Details

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample763.0ms (54.8%)

Results

452.0ms	4148×	body	256	valid
299.0ms	4108×	body	256	infinite

Bogosity

preprocess61.0ms (4.4%)

Algorithm

2×	egg-herbie

Rules

1788×	`fma-def`
1314×	`div-sub`
834×	`times-frac`
716×	`associate-l`
696×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	21	17
2	50	17
3	114	13
4	240	13
5	536	13
6	1626	13
7	5506	13
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Outputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify57.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1788×	`fma-def`
1314×	`div-sub`
834×	`times-frac`
716×	`associate-l`
696×	`associate-/r*`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	21	17
2	50	17
3	114	13
4	240	13
5	536	13
6	1626	13
7	5506	13

Stop Event

1×	node limit

Counts

1 → 4

Calls

Call 1

Inputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Outputs
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (fma.f64 x x -1))

eval1.0ms (0.1%)

Compiler: Compiled 25 to 15 computations (40% saved)

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	4	1	5

Accurracy

100.0%

Counts

5 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(exp.f64 (+.f64 (*.f64 x x) -1))
▶	100.0%	(exp.f64 (+.f64 (*.f64 x x) -1))

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize26.0ms (1.9%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(exp.f64 (+.f64 (*.f64 x x) -1))

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(exp.f64 (+.f64 (*.f64 x x) -1))
0.0ms	x	@	inf	(exp.f64 (+.f64 (*.f64 x x) -1))
0.0ms	x	@	-inf	(exp.f64 (+.f64 (*.f64 x x) -1))

rewrite73.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1590×	`pow1`
1468×	`add-exp-log`
1468×	`log1p-expm1-u`
1468×	`expm1-log1p-u`
1440×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	169	13
2	2030	13

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(exp.f64 (+.f64 (*.f64 x x) -1))

Outputs
(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
(-.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)
(*.f64 (exp.f64 (fma.f64 x x -1)) 1)
(*.f64 1 (exp.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))
(*.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
(*.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 1)
(pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)
(pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)
(pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(pow.f64 (exp.f64 1) (fma.f64 x x -1))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
(sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))
(log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))
(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))

simplify66.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1218×	`fma-def`
1106×	`times-frac`
620×	`associate-r`
556×	`associate-l`
548×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	598
1	158	590
2	460	566
3	2454	552
4	6111	552

Stop Event

1×	node limit

Counts

34 → 39

Calls

Call 1

Inputs
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
(-.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)
(*.f64 (exp.f64 (fma.f64 x x -1)) 1)
(*.f64 1 (exp.f64 (fma.f64 x x -1)))
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))
(*.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
(*.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 1)
(pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)
(pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)
(pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(pow.f64 (exp.f64 1) (fma.f64 x x -1))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
(sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))
(log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))
(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
(log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))

Outputs
(exp.f64 -1)
(+.f64 (*.f64 (exp.f64 -1) (pow.f64 x 2)) (exp.f64 -1))
(fma.f64 (exp.f64 -1) (*.f64 x x) (exp.f64 -1))
(*.f64 (exp.f64 -1) (fma.f64 x x 1))
(+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)))))
(+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))
(fma.f64 (exp.f64 -1) (.f64 x x) (fma.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)) (exp.f64 -1)))
(.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (.f64 1/2 (pow.f64 x 4))))
(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
(+.f64 (.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6))) (+.f64 (.f64 (exp.f64 -1) (pow.f64 x 2)) (+.f64 (exp.f64 -1) (.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4))))))
(fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (+.f64 (fma.f64 (exp.f64 -1) (.f64 x x) (exp.f64 -1)) (.f64 1/2 (.f64 (exp.f64 -1) (pow.f64 x 4)))))
(fma.f64 1/6 (.f64 (exp.f64 -1) (pow.f64 x 6)) (fma.f64 (exp.f64 -1) (.f64 x x) (fma.f64 1/2 (*.f64 (exp.f64 -1) (pow.f64 x 4)) (exp.f64 -1))))
(fma.f64 (exp.f64 -1) (.f64 1/6 (pow.f64 x 6)) (.f64 (exp.f64 -1) (+.f64 (fma.f64 x x 1) (*.f64 1/2 (pow.f64 x 4)))))
(.f64 (exp.f64 -1) (+.f64 (.f64 1/2 (pow.f64 x 4)) (fma.f64 1/6 (pow.f64 x 6) (fma.f64 x x 1))))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(exp.f64 (-.f64 (pow.f64 x 2) 1))
(exp.f64 (fma.f64 x x -1))
(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
(exp.f64 (fma.f64 x x -1))
(-.f64 (+.f64 1 (exp.f64 (fma.f64 x x -1))) 1)
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 (fma.f64 x x -1)) 1)
(exp.f64 (fma.f64 x x -1))
(*.f64 1 (exp.f64 (fma.f64 x x -1)))
(exp.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
(exp.f64 (fma.f64 x x -1))
(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
(exp.f64 (fma.f64 x x -1))
(*.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2))
(exp.f64 (fma.f64 x x -1))
(*.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 2) (cbrt.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))
(*.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) (sqrt.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 (fma.f64 x x -1)) 1)
(exp.f64 (fma.f64 x x -1))
(pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1))) 3)
(exp.f64 (fma.f64 x x -1))
(pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3) 1/3)
(exp.f64 (fma.f64 x x -1))
(pow.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1))) 2)
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))
(pow.f64 (exp.f64 (+.f64 x 1)) (+.f64 x -1))
(exp.f64 (fma.f64 x x -1))
(pow.f64 (exp.f64 1) (fma.f64 x x -1))
(pow.f64 (E.f64) (fma.f64 x x -1))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
(sqrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2))
(exp.f64 (fma.f64 x x -1))
(log.f64 (exp.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))
(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 3))
(exp.f64 (fma.f64 x x -1))
(expm1.f64 (log1p.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))
(log1p.f64 (expm1.f64 (exp.f64 (fma.f64 x x -1))))
(exp.f64 (fma.f64 x x -1))

eval10.0ms (0.7%)

Compiler: Compiled 432 to 329 computations (23.8% saved)

prune7.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Accurracy

100.0%

Counts

40 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
✓	100.0%	(exp.f64 (+.f64 (*.f64 x x) -1))
▶	55.0%	(exp.f64 -1)
▶	100.0%	(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
✓	100.0%	(exp.f64 (+.f64 (*.f64 x x) -1))
▶	55.0%	(exp.f64 -1)

Compiler

Compiled 36 to 28 computations (22.2% saved)

localize68.0ms (4.9%)

Compiler: Compiled 26 to 19 computations (26.9% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	1	1
Total	3	3

Accurracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
✓	100.0%	(exp.f64 (+.f64 (*.f64 x x) -1))
✓	55.0%	(exp.f64 -1)

Compiler

Compiled 41 to 30 computations (26.8% saved)

regimes14.0ms (1%)

Counts

4 → 1

Calls

Call 1

Inputs
(exp.f64 -1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
(+.f64 1 (expm1.f64 (fma.f64 x x -1)))

Outputs
(+.f64 1 (expm1.f64 (fma.f64 x x -1)))

Calls

5 calls:

4.0ms	x
3.0ms	(neg.f64 (-.f64 1 (*.f64 x x)))
3.0ms	(*.f64 x x)
2.0ms	(-.f64 1 (*.f64 x x))
2.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
100.0%	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
100.0%	1	`(-.f64 1 (*.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 50 to 34 computations (32% saved)

regimes16.0ms (1.2%)

Counts

3 → 1

Calls

Call 1

Inputs
(exp.f64 -1)
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))

Outputs
(exp.f64 (+.f64 (*.f64 x x) -1))

Calls

5 calls:

5.0ms	(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))
3.0ms	x
3.0ms	(*.f64 x x)
2.0ms	(-.f64 1 (*.f64 x x))
2.0ms	(neg.f64 (-.f64 1 (*.f64 x x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(exp.f64 (neg.f64 (-.f64 1 (*.f64 x x))))`
100.0%	1	`(neg.f64 (-.f64 1 (*.f64 x x)))`
100.0%	1	`(-.f64 1 (*.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 43 to 29 computations (32.6% saved)

regimes3.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(exp.f64 -1)

Outputs
(exp.f64 -1)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
55.0%	1	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	18	41

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 -1)

Outputs
(+.f64 1 (expm1.f64 (fma.f64 x x -1)))
(exp.f64 (+.f64 (*.f64 x x) -1))
(exp.f64 (+.f64 -1 (*.f64 x x)))
(exp.f64 -1)

Compiler

Compiled 18 to 14 computations (22.2% saved)

soundness184.0ms (13.2%)

Rules

1788×	`fma-def`
1590×	`pow1`
1468×	`add-exp-log`
1468×	`log1p-expm1-u`
1468×	`expm1-log1p-u`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	21	17
2	50	17
3	114	13
4	240	13
5	536	13
6	1626	13
7	5506	13
0	8	13
1	169	13
2	2030	13

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 76 to 49 computations (35.5% saved)

end33.0ms (2.4%)

Compiler: Compiled 48 to 36 computations (25% saved)

exp neg sub

Details

analyze0.0ms (0%)

sample763.0ms (54.8%)

preprocess61.0ms (4.4%)

simplify57.0ms (4.1%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

localize26.0ms (1.9%)

series1.0ms (0%)

rewrite73.0ms (5.2%)

simplify66.0ms (4.7%)

eval10.0ms (0.7%)

prune7.0ms (0.5%)

localize68.0ms (4.9%)

eval0.0ms (0%)

prune2.0ms (0.2%)

regimes14.0ms (1%)

regimes16.0ms (1.2%)

regimes3.0ms (0.2%)

simplify4.0ms (0.3%)

soundness184.0ms (13.2%)

end33.0ms (2.4%)

Profiling