Metrics for sintan (problem 3.4.5)

analyze383.0ms (2.5%)

Memory

23.1MiB live, 448.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.9%	50.1%	0%	0%	0%	0
0%	0%	49.9%	50.1%	0%	0%	0%	1
0%	0%	49.9%	50.1%	0%	0%	0%	2
0%	0%	49.9%	50.1%	0%	0%	0%	3
0%	0%	49.9%	50.1%	0%	0%	0%	4
0%	0%	49.9%	50.1%	0%	0%	0%	5
0%	0%	49.9%	50.1%	0%	0%	0%	6
0%	0%	49.9%	50.1%	0%	0%	0%	7
0%	0%	49.9%	50.1%	0%	0%	0%	8
0%	0%	49.9%	50.1%	0%	0%	0%	9
0%	0%	49.9%	50.1%	0%	0%	0%	10
0%	0%	49.9%	50.1%	0%	0%	0%	11
0%	0%	49.9%	50.1%	0%	0%	0%	12

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample12.0s (78%)

Memory

142.0MiB live, 10 917.2MiB allocated

Samples

8.5s	4 510×	2	valid
1.5s	2 424×	1	valid
1.5s	1 164×	3	valid
16.0ms	158×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 11.2s

ival-tan: 6.9s (61.8% of total)

ival-sin: 2.4s (21.7% of total)

const: 994.0ms (8.8% of total)

ival-sub: 302.0ms (2.7% of total)

adjust: 290.0ms (2.6% of total)

ival-div: 164.0ms (1.5% of total)

ival-<=: 87.0ms (0.8% of total)

ival-and: 13.0ms (0.1% of total)

ival-assert: 3.0ms (0% of total)

Bogosity

preprocess54.0ms (0.4%)

Memory

-0.1MiB live, 81.9MiB allocated

Algorithm

1×	egg-herbie

Rules

320×	`lower-fma.f64`
320×	`lower-fma.f32`
192×	`lower-*.f64`
192×	`lower-*.f32`
144×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Outputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Symmetry

(abs eps)

explain566.0ms (3.7%)

Memory

-54.9MiB live, 606.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
173	-	2	(4.3259129527063844e-106)	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`
85	-	0	-	`(-.f64 eps (tan.f64 eps))`
85	-	0	-	`(-.f64 eps (sin.f64 eps))`
0	-	0	-	`(tan.f64 eps)`
0	-	0	-	`eps`
0	-	0	-	`(sin.f64 eps)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`	u/u	171	0
↳	`(-.f64 eps (sin.f64 eps))`	underflow	171
↳	`(-.f64 eps (tan.f64 eps))`	underflow	171
`-.f64`	`(-.f64 eps (sin.f64 eps))`	cancellation	85	0
`-.f64`	`(-.f64 eps (tan.f64 eps))`	cancellation	85	0

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	171
2	85

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

390.0ms	272×	2	valid
66.0ms	86×	3	valid
31.0ms	150×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 68 to 28 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 460.0ms

ival-tan: 218.0ms (47.4% of total)

ival-sin: 139.0ms (30.2% of total)

adjust: 74.0ms (16.1% of total)

ival-sub: 21.0ms (4.6% of total)

ival-div: 7.0ms (1.5% of total)

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

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.2%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify29.0ms (0.2%)

Memory

3.8MiB live, 40.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(-.f64 eps (tan.f64 eps))
✓	cost-diff	(sin.f64 eps)
✓	cost-diff	(-.f64 eps (sin.f64 eps))
✓	cost-diff	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Rules

320×	`lower-fma.f64`
320×	`lower-fma.f32`
192×	`lower-*.f64`
192×	`lower-*.f32`
144×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(-.f64 eps (sin.f64 eps))
eps
(sin.f64 eps)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)

Outputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(-.f64 eps (sin.f64 eps))
eps
(sin.f64 eps)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)

localize224.0ms (1.5%)

Memory

25.4MiB live, 270.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	70.0%	(-.f64 eps (sin.f64 eps))
✓	accuracy	70.0%	(-.f64 eps (tan.f64 eps))
✓	accuracy	33.4%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Samples

164.0ms	136×	2	valid
34.0ms	43×	3	valid
14.0ms	75×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 24 to 8 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 200.0ms

ival-tan: 130.0ms (64.9% of total)

ival-sin: 52.0ms (25.9% of total)

adjust: 8.0ms (4% of total)

ival-sub: 7.0ms (3.5% of total)

ival-div: 3.0ms (1.5% of total)

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

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

series9.0ms (0.1%)

Memory

-31.2MiB live, 8.4MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))>
#<alt (-.f64 eps (sin.f64 eps))>
#<alt (sin.f64 eps)>
#<alt (-.f64 eps (tan.f64 eps))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	inf	(- eps (sin eps))
1.0ms	eps	@	inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	-inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	0	(/ (- eps (sin eps)) (- eps (tan eps)))
0.0ms	eps	@	-inf	(- eps (tan eps))

rewrite334.0ms (2.2%)

Memory

42.5MiB live, 349.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 318×	`lower-*.f64`
4 318×	`lower-*.f32`
3 264×	`lower-/.f32`
3 262×	`lower-/.f64`
2 758×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	11	19
1	51	19
2	408	19
3	5947	19
0	8258	19

Stop Event

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

Counts

4 → 419

Calls

Call 1

Inputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(-.f64 eps (sin.f64 eps))
(sin.f64 eps)
(-.f64 eps (tan.f64 eps))

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 eps (tan.f64 eps)) (-.f64 eps (sin.f64 eps)))) #s(literal -1 binary64)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps))))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (sin.f64 eps))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (sin.f64 eps))) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (*.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps))
(+.f64 (.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 1 binary64)) (.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(+.f64 (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (/.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 (/.f64 (.f64 eps eps) (+.f64 eps (sin.f64 eps))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))))
(-.f64 (/.f64 (.f64 eps eps) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 eps eps)))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))))
(-.f64 (/.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (+.f64 eps (sin.f64 eps))) (.f64 (.f64 eps eps) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal -2 binary64))))) (/.f64 (pow.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (+.f64 eps (sin.f64 eps))) (.f64 (.f64 eps eps) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal -2 binary64))))))
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(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)))) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (+.f64 (fma.f64 eps (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 4 binary64))) (pow.f64 (.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (pow.f64 (tan.f64 eps) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))))
(.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))) #s(literal 1 binary64)))
(.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (/.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))))
(.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)))))
(*.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) #s(literal 1 binary64)))
(*.f64 (+.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (tan.f64 eps))))
(.f64 (+.f64 eps (tan.f64 eps)) (.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))))
(*.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps))
(.f64 (neg.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps)))))
(.f64 (+.f64 (neg.f64 (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 eps (tan.f64 eps)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps))) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) eps) (.f64 eps eps)))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 eps (tan.f64 eps)))
(.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (fma.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (.f64 eps eps)) (.f64 eps (.f64 eps (*.f64 eps eps)))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))

simplify355.0ms (2.3%)

Memory

19.7MiB live, 644.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12 288×	`lower-fma.f64`
12 288×	`lower-fma.f32`
6 122×	`lower-*.f64`
6 122×	`lower-*.f32`
1 424×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	561
1	422	524
2	1321	499
3	5650	444
0	8479	418

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 43

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(fma.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
(fma.f64 (sin.f64 eps) (fma.f64 (sin.f64 eps) (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 (.f64 eps eps) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) eps)) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(fma.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 1 binary64))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps) #s(literal -1 binary64)) (sin.f64 eps)) eps))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) eps) (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) eps))
(* 1/6 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/6 binary64))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(.f64 eps (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* -1/3 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/3 binary64))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -2/15 binary64)) #s(literal -1/3 binary64))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -17/315 binary64)) #s(literal -2/15 binary64)) #s(literal -1/3 binary64)))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -62/2835 binary64) #s(literal -17/315 binary64)) #s(literal -2/15 binary64))) #s(literal -1/3 binary64))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))

eval44.0ms (0.3%)

Memory: -0.9MiB live, 108.3MiB allocated
Compiler: Compiled 12 434 to 1 225 computations (90.1% saved)

prune102.0ms (0.7%)

Memory

-35.1MiB live, 135.9MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	459	3	462
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	460	3	463

Accuracy

100.0%

Counts

463 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
▶	99.9%	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
▶	99.5%	#s(literal -1/2 binary64)

Status

Accuracy

Program

▶

100.0%

(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

▶

99.9%

(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

▶

99.5%

#s(literal -1/2 binary64)

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify8.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 eps #s(literal -27/2800 binary64))
✓	cost-diff	(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
✓	cost-diff	(*.f64 eps eps)
✓	cost-diff	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	(*.f64 eps eps)
✓	cost-diff	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

Rules

104×	`lower-fma.f32`
98×	`lower-fma.f64`
76×	`lower-*.f32`
72×	`lower-*.f64`
32×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	40
0	17	40
1	34	40
2	69	40
3	96	40
4	100	40
5	102	40
0	102	40

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 9/40 binary64)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(*.f64 eps #s(literal -27/2800 binary64))
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)

Outputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal 9/40 binary64)
(*.f64 eps eps)
eps
#s(literal -1/2 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(*.f64 eps #s(literal -27/2800 binary64))
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)

localize49.0ms (0.3%)

Memory

4.6MiB live, 80.2MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
✓	accuracy	99.4%	(*.f64 eps #s(literal -27/2800 binary64))
✓	accuracy	100.0%	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)

Samples

29.0ms

256×

valid

Compiler

Compiled 46 to 14 computations (69.6% saved)

Precisions

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

const: 10.0ms (48.3% of total)

ival-mult: 7.0ms (33.8% of total)

ival-add: 3.0ms (14.5% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0%)

Memory

8.2MiB live, 8.2MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))>
#<alt (*.f64 eps eps)>
#<alt (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))>
#<alt (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))>
#<alt (*.f64 eps #s(literal -27/2800 binary64))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt 9/40>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(+ (* 9/40 (* eps eps)) -1/2)
0.0ms	eps	@	0	(* eps -27/2800)
0.0ms	eps	@	inf	(+ (* (* eps eps) (+ (* eps (* eps -27/2800)) 9/40)) -1/2)
0.0ms	eps	@	inf	(+ (* 9/40 (* eps eps)) -1/2)
0.0ms	eps	@	inf	(* eps -27/2800)

rewrite394.0ms (2.6%)

Memory

13.0MiB live, 601.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 732×	`lower-fma.f32`
7 726×	`lower-fma.f64`
4 910×	`lower-*.f32`
4 906×	`lower-*.f64`
2 222×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
0	17	29
1	75	29
2	533	29
3	5666	29
0	8140	29

Stop Event

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

Counts

5 → 267

Calls

Call 1

Inputs
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(*.f64 eps eps)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(*.f64 eps #s(literal -27/2800 binary64))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 #s(literal 9/40 binary64) (/.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (.f64 eps eps)))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 eps (*.f64 #s(literal 9/40 binary64) eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (/.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) (/.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 81/1600 binary64) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 #s(literal 9/40 binary64) eps) eps #s(literal -1/2 binary64))
(fma.f64 (.f64 #s(literal 9/40 binary64) eps) (/.f64 (.f64 eps (.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 81/1600 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) (/.f64 (.f64 eps eps) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 9/40 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (/.f64 eps (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal -1/2 binary64)) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))))
(fma.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/8 binary64))) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (fma.f64 (.f64 eps eps) #s(literal -9/80 binary64) #s(literal 1/4 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64)) (neg.f64 (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)) #s(literal 1/4 binary64)))))
(neg.f64 (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64))) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)) #s(literal 1/4 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64))) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64)) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)) #s(literal 1/4 binary64)))
(/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal -1/8 binary64))) (neg.f64 (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64))) (fma.f64 (.f64 eps eps) #s(literal -9/40 binary64) #s(literal -1/2 binary64)))
(/.f64 (fma.f64 #s(literal 387420489/262144000000000 binary64) (.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal -1/512 binary64)) (.f64 (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)) #s(literal 1/4 binary64)) (-.f64 (fma.f64 #s(literal 531441/4096000000 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal -729/512000 binary64)))))
(/.f64 (fma.f64 #s(literal 531441/4096000000 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal -1/64 binary64)) (.f64 (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)) #s(literal 1/4 binary64)) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps))) #s(literal 1/8 binary64))))
(/.f64 (fma.f64 #s(literal 531441/4096000000 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal -1/64 binary64)) (.f64 (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 eps (.f64 eps (*.f64 eps eps))) #s(literal 81/6400 binary64) #s(literal 1/16 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))))) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps))))
(/.f64 (fma.f64 #s(literal 6561/2560000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal -1/16 binary64)) (.f64 (fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal 1/4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64)))))
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(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal -7625597484987/10578455953408000000000000000000 binary64) #s(literal 387420489/262144000000000 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal 387420489/481890304000000000000 binary64) #s(literal 531441/4096000000 binary64)) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal -14348907/1404928000000000 binary64))) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal 387420489/481890304000000000000 binary64) #s(literal -531441/4096000000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal -729/64000 binary64)) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal 387420489/481890304000000000000 binary64) #s(literal -531441/4096000000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal 531441/61465600000000 binary64) (fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 59049/12544000000 binary64) #s(literal 6561/2560000 binary64))) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal 531441/61465600000000 binary64) #s(literal -6561/2560000 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal 81/1600 binary64)) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal 729/64000 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64)))
(/.f64 (.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64)) #s(literal 1 binary64)) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal 729/64000 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64)))) (neg.f64 (fma.f64 (.f64 eps eps) #s(literal 27/2800 binary64) #s(literal 9/40 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 81/1600 binary64) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))))) (neg.f64 (-.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps #s(literal -27/2800 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64)))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64)))) (.f64 (.f64 (/.f64 #s(literal 81/1600 binary64) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (/.f64 #s(literal 81/1600 binary64) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64)))) (/.f64 #s(literal 81/1600 binary64) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))))) (fma.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (fma.f64 (/.f64 #s(literal 81/1600 binary64) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (/.f64 #s(literal 81/1600 binary64) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (/.f64 #s(literal 81/1600 binary64) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (/.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64)))) (.f64 (/.f64 #s(literal 81/1600 binary64) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (/.f64 #s(literal 81/1600 binary64) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))))) (fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 729/7840000 binary64) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64))) (/.f64 #s(literal 81/1600 binary64) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal -9/40 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal -7625597484987/10578455953408000000000000000000 binary64) #s(literal 387420489/262144000000000 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64)))) (-.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal 387420489/481890304000000000000 binary64) #s(literal 531441/4096000000 binary64)) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal -14348907/1404928000000000 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal 387420489/481890304000000000000 binary64) #s(literal -531441/4096000000 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64)))) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal -729/64000 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal 387420489/481890304000000000000 binary64) #s(literal -531441/4096000000 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 eps eps) #s(literal 27/2800 binary64) #s(literal 9/40 binary64)))) (fma.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal 531441/61465600000000 binary64) (fma.f64 (.f64 eps (.f64 eps (*.f64 eps eps))) #s(literal 59049/12544000000 binary64) #s(literal 6561/2560000 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal 531441/61465600000000 binary64) #s(literal -6561/2560000 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 eps eps) #s(literal 27/2800 binary64) #s(literal 9/40 binary64)))) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal 81/1600 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) #s(literal -27/2800 binary64) #s(literal 9/40 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) #s(literal -27/2800 binary64) #s(literal 9/40 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps #s(literal -27/2800 binary64)))) (-.f64 #s(literal 81/1600 binary64) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)))))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal 729/64000 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64))))
(.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 eps eps) #s(literal 27/2800 binary64) #s(literal 9/40 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal 729/64000 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 eps eps) (-.f64 (.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64)))))
(.f64 (neg.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 eps eps) #s(literal 27/2800 binary64) #s(literal 9/40 binary64))))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) #s(literal -27/2800 binary64) #s(literal 9/40 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64))) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal 729/64000 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 eps eps) #s(literal 27/2800 binary64) #s(literal 9/40 binary64))) (fma.f64 eps (.f64 eps (.f64 (*.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64)))
(.f64 (-.f64 #s(literal 81/1600 binary64) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 9/40 binary64) (.f64 eps (*.f64 eps #s(literal -27/2800 binary64))))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64)) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64))) (fma.f64 (.f64 eps eps) #s(literal -27/2800 binary64) #s(literal 9/40 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal 729/64000 binary64)) (fma.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) #s(literal 387420489/481890304000000000000 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal 243/112000 binary64) #s(literal 81/1600 binary64)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 243/112000 binary64) #s(literal 81/1600 binary64)) (fma.f64 (.f64 eps eps) #s(literal 243/112000 binary64) #s(literal 81/1600 binary64)))))) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 243/112000 binary64) #s(literal 81/1600 binary64)) (-.f64 (fma.f64 (.f64 eps eps) #s(literal 243/112000 binary64) #s(literal 81/1600 binary64)) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))))) (.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal 531441/61465600000000 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal 729/64000 binary64)) (.f64 (fma.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64)) #s(literal -243/112000 binary64)) #s(literal 81/1600 binary64)) (+.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64)) (.f64 (.f64 eps eps) #s(literal -243/112000 binary64))))) (+.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64)) (.f64 (.f64 eps eps) #s(literal -243/112000 binary64))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) #s(literal -81/1600 binary64)) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -19683/21952000000 binary64)) #s(literal -729/64000 binary64))) (fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 729/7840000 binary64))) (fma.f64 (*.f64 eps eps) #s(literal -243/112000 binary64) #s(literal 81/1600 binary64))))
(*.f64 eps #s(literal -27/2800 binary64))
(*.f64 #s(literal -27/2800 binary64) eps)

simplify328.0ms (2.1%)

Memory

22.4MiB live, 376.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6 660×	`lower-fma.f64`
6 660×	`lower-fma.f32`
3 428×	`lower-*.f64`
3 428×	`lower-*.f32`
2 464×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	338
1	68	338
2	154	338
3	343	338
4	934	338
5	2502	338
6	5702	338
0	8215	305

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
9/40
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* -27/2800 (pow eps 4))
(.f64 eps (.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* -27/2800 (pow eps 4))
(.f64 eps (.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
9/40
#s(literal 9/40 binary64)
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))

eval54.0ms (0.4%)

Memory: -39.1MiB live, 141.9MiB allocated
Compiler: Compiled 11 396 to 805 computations (92.9% saved)

prune60.0ms (0.4%)

Memory

6.0MiB live, 83.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	349	3	352

Accuracy

100.0%

Counts

352 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

✓

99.9%

(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

✓

99.5%

#s(literal -1/2 binary64)

Compiler

Compiled 49 to 29 computations (40.8% saved)

regimes4.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Outputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

Calls

2 calls:

2.0ms	eps
2.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
100.0%	1	`eps`
100.0%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes3.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

Outputs
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

Calls

2 calls:

1.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.9%	1	`eps`
99.9%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes2.0ms (0%)

Memory

4.6MiB live, 4.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)

Outputs
#s(literal -1/2 binary64)

Calls

2 calls:

1.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.5%	1	`eps`
99.5%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify14.0ms (0.1%)

Memory

-32.8MiB live, 9.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	10	18

Stop Event

1×

saturated

Calls

Call 1

Inputs

(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

#s(literal -1/2 binary64)

Outputs

(fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

#s(literal -1/2 binary64)

soundness269.0ms (1.7%)

Memory

10.1MiB live, 200.1MiB allocated

Rules

12 288×	`lower-fma.f64`
12 288×	`lower-fma.f32`
6 122×	`lower-*.f64`
6 122×	`lower-*.f32`
1 424×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	561
1	422	524
2	1321	499
3	5650	444
0	8479	418

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 40 to 24 computations (40% saved)

preprocess94.0ms (0.6%)

Memory: 9.7MiB live, 128.3MiB allocated
Remove: (abs eps)
Compiler: Compiled 174 to 102 computations (41.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22

analyze383.0ms (2.5%)

sample12.0s (78%)

preprocess54.0ms (0.4%)

explain566.0ms (3.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify29.0ms (0.2%)

localize224.0ms (1.5%)

series9.0ms (0.1%)

rewrite334.0ms (2.2%)

simplify355.0ms (2.3%)

eval44.0ms (0.3%)

prune102.0ms (0.7%)

simplify8.0ms (0.1%)

localize49.0ms (0.3%)

series4.0ms (0%)

rewrite394.0ms (2.6%)

simplify328.0ms (2.1%)

eval54.0ms (0.4%)

prune60.0ms (0.4%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify14.0ms (0.1%)

soundness269.0ms (1.7%)

preprocess94.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22