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)

sample1.0s (41.5%)

Results

953.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify44.0ms (1.8%)

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

prune2.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(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
✓	0.1b	(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))

rewrite75.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

646×	`log1p-udef_binary64`
361×	`log1p-expm1-u_binary64`
361×	`expm1-log1p-u_binary64`
327×	`add-log-exp_binary64`
317×	`pow1_binary64`

Counts

1 → 50

Calls

1 calls:

74.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	90	7
2	946	7
3	4700	7
4	5737	7
0	0	0
1	0	0

simplify69.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

724×	`distribute-lft-out_binary64`
546×	`associate-+l+_binary64`
480×	`*-commutative_binary64`
472×	`distribute-rgt-in_binary64`
380×	`fma-def_binary64`

Counts

54 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	81
1	55	79
2	130	63
3	383	56
4	1301	56
5	2119	56
6	2598	56
7	2906	56
8	3888	56
9	5066	56

prune39.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	3	58

Error

0.0b

Counts

58 → 3

Alt Table

Status	Error	Program
	0.1b	(pow.f64 (E.f64) (fma.f64 x x -1))
▶	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
✓	0.1b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 768 to 563 computations (26.7% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite48.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

528×	`log1p-expm1-u_binary64`
528×	`expm1-log1p-u_binary64`
435×	`unpow-prod-down_binary64`
285×	`log-prod_binary64`
163×	`pow2_binary64`

Counts

2 → 66

Calls

2 calls:

46.0ms	(pow.f64 (exp.f64 x) x)
46.0ms	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	130	15
2	1402	13
3	5211	13
0	0	0
1	0	0

simplify89.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

543×	`*-commutative_binary64`
512×	`fma-def_binary64`
458×	`distribute-rgt-out_binary64`
437×	`associate-l_binary64`
364×	`distribute-rgt-in_binary64`

Counts

90 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	244
1	84	216
2	195	200
3	523	195
4	1633	195
5	2742	195
6	3413	195
7	4885	195
8	4995	195
9	4908	195

prune103.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	81	4	85

Error

0.0b

Counts

85 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 (exp.f64 -1) (.f64 (pow.f64 (*.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 x 2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (/.f64 x 2))))
▶	0.1b	(pow.f64 (E.f64) (fma.f64 x x -1))
✓	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
✓	0.1b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 1222 to 767 computations (37.2% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (E.f64) (fma.f64 x x -1))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(pow.f64 (E.f64) (fma.f64 x x -1))

rewrite71.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

867×	`log1p-udef_binary64`
467×	`log1p-expm1-u_binary64`
467×	`expm1-log1p-u_binary64`
383×	`unpow-prod-down_binary64`
223×	`log-prod_binary64`

Counts

1 → 40

Calls

1 calls:

70.0ms

(pow.f64 (E.f64) (fma.f64 x x -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	119	7
2	1211	7
3	4832	7
4	6266	7
0	0	0
1	0	0

simplify64.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

726×	`distribute-lft-out_binary64`
490×	`*-commutative_binary64`
385×	`fma-def_binary64`
355×	`distribute-rgt-out_binary64`
350×	`associate-l_binary64`

Counts

52 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	137
1	58	135
2	139	119
3	406	112
4	1369	112
5	2333	112
6	3367	112
7	4551	112
8	4913	112

prune38.0ms (1.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	47	4	51

Error

0.0b

Counts

51 → 4

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (exp.f64 -1) (.f64 (pow.f64 (*.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 x 2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (/.f64 x 2))))
✓	0.1b	(pow.f64 (E.f64) (fma.f64 x x -1))
✓	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
✓	0.1b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 705 to 525 computations (25.5% saved)

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (cbrt.f64 (exp.f64 x)) 2)
✓	0.0b	(.f64 (exp.f64 -1) (.f64 (pow.f64 (*.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 x 2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (/.f64 x 2))))
✓	0.0b	(cbrt.f64 (exp.f64 x))
✓	0.0b	(.f64 (pow.f64 (.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 x 2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (/.f64 x 2)))

series297.0ms (12.1%)

Counts

4 → 48

Calls

4 calls:

135.0ms	(pow.f64 (cbrt.f64 (exp.f64 x)) 2)
132.0ms	(cbrt.f64 (exp.f64 x))
20.0ms	(.f64 (exp.f64 -1) (.f64 (pow.f64 (*.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 x 2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (/.f64 x 2))))
10.0ms	(.f64 (pow.f64 (.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 x 2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (/.f64 x 2)))

rewrite73.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

666×	`log-prod_binary64`
235×	`log-pow_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`

Counts

4 → 89

Calls

4 calls:

71.0ms	(pow.f64 (cbrt.f64 (exp.f64 x)) 2)
71.0ms	(.f64 (exp.f64 -1) (.f64 (pow.f64 (*.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 x 2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (/.f64 x 2))))
71.0ms	(cbrt.f64 (exp.f64 x))
71.0ms	(.f64 (pow.f64 (.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 x 2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (/.f64 x 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	70
1	288	40
2	3134	35
3	5266	35
0	0	0
1	0	0

simplify70.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

589×	`distribute-rgt-out_binary64`
379×	`*-commutative_binary64`
339×	`associate-/l*_binary64`
308×	`fma-def_binary64`
253×	`associate-+l+_binary64`

Counts

137 → 121

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	74	898
1	199	626
2	480	492
3	1440	421
4	2905	373
5	4800	373
6	4931	373

prune153.0ms (6.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	154	4	158

Error

0.0b

Counts

158 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (exp.f64 -1) (.f64 (pow.f64 (*.f64 (exp.f64 x) (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (/.f64 x 2)) (pow.f64 (cbrt.f64 (exp.f64 x)) (/.f64 x 2))))
✓	0.1b	(pow.f64 (E.f64) (fma.f64 x x -1))
✓	0.0b	(*.f64 (exp.f64 -1) (pow.f64 (exp.f64 x) x))
✓	0.1b	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 3470 to 2229 computations (35.8% saved)

regimes83.0ms (3.4%)

Accuracy

Total 0.0b remaining (71.5%)

Threshold costs 0.0b (71.5%)

Counts

17 → 1

Compiler

Compiled 1228 to 966 computations (21.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	11	17
2	11	17

end67.0ms (2.7%)

Compiler: Compiled 69 to 51 computations (26.1% saved)

Details

analyze4.0ms (0.2%)

sample1.0s (41.5%)

simplify44.0ms (1.8%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite75.0ms (3.1%)

simplify69.0ms (2.8%)

prune39.0ms (1.6%)

localize7.0ms (0.3%)

series7.0ms (0.3%)

rewrite48.0ms (1.9%)

simplify89.0ms (3.6%)

prune103.0ms (4.2%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite71.0ms (2.9%)

simplify64.0ms (2.6%)

prune38.0ms (1.6%)

localize15.0ms (0.6%)

series297.0ms (12.1%)

rewrite73.0ms (3%)

simplify70.0ms (2.9%)

prune153.0ms (6.2%)

regimes83.0ms (3.4%)

simplify2.0ms (0.1%)

end67.0ms (2.7%)

Profiling