) a) b))
(.f64 (.f64 a (-.f64 #s(literal 0 binary64) (/.f64 a b))) (/.f64 #s(literal -1 binary64) a))
(.f64 (.f64 a (pow.f64 b #s(literal -1/2 binary64))) (pow.f64 b #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 a b) #s(literal 1/2 binary64))) (pow.f64 (/.f64 a b) #s(literal 1/2 binary64)))
(*.f64 (/.f64 a (/.f64 b a)) (/.f64 #s(literal 1 binary64) a))
(*.f64 (/.f64 a (-.f64 #s(literal 0 binary64) (/.f64 b a))) (/.f64 #s(literal -1 binary64) a))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) a) (-.f64 #s(literal 0 binary64) (.f64 b (.f64 b b)))) (.f64 b b))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) a) (-.f64 #s(literal 0 binary64) (.f64 b b))) b)

simplify27.0ms (0.1%)

Memory

-24.5MiB live, 14.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`/-lowering-/.f32`
4×	`/-lowering-/.f64`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	144
1	7	144
0	7	144

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ 1 b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)
(/ a b)

Outputs
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ 1 b)
(/.f64 #s(literal 1 binary64) b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)
(/ a b)
(/.f64 a b)

eval30.0ms (0.1%)

Memory: 0.1MiB live, 75.7MiB allocated
Compiler: Compiled 2 857 to 512 computations (82.1% saved)

prune34.0ms (0.1%)

Memory

12.9MiB live, 95.1MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	267	7	274

Accuracy

100.0%

Counts

274 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(/.f64 (/.f64 (+.f64 b a) a) b)
✓	47.2%	(/.f64 (/.f64 b a) b)
✓	52.7%	(/.f64 (/.f64 a b) a)
✓	99.8%	(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
✓	52.8%	(/.f64 #s(literal 1 binary64) b)
✓	47.4%	(/.f64 #s(literal 1 binary64) a)
✓	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

Compiler

Compiled 159 to 85 computations (46.5% saved)

regimes15.0ms (0.1%)

Memory

0.7MiB live, 39.8MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) a)
(/.f64 #s(literal 1 binary64) b)
(/.f64 (/.f64 a b) a)
(/.f64 (/.f64 b a) b)
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 a b)) a)
(/.f64 (/.f64 (+.f64 b a) a) b)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 b (.f64 eps (+.f64 (/.f64 (exp.f64 (.f64 eps a)) (expm1.f64 (.f64 eps a))) #s(literal -1/2 binary64))))) b)
(/.f64 (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (/.f64 (expm1.f64 (.f64 a eps)) eps)) (expm1.f64 (*.f64 b eps)))
(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))

Outputs
(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

Calls

4 calls:

5.0ms	b
4.0ms	eps
4.0ms	a
3.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`eps`
100.0%	1	`(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) #s(literal 1 binary64))) (.f64 (-.f64 (exp.f64 (.f64 a eps)) #s(literal 1 binary64)) (-.f64 (exp.f64 (*.f64 b eps)) #s(literal 1 binary64))))`

Compiler

Compiled 39 to 26 computations (33.3% saved)

regimes7.0ms (0%)

Memory

22.0MiB live, 22.0MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) a)
(/.f64 #s(literal 1 binary64) b)
(/.f64 (/.f64 a b) a)
(/.f64 (/.f64 b a) b)

Outputs
(/.f64 #s(literal 1 binary64) b)
(/.f64 #s(literal 1 binary64) a)

Calls

3 calls:

2.0ms	eps
2.0ms	a
2.0ms	b

Results

Accuracy	Segments	Branch
83.7%	2	`a`
78.8%	2	`b`
58.7%	3	`eps`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes7.0ms (0%)

Memory

-23.5MiB live, 13.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) a)

Outputs
(/.f64 #s(literal 1 binary64) a)

Calls

3 calls:

4.0ms	a
1.0ms	b
1.0ms	eps

Results

Accuracy	Segments	Branch
47.4%	1	`eps`
47.4%	1	`b`
47.4%	1	`a`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch14.0ms (0.1%)

Memory

-5.7MiB live, 37.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-1.6876058548205437e-191	-1.5604207378359933e-192

Samples

10.0ms

96×

valid

Compiler

Compiled 114 to 91 computations (20.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-add: 3.0ms (41% of total)

ival-mult: 3.0ms (41% of total)

ival-div: 1.0ms (13.7% of total)

ival-expm1: 1.0ms (13.7% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

simplify7.0ms (0%)

Memory

23.1MiB live, 23.1MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	13	20

Stop Event

1×

saturated

Calls

Call 1

Inputs

(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

(if (<=.f64 a #s(literal -5297378074679453/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264 binary64)) (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

(/.f64 #s(literal 1 binary64) a)

Outputs

(+.f64 (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

(if (<=.f64 a #s(literal -5297378074679453/321053216647239593947814323906257853121968982105906607635393121525191171526921436896586092302098904493834409720225721295960658706676257560005359788247795462033399882271023229870096664909931806474077957259264 binary64)) (/.f64 #s(literal 1 binary64) b) (/.f64 #s(literal 1 binary64) a))

(/.f64 #s(literal 1 binary64) a)

soundness409.0ms (1.7%)

Memory

-8.8MiB live, 244.0MiB allocated

Rules

11 454×	`accelerator-lowering-fma.f32`
11 454×	`accelerator-lowering-fma.f64`
9 330×	`accelerator-lowering-fma.f32`
9 330×	`accelerator-lowering-fma.f64`
7 346×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	336	2612
1	1079	2564
2	3419	2564
0	8500	2144
0	625	7574
1	1915	7124
2	6207	7109
0	8063	6199

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 61 to 38 computations (37.7% saved)

preprocess69.0ms (0.3%)

Memory: -8.7MiB live, 70.4MiB allocated
Remove: (sort a b)
Compiler: Compiled 140 to 82 computations (41.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze158.0ms (0.7%)

sample17.8s (75%)

preprocess321.0ms (1.4%)

explain263.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify233.0ms (1%)

localize55.0ms (0.2%)

series20.0ms (0.1%)

rewrite480.0ms (2%)

simplify511.0ms (2.2%)

eval47.0ms (0.2%)

prune99.0ms (0.4%)

simplify281.0ms (1.2%)

localize117.0ms (0.5%)

series142.0ms (0.6%)

rewrite444.0ms (1.9%)

simplify652.0ms (2.7%)

eval205.0ms (0.9%)

prune146.0ms (0.6%)

simplify4.0ms (0%)

localize42.0ms (0.2%)

series6.0ms (0%)

rewrite389.0ms (1.6%)

simplify339.0ms (1.4%)

eval90.0ms (0.4%)

prune97.0ms (0.4%)

simplify3.0ms (0%)

localize16.0ms (0.1%)

series1.0ms (0%)

rewrite165.0ms (0.7%)

simplify27.0ms (0.1%)

eval30.0ms (0.1%)

prune34.0ms (0.1%)

regimes15.0ms (0.1%)

regimes7.0ms (0%)

regimes7.0ms (0%)

bsearch14.0ms (0.1%)

simplify7.0ms (0%)

soundness409.0ms (1.7%)

preprocess69.0ms (0.3%)

end0.0ms (0%)

Profiling