Details

analyze3.0s (39%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
10.1%	89.7%	0.2%	10
32%	67.8%	0.2%	11
39.4%	60.4%	0.2%	12
40.2%	59.6%	0.2%	13
47.5%	52.3%	0.2%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample2.2s (28.4%)

Results

1.9s	8055×	body	128	valid
107.0ms	571×	body	128	invalid
51.0ms	85×	body	1024	valid
31.0ms	65×	body	512	valid
15.0ms	51×	body	256	valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

509×	`fma-neg_binary64`
396×	`distribute-rgt-in_binary64`
366×	`distribute-lft-in_binary64`
289×	`fma-def_binary64`
260×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	55	21
2	153	21
3	362	21
4	1315	21
5	4639	21
6	5067	21

prune3.0ms (0%)

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

4.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.3b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

Compiler

Compiled 69 to 35 computations (49.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	3.9b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series288.0ms (3.8%)

Counts

2 → 72

Calls

2 calls:

231.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
56.0ms	(tanh.f64 (/.f64 t y))

rewrite72.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

569×	`prod-diff_binary64`
161×	`add-sqr-sqrt_binary64`
152×	`log1p-expm1-u_binary64`
152×	`expm1-log1p-u_binary64`
150×	`add-log-exp_binary64`

Counts

2 → 56

Calls

2 calls:

71.0ms	(tanh.f64 (/.f64 t y))
71.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	289	27
2	4336	27
3	5512	27
0	0	0
1	0	0

simplify141.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

553×	`times-frac_binary64`
492×	`fma-neg_binary64`
412×	`fma-def_binary64`
362×	`associate-/l*_binary64`
275×	`associate-/r*_binary64`

Counts

128 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	5421
1	433	5071
2	1465	4272
3	4744	4272
4	5118	4272

prune68.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	4	98

Error

0.3b

Counts

98 → 4

Alt Table

Status	Error	Program
✓	4.3b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
	45.4b	(sqrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2))
	47.0b	(-.f64 (+.f64 (fma.f64 z t x) (.f64 (/.f64 1/3 y) (-.f64 (/.f64 (.f64 z (pow.f64 x 3)) y) (/.f64 (.f64 z (pow.f64 t 3)) y)))) (.f64 x z))
▶	30.0b	(+.f64 x (*.f64 z (-.f64 t x)))

Compiler

Compiled 3269 to 1133 computations (65.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 z (-.f64 t x)))
✓	0.0b	(*.f64 z (-.f64 t x))

series14.0ms (0.2%)

Counts

2 → 72

Calls

2 calls:

7.0ms	(+.f64 x (*.f64 z (-.f64 t x)))
7.0ms	(*.f64 z (-.f64 t x))

rewrite68.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

901×	`log1p-expm1-u_binary64`
901×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
78×	`add-log-exp_binary64`
77×	`add-cube-cbrt_binary64`

Counts

2 → 56

Calls

2 calls:

66.0ms	(+.f64 x (*.f64 z (-.f64 t x)))
66.0ms	(*.f64 z (-.f64 t x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	158	15
2	2197	15
3	5428	15
0	0	0
1	0	0

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

274×	`fma-neg_binary64`
259×	`fma-def_binary64`
58×	`distribute-rgt-in_binary64`
38×	`cancel-sign-sub-inv_binary64`
36×	`unsub-neg_binary64`

Counts

128 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	585
1	62	558
2	113	558
3	194	504
4	358	504
5	564	504
6	642	504
7	666	504
8	623	504

prune34.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	69	3	72

Error

0.3b

Counts

72 → 3

Alt Table

Status	Error	Program
▶	30.0b	(fma.f64 (-.f64 t x) z x)
✓	4.3b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
	45.4b	(sqrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2))

Compiler

Compiled 914 to 308 computations (66.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (-.f64 t x) z x)

series7.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

7.0ms

(fma.f64 (-.f64 t x) z x)

rewrite46.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

682×	`log1p-expm1-u_binary64`
682×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
126×	`log1p-udef_binary64`
69×	`add-sqr-sqrt_binary64`

Counts

1 → 23

Calls

1 calls:

45.0ms

(fma.f64 (-.f64 t x) z x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	130	8
2	1683	8
3	5161	8
0	0	0
1	0	0

simplify35.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

275×	`fma-neg_binary64`
255×	`fma-def_binary64`
63×	`distribute-rgt-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
36×	`unsub-neg_binary64`

Counts

59 → 35

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	345
1	54	318
2	111	318
3	184	264
4	358	264
5	564	264
6	642	264
7	666	264
8	623	264

prune13.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	35	3	38

Error

0.3b

Counts

38 → 3

Alt Table

Status	Error	Program
✓	30.0b	(fma.f64 (-.f64 t x) z x)
✓	4.3b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
▶	45.4b	(sqrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2))

Compiler

Compiled 397 to 139 computations (65% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(tanh.f64 (/.f64 t y))
✓	0.2b	(pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2)
	3.9b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	22.8b	(sqrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2))

series650.0ms (8.5%)

Counts

2 → 96

Calls

2 calls:

419.0ms	(pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2)
231.0ms	(sqrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2))

rewrite83.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

569×	`prod-diff_binary64`
178×	`add-sqr-sqrt_binary64`
170×	`log1p-expm1-u_binary64`
170×	`expm1-log1p-u_binary64`
167×	`add-log-exp_binary64`

Counts

2 → 49

Calls

2 calls:

81.0ms	(pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2)
81.0ms	(sqrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	45
1	333	45
2	4682	45
3	5814	45
0	0	0
1	0	0

simplify351.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-def_binary64`
387×	`associate-/l*_binary64`
377×	`times-frac_binary64`
257×	`associate-/r*_binary64`
218×	`+-commutative_binary64`

Counts

145 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	553	20757
1	1821	18683
2	4947	18651
3	4978	18651

prune221.0ms (2.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	231	3	234

Error

0.3b

Counts

234 → 3

Alt Table

Status	Error	Program
✓	30.0b	(fma.f64 (-.f64 t x) z x)
✓	4.3b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	45.4b	(sqrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 2))

Compiler

Compiled 18692 to 6517 computations (65.1% saved)

regimes197.0ms (2.6%)

Accuracy

Total 2.2b remaining (89.4%)

Threshold costs 0b (0%)

Counts

32 → 2

Compiler

Compiled 2788 to 1711 computations (38.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	56
1	28	56
2	36	56
3	40	56
4	42	56
5	42	56

end68.0ms (0.9%)

Compiler: Compiled 131 to 67 computations (48.9% saved)

Iter	Nodes	Cost
0	23	585
1	62	558
2	113	558
3	194	504
4	358	504
5	564	504
6	642	504
7	666	504
8	623	504

Iter	Nodes	Cost
0	21	345
1	54	318
2	111	318
3	184	264
4	358	264
5	564	264
6	642	264
7	666	264
8	623	264

Iter	Nodes	Cost
0	23	585
1	62	558
2	113	558
3	194	504
4	358	504
5	564	504
6	642	504
7	666	504
8	623	504

Iter	Nodes	Cost
0	21	345
1	54	318
2	111	318
3	184	264
4	358	264
5	564	264
6	642	264
7	666	264
8	623	264

Details

analyze3.0s (39%)

sample2.2s (28.4%)

simplify43.0ms (0.6%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series288.0ms (3.8%)

rewrite72.0ms (0.9%)

simplify141.0ms (1.9%)

prune68.0ms (0.9%)

localize6.0ms (0.1%)

series14.0ms (0.2%)

rewrite68.0ms (0.9%)

simplify42.0ms (0.5%)

prune34.0ms (0.4%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite46.0ms (0.6%)

simplify35.0ms (0.5%)

prune13.0ms (0.2%)

localize13.0ms (0.2%)

series650.0ms (8.5%)

rewrite83.0ms (1.1%)

simplify351.0ms (4.6%)

prune221.0ms (2.9%)

regimes197.0ms (2.6%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end68.0ms (0.9%)

Profiling

Iter	Nodes	Cost
0	23	585
1	62	558
2	113	558
3	194	504
4	358	504
5	564	504
6	642	504
7	666	504
8	623	504

Iter	Nodes	Cost
0	21	345
1	54	318
2	111	318
3	184	264
4	358	264
5	564	264
6	642	264
7	666	264
8	623	264