Details

analyze1.6s (21.9%)

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 (31.1%)

Results

1.8s	7995×	body	128	valid
212.0ms	604×	body	128	invalid
56.0ms	81×	body	1024	valid
47.0ms	110×	body	512	valid
15.0ms	69×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify39.0ms (0.5%)

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

3.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.8b	(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)

localize255.0ms (3.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 x y))
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	3.6b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series483.0ms (6.7%)

Counts

4 → 132

Calls

4 calls:

230.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
151.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
52.0ms	(tanh.f64 (/.f64 t y))
50.0ms	(tanh.f64 (/.f64 x y))

rewrite101.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`prod-diff_binary64`
190×	`egg-rr`
161×	`add-sqr-sqrt_binary64`
152×	`log1p-expm1-u_binary64`
152×	`expm1-log1p-u_binary64`

Counts

4 → 190

Calls

4 calls:

96.0ms	(tanh.f64 (/.f64 x y))
96.0ms	(tanh.f64 (/.f64 t y))
96.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
96.0ms	(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	47
1	289	47
2	4336	47
3	5512	47

simplify316.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
648×	`times-frac_binary64`
594×	`fma-neg_binary64`
349×	`cancel-sign-sub-inv_binary64`
318×	`sub-neg_binary64`

Counts

322 → 267

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	9459
1	617	8209
2	2088	7471
3	4686	7471
4	5092	7471

prune199.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	262	5	267
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	262	6	268

Error

0.0b

Counts

268 → 6

Alt Table

Status	Error	Program
	37.5b	(fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (.f64 (.f64 2 (sinh.f64 (/.f64 x y))) (/.f64 1 (.f64 2 (cosh.f64 (/.f64 x y)))))) x)
	36.2b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) 2)
▶	5.9b	(fma.f64 (*.f64 y z) (cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)) x)
	41.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
	27.5b	(+.f64 x (*.f64 z (-.f64 t x)))
✓	3.8b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

Compiler

Compiled 9797 to 3763 computations (61.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	0.1b	(pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)
✓	3.6b	(fma.f64 (*.f64 y z) (cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)) x)
✓	7.7b	(cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3))

series692.0ms (9.6%)

Counts

3 → 120

Calls

3 calls:

319.0ms

(pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)

219.0ms

(fma.f64 (*.f64 y z) (cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)) x)

153.0ms

(cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3))

rewrite98.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Counts

3 → 159

Calls

3 calls:

93.0ms

(pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)

93.0ms

(fma.f64 (*.f64 y z) (cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)) x)

93.0ms

(cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	52
1	334	52
2	4748	52
3	5865	52

simplify190.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

389×	`fma-def_binary64`
326×	`times-frac_binary64`
286×	`associate-/r*_binary64`
276×	`associate-/l*_binary64`
233×	`associate-r_binary64`

Counts

279 → 252

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	464	13904
1	1582	12847
2	5252	12847

prune368.0ms (5.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	378	0	378
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	378	6	384

Error

0.0b

Counts

384 → 6

Alt Table

Status	Error	Program
	37.5b	(fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (.f64 (.f64 2 (sinh.f64 (/.f64 x y))) (/.f64 1 (.f64 2 (cosh.f64 (/.f64 x y)))))) x)
	36.2b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) 2)
✓	5.9b	(fma.f64 (*.f64 y z) (cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)) x)
	41.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
▶	27.5b	(+.f64 x (*.f64 z (-.f64 t x)))
✓	3.8b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

Compiler

Compiled 20419 to 8813 computations (56.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series14.0ms (0.2%)

Counts

2 → 72

Calls

2 calls:

8.0ms	(+.f64 x (*.f64 z (-.f64 t x)))
6.0ms	(*.f64 z (-.f64 t x))

rewrite52.0ms (0.7%)

Algorithm

1×	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 → 57

Calls

2 calls:

51.0ms	(*.f64 z (-.f64 t x))
51.0ms	(+.f64 x (*.f64 z (-.f64 t x)))

Iterations

Useful iterations: 1 (0.0ms)

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

simplify40.0ms (0.6%)

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

129 → 69

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

prune44.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	69	6	75

Error

Counts

75 → 6

Alt Table

Status	Error	Program
▶	27.5b	(fma.f64 z (-.f64 t x) x)
	37.5b	(fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (.f64 (.f64 2 (sinh.f64 (/.f64 x y))) (/.f64 1 (.f64 2 (cosh.f64 (/.f64 x y)))))) x)
	36.2b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) 2)
✓	5.9b	(fma.f64 (*.f64 y z) (cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)) x)
	41.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
✓	3.8b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

Compiler

Compiled 1036 to 387 computations (62.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

10.0ms

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

rewrite40.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
69×	`add-sqr-sqrt_binary64`
64×	`add-log-exp_binary64`

Counts

1 → 24

Calls

1 calls:

39.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	130	8
2	1689	8
3	4956	8

simplify32.0ms (0.4%)

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

60 → 34

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

prune16.0ms (0.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	34	6	40

Error

Counts

40 → 6

Alt Table

Status	Error	Program
✓	27.5b	(fma.f64 z (-.f64 t x) x)
	37.5b	(fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (.f64 (.f64 2 (sinh.f64 (/.f64 x y))) (/.f64 1 (.f64 2 (cosh.f64 (/.f64 x y)))))) x)
	36.2b	(pow.f64 (sqrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) 2)
✓	5.9b	(fma.f64 (*.f64 y z) (cbrt.f64 (pow.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) 3)) x)
	41.0b	(cbrt.f64 (pow.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) 3))
✓	3.8b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

Compiler

Compiled 444 to 170 computations (61.7% saved)

regimes255.0ms (3.5%)

Accuracy

Total 1.2b remaining (85.7%)

Threshold costs 0b (0%)

Counts

34 → 3

Compiler

Compiled 2758 to 1791 computations (35.1% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

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	24	92
1	32	92
2	40	92
3	44	92
4	46	92
5	46	92

end106.0ms (1.5%)

Compiler: Compiled 250 to 122 computations (51.2% 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

analyze1.6s (21.9%)

sample2.2s (31.1%)

simplify39.0ms (0.5%)

prune3.0ms (0%)

localize255.0ms (3.5%)

series483.0ms (6.7%)

rewrite101.0ms (1.4%)

simplify316.0ms (4.4%)

prune199.0ms (2.8%)

localize14.0ms (0.2%)

series692.0ms (9.6%)

rewrite98.0ms (1.4%)

simplify190.0ms (2.6%)

prune368.0ms (5.1%)

localize4.0ms (0.1%)

series14.0ms (0.2%)

rewrite52.0ms (0.7%)

simplify40.0ms (0.6%)

prune44.0ms (0.6%)

localize4.0ms (0.1%)

series10.0ms (0.1%)

rewrite40.0ms (0.6%)

simplify32.0ms (0.4%)

prune16.0ms (0.2%)

regimes255.0ms (3.5%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end106.0ms (1.5%)

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