Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50%	0.4%	49.6%	10
50.2%	0.2%	49.6%	11
50.2%	0.1%	49.7%	12
50.2%	0%	49.8%	13
50.2%	0%	49.8%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample896.0ms (50.3%)

Results

830.0ms	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify43.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

668×	`div-sub_binary64`
499×	`fma-def_binary64`
417×	`times-frac_binary64`
411×	`associate-/l*_binary64`
366×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	19	9
2	45	9
3	89	7
4	191	7
5	438	7
6	1294	7
7	3635	7
8	5317	7

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 25 to 17 computations (32% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 x x -1))

series2.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

2.0ms

(exp.f64 (fma.f64 x x -1))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`exp-prod_binary64`
2×	`add-log-exp_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 14

Calls

1 calls:

1.0ms

(exp.f64 (fma.f64 x x -1))

simplify56.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

431×	`fma-def_binary64`
418×	`exp-sum_binary64`
378×	`associate-l_binary64`
330×	`unswap-sqr_binary64`
324×	`distribute-lft-out_binary64`

Counts

18 → 23

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	221
1	84	206
2	178	190
3	528	183
4	1777	183
5	4482	183
6	5315	183

prune18.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	2	24

Error

0.0b

Counts

24 → 2

Alt Table

Status	Error	Program
	0.0b	(pow.f64 (E.f64) (fma.f64 x x -1))
▶	0.0b	(.f64 (exp.f64 (.f64 x x)) (exp.f64 -1))

Compiler

Compiled 280 to 209 computations (25.4% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (exp.f64 (.f64 x x)) (exp.f64 -1))
✓	0.0b	(exp.f64 (*.f64 x x))

series7.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

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

rewrite7.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`pow1_binary64`

Counts

2 → 32

Calls

2 calls:

5.0ms	(.f64 (exp.f64 (.f64 x x)) (exp.f64 -1))
1.0ms	(exp.f64 (*.f64 x x))

simplify67.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

839×	`fma-def_binary64`
478×	`distribute-rgt-in_binary64`
436×	`unswap-sqr_binary64`
393×	`distribute-lft-in_binary64`
249×	`exp-sum_binary64`

Counts

56 → 58

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	67	564
1	152	511
2	383	495
3	1042	490
4	2439	490
5	4633	489
6	4916	489

prune33.0ms (1.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	58	2	60

Error

0.0b

Counts

60 → 2

Alt Table

Status	Error	Program
	0.0b	(exp.f64 (+.f64 (*.f64 x x) -1))
▶	0.0b	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))

Compiler

Compiled 719 to 436 computations (39.4% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 x) x)
✓	0.0b	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))

series8.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
2.0ms	(pow.f64 (exp.f64 x) x)

rewrite9.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-l_binary64`
7×	`unpow-prod-down_binary64`

Counts

2 → 49

Calls

2 calls:

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

simplify70.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

458×	`distribute-rgt-in_binary64`
413×	`distribute-lft-in_binary64`
393×	`associate-l_binary64`
328×	`associate-r_binary64`
324×	`prod-exp_binary64`

Counts

73 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	94	814
1	207	728
2	546	712
3	1685	705
4	4496	700
5	5060	700

prune59.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	90	3	93

Error

0.0b

Counts

93 → 3

Alt Table

Status	Error	Program
	0.0b	(exp.f64 (+.f64 (*.f64 x x) -1))
✓	0.0b	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
▶	0.0b	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))) (sqrt.f64 (*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))))

Compiler

Compiled 1174 to 673 computations (42.7% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1)))
	0.0b	(pow.f64 (exp.f64 x) x)
	0.0b	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
✓	0.0b	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))) (sqrt.f64 (*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))))

series14.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(sqrt.f64 (*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1)))
6.0ms	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))) (sqrt.f64 (*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))))

rewrite19.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`pow1_binary64`
9×	`sqrt-pow1_binary64`
9×	`pow1/2_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 calls:

11.0ms	(.f64 (sqrt.f64 (.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))) (sqrt.f64 (*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))))
4.0ms	(sqrt.f64 (*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1)))

simplify87.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-def_binary64`
748×	`unswap-sqr_binary64`
586×	`associate-r_binary64`
367×	`prod-exp_binary64`
301×	`exp-prod_binary64`

Counts

76 → 94

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	83	1103
1	175	813
2	550	761
3	1700	712
4	3773	693
5	4578	693
6	5137	693

prune229.0ms (12.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	304	1	305
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	306	2	308

Error

Counts

308 → 2

Alt Table

Status	Error	Program
	0.0b	(sqrt.f64 (pow.f64 (exp.f64 2) (fma.f64 x x -1)))
✓	0.0b	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))

Compiler

Compiled 6542 to 3878 computations (40.7% saved)

regimes76.0ms (4.2%)

Accuracy

Total 0.0b remaining (54.1%)

Threshold costs 0.0b (54.1%)

Counts

16 → 1

Compiler

Compiled 843 to 637 computations (24.4% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end46.0ms (2.6%)

Compiler: Compiled 33 to 25 computations (24.2% saved)

Details

analyze4.0ms (0.2%)

sample896.0ms (50.3%)

simplify43.0ms (2.4%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite2.0ms (0.1%)

simplify56.0ms (3.2%)

prune18.0ms (1%)

localize6.0ms (0.4%)

series7.0ms (0.4%)

rewrite7.0ms (0.4%)

simplify67.0ms (3.8%)

prune33.0ms (1.9%)

localize5.0ms (0.3%)

series8.0ms (0.5%)

rewrite9.0ms (0.5%)

simplify70.0ms (3.9%)

prune59.0ms (3.3%)

localize7.0ms (0.4%)

series14.0ms (0.8%)

rewrite19.0ms (1.1%)

simplify87.0ms (4.9%)

prune229.0ms (12.8%)

regimes76.0ms (4.2%)

simplify3.0ms (0.2%)

end46.0ms (2.6%)

Profiling