Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample720.0ms (46.7%)

Results

708.0ms

8256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

preprocess45.0ms (2.9%)

Algorithm

2×	egg-herbie

Rules

492×	`fma-neg_binary64`
454×	`unsub-neg_binary64`
409×	`distribute-rgt-in_binary64`
370×	`fma-def_binary64`
360×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	14	10
2	21	10
3	32	10
4	49	10
5	77	8
6	131	8
7	335	8
8	686	8
9	1461	8
10	2785	8
11	4171	8
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 8 to 6 computations (25% saved)

simplify31.0ms (2%)

Algorithm

1×	egg-herbie

Rules

492×	`fma-neg_binary64`
454×	`unsub-neg_binary64`
409×	`distribute-rgt-in_binary64`
370×	`fma-def_binary64`
360×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	14	10
2	21	10
3	32	10
4	49	10
5	77	8
6	131	8
7	335	8
8	686	8
9	1461	8
10	2785	8
11	4171	8

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (0.4%)

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 -10 (fma.f64 x x -1))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 -10 (fma.f64 x x -1))

series3.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(/.f64 -10 (fma.f64 x x -1))	x	-inf
1.0ms	(/.f64 -10 (fma.f64 x x -1))	x	inf
1.0ms	(/.f64 -10 (fma.f64 x x -1))	x	0

rewrite31.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

549×	`pow1_binary64`
512×	`add-log-exp_binary64`
512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
503×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	122	8
2	1370	8

Stop Event

1×	node limit

Counts

1 → 20

simplify32.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-def_binary64`
413×	`unswap-sqr_binary64`
246×	`associate-l_binary64`
236×	`associate-/r*_binary64`
220×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	227
1	117	209
2	342	206
3	1127	203
4	4523	203

Stop Event

1×	node limit

Counts

32 → 35

prune24.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	28	7	35
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	8	36

Error

0.1b

Counts

36 → 8

Alt Table

Status	Error	Program
	20.7b	(exp.f64 (log.f64 (/.f64 -10 (fma.f64 x x -1))))
	20.8b	(expm1.f64 (log1p.f64 (/.f64 -10 (fma.f64 x x -1))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 -10 (fma.f64 x x -1)) 3))
	19.4b	(sqrt.f64 (/.f64 100 (pow.f64 (fma.f64 x x -1) 2)))
	0.5b	(pow.f64 (*.f64 (fma.f64 x x -1) -1/10) -1)
✓	0.3b	(/.f64 -10 (fma.f64 x x -1))
	1.4b	(*.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) 2))
▶	0.4b	(*.f64 -10 (/.f64 1 (fma.f64 x x -1)))

Compiler

Compiled 551 to 429 computations (22.1% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (fma.f64 x x -1))
✓	0.3b	(*.f64 -10 (/.f64 1 (fma.f64 x x -1)))

series5.0ms (0.4%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(*.f64 -10 (/.f64 1 (fma.f64 x x -1)))	x	-inf
1.0ms	(*.f64 -10 (/.f64 1 (fma.f64 x x -1)))	x	inf
1.0ms	(/.f64 1 (fma.f64 x x -1))	x	-inf
1.0ms	(/.f64 1 (fma.f64 x x -1))	x	inf
1.0ms	(*.f64 -10 (/.f64 1 (fma.f64 x x -1)))	x	0

rewrite35.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

637×	`pow1_binary64`
591×	`add-log-exp_binary64`
590×	`log1p-expm1-u_binary64`
590×	`expm1-log1p-u_binary64`
71×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	155	16
2	1641	16

Stop Event

1×	node limit

Counts

2 → 38

simplify25.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

394×	`fma-neg_binary64`
303×	`cancel-sign-sub-inv_binary64`
278×	`associate-l_binary64`
235×	`associate-/r*_binary64`
187×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	437
1	161	411
2	484	406
3	1539	406

Stop Event

1×	node limit

Counts

62 → 68

prune43.0ms (2.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	65	11	76

Error

0.0b

Counts

76 → 11

Alt Table

Status	Error	Program
	20.7b	(exp.f64 (log.f64 (/.f64 -10 (fma.f64 x x -1))))
	0.9b	(.f64 -10 (.f64 (cbrt.f64 (/.f64 1 (fma.f64 x x -1))) (cbrt.f64 (pow.f64 (fma.f64 x x -1) -2))))
	0.7b	(cbrt.f64 (pow.f64 (/.f64 -10 (fma.f64 x x -1)) 3))
	19.4b	(sqrt.f64 (*.f64 100 (pow.f64 (fma.f64 x x -1) -2)))
	19.4b	(sqrt.f64 (/.f64 100 (pow.f64 (fma.f64 x x -1) 2)))
	1.3b	(/.f64 (/.f64 -10 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (fma.f64 x x -1)))
▶	0.4b	(/.f64 1 (/.f64 (fma.f64 x x -1) -10))
✓	0.3b	(/.f64 -10 (fma.f64 x x -1))
	1.4b	(*.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) 2))
	0.7b	(*.f64 -10 (cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 x x -1)) 3)))
	44.7b	(*.f64 -10 (pow.f64 (pow.f64 (fma.f64 x x -1) -1/2) 2))

Compiler

Compiled 1060 to 834 computations (21.3% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (fma.f64 x x -1) -10)
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 x x -1) -10))

series12.0ms (0.8%)

Counts

2 → 24

Calls

6 calls:

8.0ms	(/.f64 1 (/.f64 (fma.f64 x x -1) -10))	x	-inf
1.0ms	(/.f64 1 (/.f64 (fma.f64 x x -1) -10))	x	inf
1.0ms	(/.f64 (fma.f64 x x -1) -10)	x	-inf
1.0ms	(/.f64 (fma.f64 x x -1) -10)	x	inf
1.0ms	(/.f64 1 (/.f64 (fma.f64 x x -1) -10))	x	0

rewrite48.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

693×	`pow1_binary64`
649×	`add-log-exp_binary64`
648×	`log1p-expm1-u_binary64`
648×	`expm1-log1p-u_binary64`
76×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	163	16
2	1827	16

Stop Event

1×	node limit

Counts

2 → 48

simplify35.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary64`
268×	`associate-l_binary64`
238×	`associate-/r*_binary64`
229×	`sub-neg_binary64`
209×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	332
1	128	314
2	368	293
3	1216	290
4	4721	290

Stop Event

1×	node limit

Counts

72 → 68

prune55.0ms (3.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	69	10	79

Error

0.0b

Counts

79 → 10

Alt Table

Status	Error	Program
	0.7b	(cbrt.f64 (pow.f64 (/.f64 -10 (fma.f64 x x -1)) 3))
	19.4b	(sqrt.f64 (*.f64 100 (pow.f64 (fma.f64 x x -1) -2)))
▶	0.5b	(/.f64 1 (*.f64 (fma.f64 x x -1) -1/10))
	0.8b	(.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) (cbrt.f64 (pow.f64 (.f64 (fma.f64 x x -1) -1/10) -2)))
	0.9b	(.f64 -10 (.f64 (cbrt.f64 (/.f64 1 (fma.f64 x x -1))) (cbrt.f64 (pow.f64 (fma.f64 x x -1) -2))))
✓	0.4b	(/.f64 1 (/.f64 (fma.f64 x x -1) -10))
✓	0.3b	(/.f64 -10 (fma.f64 x x -1))
	1.4b	(*.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) 2))
	0.7b	(*.f64 -10 (cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 x x -1)) 3)))
	44.7b	(*.f64 -10 (pow.f64 (pow.f64 (fma.f64 x x -1) -1/2) 2))

Compiler

Compiled 999 to 787 computations (21.2% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 (fma.f64 x x -1) -1/10))
✓	0.4b	(*.f64 (fma.f64 x x -1) -1/10)

series7.0ms (0.5%)

Counts

2 → 24

Calls

6 calls:

2.0ms	(/.f64 1 (*.f64 (fma.f64 x x -1) -1/10))	x	-inf
1.0ms	(/.f64 1 (*.f64 (fma.f64 x x -1) -1/10))	x	inf
1.0ms	(*.f64 (fma.f64 x x -1) -1/10)	x	inf
1.0ms	(*.f64 (fma.f64 x x -1) -1/10)	x	-inf
1.0ms	(/.f64 1 (*.f64 (fma.f64 x x -1) -1/10))	x	0

rewrite36.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

660×	`pow1_binary64`
614×	`add-log-exp_binary64`
613×	`log1p-expm1-u_binary64`
613×	`expm1-log1p-u_binary64`
72×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	155	16
2	1696	16

Stop Event

1×	node limit

Counts

2 → 44

simplify34.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-def_binary64`
269×	`associate-l_binary64`
238×	`associate-/r*_binary64`
229×	`sub-neg_binary64`
209×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	332
1	128	314
2	368	293
3	1209	290
4	4728	290

Stop Event

1×	node limit

Counts

68 → 64

prune34.0ms (2.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	64	10	74

Error

0.0b

Counts

74 → 10

Alt Table

Status	Error	Program
	0.7b	(cbrt.f64 (pow.f64 (/.f64 -10 (fma.f64 x x -1)) 3))
	19.4b	(sqrt.f64 (*.f64 100 (pow.f64 (fma.f64 x x -1) -2)))
✓	0.5b	(/.f64 1 (*.f64 (fma.f64 x x -1) -1/10))
	0.8b	(.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) (cbrt.f64 (pow.f64 (.f64 (fma.f64 x x -1) -1/10) -2)))
	0.9b	(.f64 -10 (.f64 (cbrt.f64 (/.f64 1 (fma.f64 x x -1))) (cbrt.f64 (pow.f64 (fma.f64 x x -1) -2))))
✓	0.4b	(/.f64 1 (/.f64 (fma.f64 x x -1) -10))
✓	0.3b	(/.f64 -10 (fma.f64 x x -1))
	1.4b	(*.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (/.f64 -10 (fma.f64 x x -1))) 2))
	0.7b	(*.f64 -10 (cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 x x -1)) 3)))
	44.7b	(*.f64 -10 (pow.f64 (pow.f64 (fma.f64 x x -1) -1/2) 2))

Compiler

Compiled 835 to 661 computations (20.8% saved)

regimes142.0ms (9.2%)

Accuracy

Total 0.2b remaining (90.8%)

Threshold costs 0.2b (90.8%)

Counts

36 → 1

Compiler

Compiled 1668 to 1318 computations (21% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8

Stop Event

1×

saturated

end118.0ms (7.6%)

Stop Event

1×

fuel

Compiler

Compiled 136 to 106 computations (22.1% saved)

Details

analyze3.0ms (0.2%)

sample720.0ms (46.7%)

preprocess45.0ms (2.9%)

simplify31.0ms (2%)

prune6.0ms (0.4%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite31.0ms (2%)

simplify32.0ms (2.1%)

prune24.0ms (1.6%)

localize4.0ms (0.3%)

series5.0ms (0.4%)

rewrite35.0ms (2.2%)

simplify25.0ms (1.6%)

prune43.0ms (2.8%)

localize4.0ms (0.3%)

series12.0ms (0.8%)

rewrite48.0ms (3.1%)

simplify35.0ms (2.3%)

prune55.0ms (3.6%)

localize5.0ms (0.3%)

series7.0ms (0.5%)

rewrite36.0ms (2.3%)

simplify34.0ms (2.2%)

prune34.0ms (2.2%)

regimes142.0ms (9.2%)

simplify2.0ms (0.1%)

end118.0ms (7.6%)

Profiling