Metrics for expm1 (example 3.7)

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample460.0ms (6.7%)

Memory

50.9MiB live, 749.4MiB allocated

Samples

307.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 164.0ms

ival-expm1: 84.0ms (51.3% of total)

ival-fabs: 46.0ms (28.1% of total)

ival-<=: 25.0ms (15.3% of total)

exact: 5.0ms (3.1% of total)

ival-assert: 3.0ms (1.8% of total)

Bogosity

preprocess15.0ms (0.2%)

Memory

-18.1MiB live, 20.4MiB allocated

Algorithm

2×	egg-herbie

Rules

28×	`sub-neg`
20×	`+-commutative`
10×	`*-commutative`
10×	`associate--r+`
8×	`--rgt-identity`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	19	15
2	38	14
3	57	14
4	73	14
5	93	14
6	111	14
7	126	14
8	138	14
9	142	14
10	143	14
0	4	4
1	9	4
2	10	4
0	10	2

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (exp x) 1)

Outputs
(- (exp x) 1)
(expm1.f64 x)

Call 2

Inputs
(- (exp x) 1)
(- (exp (neg x)) 1)
(neg (- (exp (neg x)) 1))

Outputs
(- (exp x) 1)
(+ (exp x) -1)
(- (exp (neg x)) 1)
(+ (exp (neg x)) -1)
(neg (- (exp (neg x)) 1))
(- 1 (exp (neg x)))

explain70.0ms (1%)

Memory

-10.0MiB live, 70.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
255	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(exp.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	255	0

Confusion

	Predicted +	Predicted -
+	255	0
-	0	1

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	255	0	0
-	0	0	1

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	1
1	255

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms

512×

valid

Compiler

Compiled 30 to 20 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-exp: 4.0ms (49% of total)

ival-expm1: 3.0ms (36.7% 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.5%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(exp.f64 x)
✓	cost-diff	192	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`accelerator-lowering-expm1.f32`
2×	`exp-lowering-exp.f32`
2×	`accelerator-lowering-expm1.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (exp x) 1)
(exp x)
x
1

Outputs
(- (exp x) 1)
(expm1.f64 x)
(exp x)
(exp.f64 x)
x
1
#s(literal 1 binary64)

localize16.0ms (0.2%)

Memory

-5.2MiB live, 32.9MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	7.5%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

9.0ms

256×

valid

Compiler

Compiled 10 to 6 computations (40% saved)

Precisions

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

ival-exp: 2.0ms (47.3% of total)

ival-expm1: 2.0ms (47.3% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (- (exp x) 1)>
#<alt (exp x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(- (exp x) 1)
0.0ms	x	@	inf	(- (exp x) 1)
0.0ms	x	@	-inf	(- (exp x) 1)
0.0ms	x	@	0	(exp x)
0.0ms	x	@	inf	(exp x)

rewrite100.0ms (1.5%)

Memory

12.6MiB live, 105.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

594×	`accelerator-lowering-fma.f32`
594×	`accelerator-lowering-fma.f64`
574×	`/-lowering-/.f32`
574×	`/-lowering-/.f64`
536×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	22	6
2	128	6
0	1139	4

Stop Event

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

Counts

2 → 84

Calls

Call 1

Inputs
(- (exp x) 1)
(exp x)

Outputs
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) #s(literal -1 binary64))))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(fma.f64 (exp.f64 x) (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 (exp.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(fma.f64 (exp.f64 (.f64 x #s(literal 3/2 binary64))) (/.f64 (exp.f64 (.f64 x #s(literal 3/2 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(fma.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 x) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (expm1.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(fma.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))) (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(fma.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (-.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (+.f64 x x)) (exp.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(expm1.f64 x)
(neg.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))) (expm1.f64 (.f64 x #s(literal 3 binary64)))))
(/.f64 (expm1.f64 x) #s(literal 1 binary64))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))))))
(/.f64 (expm1.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))))))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal -1 binary64) (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (exp.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(/.f64 (*.f64 (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (*.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))) (+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(/.f64 (-.f64 (.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))) (+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (.f64 (expm1.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (exp.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (*.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (expm1.f64 x))
(.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) #s(literal -1 binary64))))))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (.f64 (expm1.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (/.f64 (expm1.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(.f64 (neg.f64 (expm1.f64 (.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64))))))
(*.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (expm1.f64 (.f64 x #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (expm1.f64 (+.f64 x x)))
(*.f64 (/.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (expm1.f64 x))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (expm1.f64 x))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (-.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (exp.f64 (+.f64 x x))) (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x)))))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (-.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (+.f64 x x)) (exp.f64 x)))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(exp.f64 x)
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))

simplify35.0ms (0.5%)

Memory

-15.3MiB live, 60.7MiB allocated

Algorithm

1×	egg-herbie

Rules

1 308×	`accelerator-lowering-fma.f32`
1 308×	`accelerator-lowering-fma.f64`
364×	`-lowering-.f32`
364×	`-lowering-.f64`
308×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	108
1	77	108
2	168	108
3	371	108
4	587	108
5	718	108
6	723	108
0	723	81

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)

Outputs
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)

eval13.0ms (0.2%)

Memory: -6.4MiB live, 32.4MiB allocated
Compiler: Compiled 1 873 to 240 computations (87.2% saved)

prune15.0ms (0.2%)

Memory

-3.2MiB live, 41.0MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Accuracy

100.0%

Counts

109 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
▶	99.7%	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
▶	99.4%	(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
▶	6.8%	(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
▶	100.0%	(expm1.f64 x)
▶	98.6%	x

Compiler

Compiled 82 to 50 computations (39% saved)

simplify519.0ms (7.6%)

Memory

41.8MiB live, 709.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	384	(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(expm1.f64 x)

Rules

16 150×	`accelerator-lowering-fma.f32`
16 150×	`accelerator-lowering-fma.f64`
3 166×	`+-lowering-+.f64`
3 166×	`+-lowering-+.f32`
3 010×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	35	46
2	59	46
3	344	46
4	2555	46
5	5472	46
6	7012	46
0	8208	40

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(- (exp x) 1)
x
x
(- (+ x 1) 1)
(+ x 1)
x
1
(+ (* x (* x 1/2)) x)
x
(* x 1/2)
1/2
(+ (* (+ (* x 1/6) 1/2) (* x x)) x)
(+ (* x 1/6) 1/2)
x
1/6
1/2
(* x x)

Outputs
(- (exp x) 1)
(expm1.f64 x)
x
x
(- (+ x 1) 1)
x
(+ x 1)
(+.f64 x #s(literal 1 binary64))
x
1
#s(literal 1 binary64)
(+ (* x (* x 1/2)) x)
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
x
(* x 1/2)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(+ (* (+ (* x 1/6) 1/2) (* x x)) x)
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
x
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)

localize82.0ms (1.2%)

Memory

-2.8MiB live, 114.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	7.5%	(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(expm1.f64 x)

Samples

40.0ms	153×	1	valid
23.0ms	97×	2	valid
1.0ms	6×	0	valid

Compiler

Compiled 46 to 17 computations (63% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

adjust: 23.0ms (49.9% of total)

ival-add: 7.0ms (15.2% of total)

ival-mult: 7.0ms (15.2% of total)

const: 4.0ms (8.7% of total)

ival-sub: 3.0ms (6.5% of total)

ival-expm1: 2.0ms (4.3% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

8 → 96

Calls

Call 1

Inputs
#<alt (- (exp x) 1)>
#<alt (- (+ x 1) 1)>
#<alt (+ x 1)>
#<alt (+ (* x (* x 1/2)) x)>
#<alt (* x 1/2)>
#<alt (+ (* (+ (* x 1/6) 1/2) (* x x)) x)>
#<alt (+ (* x 1/6) 1/2)>
#<alt (* x x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(* x 1/2)
0.0ms	x	@	0	(+ (* x (* x 1/2)) x)
0.0ms	x	@	inf	(- (+ x 1) 1)
0.0ms	x	@	-inf	(* x 1/2)
0.0ms	x	@	0	(* x 1/2)

rewrite409.0ms (6%)

Memory

5.0MiB live, 559.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 808×	`accelerator-lowering-fma.f32`
8 808×	`accelerator-lowering-fma.f64`
4 114×	`-lowering-.f32`
4 114×	`-lowering-.f64`
3 462×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	103	37
2	831	37
0	8498	31

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 750

Calls

Call 1

Inputs
(- (exp x) 1)
(- (+ x 1) 1)
(+ x 1)
(+ (* x (* x 1/2)) x)
(* x 1/2)
(+ (* (+ (* x 1/6) 1/2) (* x x)) x)
(+ (* x 1/6) 1/2)
(* x x)

Outputs
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
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(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (pow.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 (+.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 2 binary64) (fma.f64 (+.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))) #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 (+.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 (+.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 (+.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 2 binary64) (fma.f64 (+.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 2 binary64) (fma.f64 (+.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))))))
(.f64 (.f64 (.f64 (+.f64 x #s(literal 2 binary64)) x) (.f64 (+.f64 x #s(literal 2 binary64)) x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64)))))

simplify544.0ms (7.9%)

Memory

4.2MiB live, 478.9MiB allocated

Algorithm

1×	egg-herbie

Rules

15 336×	`accelerator-lowering-fma.f32`
15 336×	`accelerator-lowering-fma.f64`
4 042×	`-lowering-.f32`
4 042×	`-lowering-.f64`
2 216×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	408
1	152	408
2	364	408
3	1370	408
4	4679	408
5	7474	408
0	8127	353

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
x
x
x
x
x
x
x
x
x
x
x
x
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
x
x
x
x
x
x
x
x
x
x
x
x
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval190.0ms (2.8%)

Memory: -8.0MiB live, 145.2MiB allocated
Compiler: Compiled 18 367 to 1 645 computations (91% saved)

prune390.0ms (5.7%)

Memory

19.6MiB live, 179.2MiB allocated

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	843	3	846
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	843	9	852

Accuracy

100.0%

Counts

852 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	99.7%	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
▶	99.4%	(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
✓	99.4%	(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
✓	6.8%	(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
▶	6.9%	(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
▶	99.7%	(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
✓	100.0%	(expm1.f64 x)
✓	98.6%	x

Compiler

Compiled 67 to 44 computations (34.3% saved)

simplify931.0ms (13.5%)

Memory

-13.4MiB live, 699.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
✓	cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
✓	cost-diff	256	(fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(+.f64 x #s(literal -1 binary64))
✓	cost-diff	384	(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)

Rules

24 842×	`accelerator-lowering-fma.f32`
24 842×	`accelerator-lowering-fma.f64`
4 302×	`-lowering-.f32`
4 302×	`-lowering-.f64`
4 296×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	97
1	67	97
2	144	89
3	791	89
4	1162	89
5	1490	89
6	2822	89
7	4401	89
8	6734	89
9	7698	89
10	7751	89
11	7751	89
0	8393	77

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (+ (* x (+ (* x 1/6) 1/2)) 1) x)
(+ (* x (+ (* x 1/6) 1/2)) 1)
x
(+ (* x 1/6) 1/2)
1/6
1/2
1
(+ (+ x -1) 1)
(+ x -1)
x
-1
1
(+ (* x (+ (* (+ x 1) 1/2) -1/2)) x)
x
(+ (* (+ x 1) 1/2) -1/2)
(+ x 1)
1
1/2
-1/2
(+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x)
(+ (* x (+ (* x 1/24) 1/6)) 1/2)
x
(+ (* x 1/24) 1/6)
1/24
1/6
1/2
(* x x)

Outputs
(* (+ (* x (+ (* x 1/6) 1/2)) 1) x)
(fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(+ (* x (+ (* x 1/6) 1/2)) 1)
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
x
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
(+ (+ x -1) 1)
x
(+ x -1)
(+.f64 x #s(literal -1 binary64))
x
-1
#s(literal -1 binary64)
1
#s(literal 1 binary64)
(+ (* x (+ (* (+ x 1) 1/2) -1/2)) x)
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
x
(+ (* (+ x 1) 1/2) -1/2)
(*.f64 x #s(literal 1/2 binary64))
(+ x 1)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
1/2
#s(literal 1/2 binary64)
-1/2
#s(literal -1/2 binary64)
(+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x)
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(+ (* x (+ (* x 1/24) 1/6)) 1/2)
(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
x
(+ (* x 1/24) 1/6)
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
1/24
#s(literal 1/24 binary64)
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)

localize153.0ms (2.2%)

Memory

7.3MiB live, 368.0MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	9.0%	(fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 x #s(literal -1 binary64))
✓	accuracy	9.1%	(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)

Samples

57.0ms	154×	1	valid
50.0ms	92×	2	valid
3.0ms	4×	5	exit
1.0ms	6×	0	valid

Compiler

Compiled 89 to 28 computations (68.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-mult: 26.0ms (31.1% of total)

ival-add: 25.0ms (29.9% of total)

adjust: 21.0ms (25.1% of total)

const: 10.0ms (12% of total)

exact: 1.0ms (1.2% of total)

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

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

series8.0ms (0.1%)

Memory

-17.8MiB live, 20.6MiB allocated

Counts

12 → 144

Calls

Call 1

Inputs
#<alt (* (+ (* x (+ (* x 1/6) 1/2)) 1) x)>
#<alt (+ (* x (+ (* x 1/6) 1/2)) 1)>
#<alt (+ (* x 1/6) 1/2)>
#<alt (+ (+ x -1) 1)>
#<alt (+ x -1)>
#<alt (+ (* (+ x 1) 1/2) -1/2)>
#<alt (+ (* x (+ (* (+ x 1) 1/2) -1/2)) x)>
#<alt (+ x 1)>
#<alt (+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x)>
#<alt (+ (* x (+ (* x 1/24) 1/6)) 1/2)>
#<alt (+ (* x 1/24) 1/6)>
#<alt (* x x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt -1>
#<alt (- x 1)>
#<alt (- x 1)>
#<alt (- x 1)>
#<alt x>
#<alt (* x (- 1 (/ 1 x)))>
#<alt (* x (- 1 (/ 1 x)))>
#<alt (* x (- 1 (/ 1 x)))>
#<alt x>
#<alt (* -1 (* x (- (/ 1 x) 1)))>
#<alt (* -1 (* x (- (/ 1 x) 1)))>
#<alt (* -1 (* x (- (/ 1 x) 1)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* x (+ 1/6 (* 1/24 x))))>
#<alt (+ 1/2 (* x (+ 1/6 (* 1/24 x))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt 1/6>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (+ 1/6 (* 1/24 x))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* x (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

36 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* (+ (* x (+ (* x 1/6) 1/2)) 1) x)
0.0ms	x	@	inf	(+ (* x (+ (* (+ x 1) 1/2) -1/2)) x)
0.0ms	x	@	0	(+ (* (+ x 1) 1/2) -1/2)
0.0ms	x	@	-inf	(+ (* (+ x 1) 1/2) -1/2)
0.0ms	x	@	-inf	(+ (* x (+ (* (+ x 1) 1/2) -1/2)) x)

rewrite361.0ms (5.3%)

Memory

9.0MiB live, 755.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 916×	`accelerator-lowering-fma.f32`
4 916×	`accelerator-lowering-fma.f64`
4 376×	`-lowering-.f32`
4 376×	`-lowering-.f64`
4 044×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	84
1	181	82
2	1538	82
0	8408	68

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 621

Calls

Call 1

Inputs
(* (+ (* x (+ (* x 1/6) 1/2)) 1) x)
(+ (* x (+ (* x 1/6) 1/2)) 1)
(+ (* x 1/6) 1/2)
(+ (+ x -1) 1)
(+ x -1)
(+ (* (+ x 1) 1/2) -1/2)
(+ (* x (+ (* (+ x 1) 1/2) -1/2)) x)
(+ x 1)
(+ (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)) x)
(+ (* x (+ (* x 1/24) 1/6)) 1/2)
(+ (* x 1/24) 1/6)
(* x x)

Outputs
(+.f64 x (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(+.f64 x (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(+.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) x)
(+.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) x)
(fma.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(fma.f64 x #s(literal 1 binary64) (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x x)
(fma.f64 #s(literal 1 binary64) x (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(fma.f64 (.f64 x (+.f64 x #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (.f64 x (+.f64 x #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))) (.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(fma.f64 (pow.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64)) (.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(fma.f64 (pow.f64 (.f64 x (+.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)) (.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (.f64 x (+.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))) #s(literal 1 binary64)) (.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x))
(/.f64 (.f64 x (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64))) (-.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(/.f64 (.f64 x (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) x) (-.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) x) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) (neg.f64 (-.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)))) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) x)) (neg.f64 (-.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64)) x)) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(/.f64 (fma.f64 x (.f64 x x) (pow.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (.f64 x (.f64 x (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))))
(/.f64 (fma.f64 x (.f64 x x) (pow.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)) (.f64 x (.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (fma.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) x))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) #s(literal 3 binary64)) (.f64 x (.f64 x x))) (fma.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) (-.f64 (.f64 x x) (.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x) x))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(+.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x))) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))) (/.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
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(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal 1/36 binary64)) (.f64 x #s(literal 1/144 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/576 binary64) #s(literal -1/36 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64) #s(literal 1/216 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal 1/36 binary64)) (*.f64 x #s(literal 1/144 binary64)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/576 binary64) #s(literal -1/36 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/24 binary64) #s(literal -1/6 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 (pow.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) #s(literal 2 binary64)))
(.f64 (pow.f64 (.f64 x (+.f64 x #s(literal -2 binary64))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify272.0ms (4%)

Memory

27.1MiB live, 541.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 938×	`accelerator-lowering-fma.f32`
11 938×	`accelerator-lowering-fma.f64`
3 704×	`-lowering-.f32`
3 704×	`-lowering-.f64`
1 576×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	734
1	269	726
2	681	726
3	2260	718
4	5927	718
0	8177	630

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
x
x
x
x
x
x
x
x
x
x
x
x
-1
(- x 1)
(- x 1)
(- x 1)
x
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
x
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
1/6
(+ 1/6 (* 1/24 x))
(+ 1/6 (* 1/24 x))
(+ 1/6 (* 1/24 x))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* 1/24 x)
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (.f64 x x))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
x
x
x
x
x
x
x
x
x
x
x
x
-1
#s(literal -1 binary64)
(- x 1)
(+.f64 x #s(literal -1 binary64))
(- x 1)
(+.f64 x #s(literal -1 binary64))
(- x 1)
(+.f64 x #s(literal -1 binary64))
x
(* x (- 1 (/ 1 x)))
(+.f64 x #s(literal -1 binary64))
(* x (- 1 (/ 1 x)))
(+.f64 x #s(literal -1 binary64))
(* x (- 1 (/ 1 x)))
(+.f64 x #s(literal -1 binary64))
x
(* -1 (* x (- (/ 1 x) 1)))
(+.f64 x #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(+.f64 x #s(literal -1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(+.f64 x #s(literal -1 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* 1/2 (pow x 2))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x)
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x))) x))
(* 1/24 (pow x 4))
(.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x))))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/24 binary64) (/.f64 #s(literal 1/6 binary64) x)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(fma.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (fma.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (.f64 x x))) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 1/6 (* 1/24 x))))
(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/6 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* 1/24 x))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(+ 1/6 (* 1/24 x))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(+ 1/6 (* 1/24 x))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(* x (+ 1/24 (* 1/6 (/ 1 x))))
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval108.0ms (1.6%)

Memory: -0.7MiB live, 186.2MiB allocated
Compiler: Compiled 28 224 to 2 053 computations (92.7% saved)

prune84.0ms (1.2%)

Memory

28.9MiB live, 187.4MiB allocated

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	763	2	765
Fresh	0	0	0
Picked	0	4	4
Done	0	5	5
Total	763	11	774

Accuracy

100.0%

Counts

774 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.6%	(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
✓	99.7%	(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	99.7%	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	99.4%	(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
✓	99.4%	(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
✓	6.8%	(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
✓	6.9%	(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
▶	99.7%	(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) x)
✓	99.7%	(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
✓	100.0%	(expm1.f64 x)
✓	98.6%	x

Compiler

Compiled 118 to 69 computations (41.5% saved)

simplify405.0ms (5.9%)

Memory

-7.2MiB live, 321.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))
✓	cost-diff	192	(fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
✓	cost-diff	320	(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
✓	cost-diff	384	(-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))
✓	cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) x)
✓	cost-diff	320	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))

Rules

11 652×	`accelerator-lowering-fma.f32`
11 652×	`accelerator-lowering-fma.f64`
2 406×	`+-lowering-+.f64`
2 406×	`+-lowering-+.f32`
2 118×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	163
1	71	151
2	210	151
3	654	143
4	2253	137
5	6070	137
0	8185	119

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (+ (* (* x x) 1/6) (+ (* x 1/2) 1)) x)
(+ (* (* x x) 1/6) (+ (* x 1/2) 1))
(* x x)
x
1/6
(+ (* x 1/2) 1)
1/2
1
(+ (* (+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1) (/ 1 (- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1)))) (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)))
(+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1)
(+ x -1)
x
-1
(* (+ x -1) (+ x -1))
1
(/ 1 (- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1)))
(- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1))
(+ (* (+ x -1) (+ x -1)) 1)
(* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x))
(+ (* x (+ (* x 1/24) 1/6)) 1/2)
(+ (* x 1/24) 1/6)
1/24
1/6
1/2
(* x x)

Outputs
(* (+ (* (* x x) 1/6) (+ (* x 1/2) 1)) x)
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(+ (* (* x x) 1/6) (+ (* x 1/2) 1))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* x x)
(*.f64 x x)
x
1/6
#s(literal 1/6 binary64)
(+ (* x 1/2) 1)
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
(+ (* (+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1) (/ 1 (- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1)))) (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)))
(fma.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (/.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64))))
(+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1)
(fma.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(+ x -1)
(+.f64 x #s(literal -1 binary64))
x
-1
#s(literal -1 binary64)
(* (+ x -1) (+ x -1))
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(/ 1 (- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1)))
(/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64)))
(- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1))
(fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64))
(+ (* (+ x -1) (+ x -1)) 1)
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 2 binary64))
(* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x))
(.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(+ (* x (+ (* x 1/24) 1/6)) 1/2)
(fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))
(+ (* x 1/24) 1/6)
(fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))
1/24
#s(literal 1/24 binary64)
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)

localize137.0ms (2%)

Memory

-8.9MiB live, 190.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
✓	accuracy	100.0%	(*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))
✓	accuracy	99.5%	(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
✓	accuracy	7.7%	(fma.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓	accuracy	100.0%	(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) x)

Samples

95.0ms	248×	1	valid
1.0ms	8×	0	valid

Compiler

Compiled 158 to 28 computations (82.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

ival-mult: 26.0ms (34% of total)

ival-add: 20.0ms (26.2% of total)

adjust: 13.0ms (17% of total)

const: 11.0ms (14.4% of total)

ival-div: 4.0ms (5.2% of total)

ival-sub: 2.0ms (2.6% of total)

exact: 1.0ms (1.3% of total)

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

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

series6.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (+ (* (* x x) 1/6) (+ (* x 1/2) 1))>
#<alt (* (+ (* (* x x) 1/6) (+ (* x 1/2) 1)) x)>
#<alt (* x x)>
#<alt (+ (* x 1/2) 1)>
#<alt (- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1))>
#<alt (+ (* (+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1) (/ 1 (- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1)))) (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)))>
#<alt (+ (* (+ x -1) (+ x -1)) 1)>
#<alt (* (+ x -1) (+ x -1))>
#<alt (+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1)>
#<alt (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x))>

Outputs
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt 3>
#<alt (+ 3 (* -3 x))>
#<alt (+ 3 (* x (- x 3)))>
#<alt (+ 3 (* x (- x 3)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 3 (* 3 (/ 1 x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 3 (* 3 (/ 1 x))) x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))>
#<alt 2>
#<alt (+ 2 (* -2 x))>
#<alt (+ 2 (* x (- x 2)))>
#<alt (+ 2 (* x (- x 2)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 2 (pow x 2))) (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 2 (pow x 2))) (* 2 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 2 (* 2 (/ 1 x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 2 (* 2 (/ 1 x))) x))))>
#<alt 1>
#<alt (+ 1 (* -2 x))>
#<alt (+ 1 (* x (- x 2)))>
#<alt (+ 1 (* x (- x 2)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))>
#<alt (* 3 x)>
#<alt (* x (+ 3 (* -3 x)))>
#<alt (* x (+ 3 (* x (- x 3))))>
#<alt (* x (+ 3 (* x (- x 3))))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (- 1 (* 3 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))>
#<alt (pow x 3)>
#<alt (* -1 (* (pow x 3) (- (* 3 (/ 1 x)) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 3 (/ 1 x)) 3) x)) 1)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 3 (/ 1 x)) 3) x)) 1)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))>
#<alt (* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* 1/24 (pow x 4))>
#<alt (* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>
#<alt (* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1))
0.0ms	x	@	-inf	(+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1)
0.0ms	x	@	-inf	(+ (* (+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1) (/ 1 (- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1)))) (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)))
0.0ms	x	@	0	(+ (* (+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1) (/ 1 (- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1)))) (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)))
0.0ms	x	@	inf	(- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1))

rewrite401.0ms (5.8%)

Memory

-3.7MiB live, 537.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 450×	`-lowering-.f32`
5 450×	`-lowering-.f64`
4 716×	`accelerator-lowering-fma.f32`
4 716×	`accelerator-lowering-fma.f64`
4 492×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	108
1	187	100
2	1877	100
0	9621	90

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 464

Calls

Call 1

Inputs
(+ (* (* x x) 1/6) (+ (* x 1/2) 1))
(* (+ (* (* x x) 1/6) (+ (* x 1/2) 1)) x)
(* x x)
(+ (* x 1/2) 1)
(- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1))
(+ (* (+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1) (/ 1 (- (+ (* (+ x -1) (+ x -1)) 1) (+ x -1)))) (* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x)))
(+ (* (+ x -1) (+ x -1)) 1)
(* (+ x -1) (+ x -1))
(+ (* (+ x -1) (* (+ x -1) (+ x -1))) 1)
(* (+ (* x (+ (* x 1/24) 1/6)) 1/2) (* x x))

Outputs
(+.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/6 binary64))))
(+.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(+.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
(+.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))
(+.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64)) (.f64 x #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 (.f64 x x) #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (/.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (-.f64 (.f64 (*.f64 x x) #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1/6 binary64)))) (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (.f64 (*.f64 x x) #s(literal 1/6 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))) (-.f64 (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(fma.f64 x #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
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(/.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal -1/4 binary64))) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))) #s(literal 1/8 binary64)) (.f64 x x)) (-.f64 (fma.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal -1/4 binary64)) (.f64 x x)) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))) #s(literal 1/8 binary64)))) (neg.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))) #s(literal 1/8 binary64)) (.f64 x x))) (neg.f64 (-.f64 (fma.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) (.f64 x (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) #s(literal 1/4 binary64)) (.f64 x (.f64 (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) #s(literal -1/4 binary64)) (.f64 x x))) (neg.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal -1/2 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (.f64 (.f64 x x) #s(literal 1/2 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) (.f64 (.f64 x x) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))) (.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (.f64 (.f64 x x) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) (.f64 (.f64 x x) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (.f64 (.f64 x x) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)))) (.f64 (.f64 x x) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x x)) (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x x))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x x)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x x)) (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x x)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (.f64 x x))))))
(.f64 x (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x))
(.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) x)

simplify349.0ms (5.1%)

Memory

1.6MiB live, 399.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 260×	`accelerator-lowering-fma.f32`
13 260×	`accelerator-lowering-fma.f64`
3 534×	`-lowering-.f32`
3 534×	`-lowering-.f64`
1 844×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	126	924
1	414	908
2	1099	852
3	3411	812
4	6065	812
0	8170	724

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
3
(+ 3 (* -3 x))
(+ 3 (* x (- x 3)))
(+ 3 (* x (- x 3)))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 3 (* 3 (/ 1 x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 3 (* 3 (/ 1 x))) x))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
2
(+ 2 (* -2 x))
(+ 2 (* x (- x 2)))
(+ 2 (* x (- x 2)))
(pow x 2)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 2 (pow x 2))) (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 2 (pow x 2))) (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (* 2 (/ 1 x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (* 2 (/ 1 x))) x))))
1
(+ 1 (* -2 x))
(+ 1 (* x (- x 2)))
(+ 1 (* x (- x 2)))
(pow x 2)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(* 3 x)
(* x (+ 3 (* -3 x)))
(* x (+ 3 (* x (- x 3))))
(* x (+ 3 (* x (- x 3))))
(pow x 3)
(* (pow x 3) (- 1 (* 3 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))
(pow x 3)
(* -1 (* (pow x 3) (- (* 3 (/ 1 x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 3 (/ 1 x)) 3) x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 3 (/ 1 x)) 3) x)) 1)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* 1/24 (pow x 4))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
3
#s(literal 3 binary64)
(+ 3 (* -3 x))
(fma.f64 x #s(literal -3 binary64) #s(literal 3 binary64))
(+ 3 (* x (- x 3)))
(fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64))
(+ 3 (* x (- x 3)))
(fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal -3 binary64)))
(* (pow x 2) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) x))))
(* (pow x 2) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal -3 binary64)))
(* (pow x 2) (+ 1 (* -1 (/ (- 3 (* 3 (/ 1 x))) x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 3 (* 3 (/ 1 x))) x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) x))))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 (*.f64 x x) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (+ (* 1/6 (/ 1 x)) (/ 1 (pow x 3))))))
(fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(* 1/24 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 (*.f64 x x) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 4) (+ 1/24 (* -1 (/ (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6) x))))
(fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (* -2 x))
(fma.f64 x #s(literal -2 binary64) #s(literal 2 binary64))
(+ 2 (* x (- x 2)))
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 2 binary64))
(+ 2 (* x (- x 2)))
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal -2 binary64)))
(* (pow x 2) (- (+ 1 (/ 2 (pow x 2))) (* 2 (/ 1 x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x))))
(* (pow x 2) (- (+ 1 (/ 2 (pow x 2))) (* 2 (/ 1 x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal -2 binary64)))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (* 2 (/ 1 x))) x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x))))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (* 2 (/ 1 x))) x))))
(*.f64 x (+.f64 x (+.f64 #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) x))))
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(fma.f64 x #s(literal -2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- x 2)))
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- x 2)))
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal -2 binary64)))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(*.f64 x (+.f64 x #s(literal -2 binary64)))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(fma.f64 x (+.f64 x #s(literal -2 binary64)) #s(literal 1 binary64))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* x (+ 3 (* -3 x)))
(*.f64 x (fma.f64 x #s(literal -3 binary64) #s(literal 3 binary64)))
(* x (+ 3 (* x (- x 3))))
(*.f64 x (fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64)))
(* x (+ 3 (* x (- x 3))))
(*.f64 x (fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64)))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (- 1 (* 3 (/ 1 x))))
(.f64 (.f64 x x) (+.f64 x #s(literal -3 binary64)))
(* (pow x 3) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))
(fma.f64 x (.f64 x (+.f64 x #s(literal -3 binary64))) (neg.f64 (.f64 x #s(literal -3 binary64))))
(* (pow x 3) (- (+ 1 (/ 3 (pow x 2))) (* 3 (/ 1 x))))
(fma.f64 x (.f64 x (+.f64 x #s(literal -3 binary64))) (neg.f64 (.f64 x #s(literal -3 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* -1 (* (pow x 3) (- (* 3 (/ 1 x)) 1)))
(.f64 (.f64 x x) (+.f64 x #s(literal -3 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 3 (/ 1 x)) 3) x)) 1)))
(fma.f64 x (.f64 x (+.f64 x #s(literal -3 binary64))) (neg.f64 (.f64 x #s(literal -3 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 3 (/ 1 x)) 3) x)) 1)))
(fma.f64 x (.f64 x (+.f64 x #s(literal -3 binary64))) (neg.f64 (.f64 x #s(literal -3 binary64))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* 1/24 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 (*.f64 x x) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* 1/24 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(* (pow x 4) (+ 1/24 (* 1/6 (/ 1 x))))
(.f64 x (.f64 (*.f64 x x) (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64))))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(* (pow x 4) (+ 1/24 (+ (/ 1/2 (pow x 2)) (* 1/6 (/ 1 x)))))
(.f64 (.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))

eval95.0ms (1.4%)

Memory: 18.4MiB live, 169.8MiB allocated
Compiler: Compiled 34 136 to 2 121 computations (93.8% saved)

prune67.0ms (1%)

Memory

-15.7MiB live, 143.4MiB allocated

Pruning

12 alts after pruning (2 fresh and 10 done)

	Pruned	Kept	Total
New	600	2	602
Fresh	0	0	0
Picked	1	1	2
Done	0	9	9
Total	601	12	613

Accuracy

100.0%

Counts

613 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.6%	(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
	7.6%	(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 x (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) x))))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
✓	99.7%	(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	99.7%	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	99.4%	(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
✓	99.4%	(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
✓	6.8%	(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
✓	6.9%	(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
✓	99.7%	(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) x)
✓	99.7%	(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
✓	100.0%	(expm1.f64 x)
✓	98.6%	x

Compiler

Compiled 327 to 140 computations (57.2% saved)

regimes12.0ms (0.2%)

Memory

27.1MiB live, 27.1MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
x
(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) x)
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 x (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) x))))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))
(expm1.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))

Outputs
(expm1.f64 x)

Calls

3 calls:

4.0ms	x
4.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
4.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
100.0%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes32.0ms (0.5%)

Memory

-25.4MiB live, 13.5MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
x
(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) x)
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -3 binary64)) #s(literal 3 binary64))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
(fma.f64 (fma.f64 (+.f64 x #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 x (+.f64 #s(literal -3 binary64) (/.f64 #s(literal 3 binary64) x))))) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (.f64 x x)))

Outputs
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)

Calls

3 calls:

24.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
4.0ms	x
3.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.7%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes8.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
x
(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/6 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) x)

Outputs
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)

Calls

3 calls:

3.0ms	x
2.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
2.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.7%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
x
(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)

Outputs
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)

Calls

3 calls:

2.0ms	x
2.0ms	(exp.f64 x)
2.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.7%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
x
(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)

Outputs
(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)

Calls

3 calls:

2.0ms	x
2.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
2.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.4%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes28.0ms (0.4%)

Memory

-31.4MiB live, 7.3MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
x
(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)

Outputs
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)

Calls

3 calls:

24.0ms	x
2.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
2.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
99.4%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Accuracy

Total -58.7b remaining (-6628.9%)

Threshold costs -58.7b (-6628.9%)

Counts

3 → 1

Calls

Call 1

Inputs
x
(+.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))

Outputs
x

Calls

3 calls:

2.0ms	x
1.0ms	(exp.f64 x)
1.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
98.6%	1	`(exp.f64 x)`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	48
1	26	48

Stop Event

1×

saturated

Calls

Call 1

Inputs
(expm1.f64 x)
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
x

Outputs
(expm1.f64 x)
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) x)
(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
(*.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(fma.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)) x)
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
x

soundness463.0ms (6.7%)

Memory

-62.2MiB live, 153.7MiB allocated

Rules

8 808×	`accelerator-lowering-fma.f32`
8 808×	`accelerator-lowering-fma.f64`
4 114×	`-lowering-.f32`
4 114×	`-lowering-.f64`
3 462×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	22	6
2	128	6
0	1139	4
0	25	108
1	77	108
2	168	108
3	371	108
4	587	108
5	718	108
6	723	108
0	723	81
0	16	39
1	103	37
2	831	37
0	8498	31

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 121 to 65 computations (46.3% saved)

preprocess67.0ms (1%)

Memory: 11.8MiB live, 131.2MiB allocated
Compiler: Compiled 114 to 52 computations (54.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	15
1	19	15
2	38	14
3	57	14
4	73	14
5	93	14
6	111	14
7	126	14
8	138	14
9	142	14
10	143	14
0	4	4
1	9	4
2	10	4
0	10	2

Iter	Nodes	Cost
0	8	15
1	19	15
2	38	14
3	57	14
4	73	14
5	93	14
6	111	14
7	126	14
8	138	14
9	142	14
10	143	14
0	4	4
1	9	4
2	10	4
0	10	2

analyze0.0ms (0%)

sample460.0ms (6.7%)

preprocess15.0ms (0.2%)

explain70.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize16.0ms (0.2%)

series1.0ms (0%)

rewrite100.0ms (1.5%)

simplify35.0ms (0.5%)

eval13.0ms (0.2%)

prune15.0ms (0.2%)

simplify519.0ms (7.6%)

localize82.0ms (1.2%)

series4.0ms (0.1%)

rewrite409.0ms (6%)

simplify544.0ms (7.9%)

eval190.0ms (2.8%)

prune390.0ms (5.7%)

simplify931.0ms (13.5%)

localize153.0ms (2.2%)

series8.0ms (0.1%)

rewrite361.0ms (5.3%)

simplify272.0ms (4%)

eval108.0ms (1.6%)

prune84.0ms (1.2%)

simplify405.0ms (5.9%)

localize137.0ms (2%)

series6.0ms (0.1%)

rewrite401.0ms (5.8%)

simplify349.0ms (5.1%)

eval95.0ms (1.4%)

prune67.0ms (1%)

regimes12.0ms (0.2%)

regimes32.0ms (0.5%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes28.0ms (0.4%)

regimes5.0ms (0.1%)

simplify7.0ms (0.1%)

soundness463.0ms (6.7%)

preprocess67.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	15
1	19	15
2	38	14
3	57	14
4	73	14
5	93	14
6	111	14
7	126	14
8	138	14
9	142	14
10	143	14
0	4	4
1	9	4
2	10	4
0	10	2