Details

analyze1.2s (4.7%)

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
7.8%	92%	0.2%	8
7.8%	92%	0.2%	9
10.9%	88.9%	0.2%	10
34.7%	65.1%	0.2%	11
43.1%	56.7%	0.2%	12
44.2%	55.7%	0.2%	13
49.5%	50.3%	0.2%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample34.0ms (0.1%)

Algorithm

1×

intervals

Results

16.0ms	250×	body	128	valid
1.0ms	15×	body	128	invalid
1.0ms	3×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 43 to 29 computations (32.6% saved)

simplify41.0ms (0.2%)

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

4.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.7b	(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)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	0.0b	(tanh.f64 (/.f64 x y))
✓	4.4b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series818.0ms (3.1%)

Counts

3 → 96

Calls

3 calls:

594.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
114.0ms	(tanh.f64 (/.f64 x y))
108.0ms	(tanh.f64 (/.f64 t y))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`
3×	`add-exp-log_binary64`

Counts

3 → 34

Calls

3 calls:

2.0ms	(tanh.f64 (/.f64 x y))
2.0ms	(tanh.f64 (/.f64 t y))
1.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

simplify248.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64`
501×	`fma-neg_binary64`
469×	`fma-def_binary64`
285×	`cancel-sign-sub-inv_binary64`
217×	`sub-neg_binary64`

Counts

130 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	6111
1	577	5584
2	1902	4863
3	4810	4863
4	5177	4863

prune125.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Error

Counts

92 → 4

Alt Table

Status	Error	Program
▶	4.8b	(fma.f64 (.f64 y z) (-.f64 (.f64 (*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (tanh.f64 (/.f64 x y))) x)
	19.7b	(fma.f64 (.f64 y z) (-.f64 (/.f64 (expm1.f64 (.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y))) x)
	5.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	29.2b	(+.f64 x (*.f64 z (-.f64 t x)))

Compiler

Compiled 3243 to 1132 computations (65.1% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y))))
✓	0.2b	(*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y))))
✓	4.4b	(fma.f64 (.f64 y z) (-.f64 (.f64 (*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (tanh.f64 (/.f64 x y))) x)
✓	7.0b	(cbrt.f64 (tanh.f64 (/.f64 t y)))

series3.1s (11.6%)

Counts

4 → 120

Calls

4 calls:

1.5s	(*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y))))
1.3s	(cbrt.f64 (tanh.f64 (/.f64 t y)))
267.0ms	(fma.f64 (.f64 y z) (-.f64 (.f64 (*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (tanh.f64 (/.f64 x y))) x)
61.0ms	(.f64 (.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y))))

rewrite52.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`cbrt-div_binary64`
90×	`frac-times_binary64`
57×	`tanh-def-a_binary64`
57×	`tanh-def-b_binary64`
57×	`tanh-def-c_binary64`

Counts

4 → 184

Calls

4 calls:

14.0ms	(.f64 (.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y))))
8.0ms	(*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y))))
2.0ms	(cbrt.f64 (tanh.f64 (/.f64 t y)))
0.0ms	(fma.f64 (.f64 y z) (-.f64 (.f64 (*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (tanh.f64 (/.f64 x y))) x)

simplify323.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary64`
274×	`sub-neg_binary64`
271×	`associate-l_binary64`
245×	`fma-neg_binary64`
213×	`associate-r_binary64`

Counts

304 → 340

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	490	14612
1	1119	13089
2	3536	12512
3	4954	12512
4	4888	12512

prune358.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	426	0	426
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	426	4	430

Error

Counts

430 → 4

Alt Table

Status	Error	Program
✓	4.8b	(fma.f64 (.f64 y z) (-.f64 (.f64 (*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (tanh.f64 (/.f64 x y))) x)
	19.7b	(fma.f64 (.f64 y z) (-.f64 (/.f64 (expm1.f64 (.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y))) x)
▶	5.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	29.2b	(+.f64 x (*.f64 z (-.f64 t x)))

Compiler

Compiled 20159 to 7024 computations (65.2% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
✓	0.5b	(cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))
	4.4b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series14.2s (53.1%)

Counts

3 → 144

Calls

3 calls:

9.9s

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

4.0s

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

249.0ms

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

rewrite40.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

12.0ms

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

8.0ms

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

1.0ms

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

simplify1.2s (4.4%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
259×	`times-frac_binary64`
70×	`sub-neg_binary64`
36×	`unpow1/3_binary64`
15×	`unpow2_binary64`

Counts

237 → 257

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3399	130947
1	5047	130947

prune2.3s (8.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	548	0	548
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	548	4	552

Error

Counts

552 → 4

Alt Table

Status	Error	Program
✓	4.8b	(fma.f64 (.f64 y z) (-.f64 (.f64 (*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (tanh.f64 (/.f64 x y))) x)
▶	19.7b	(fma.f64 (.f64 y z) (-.f64 (/.f64 (expm1.f64 (.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y))) x)
✓	5.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	29.2b	(+.f64 x (*.f64 z (-.f64 t x)))

Compiler

Compiled 233388 to 75830 computations (67.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(tanh.f64 (/.f64 x y))
✓	0.2b	(-.f64 (/.f64 (expm1.f64 (*.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y)))
✓	0.3b	(/.f64 (expm1.f64 (*.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2)))
✓	4.4b	(fma.f64 (.f64 y z) (-.f64 (/.f64 (expm1.f64 (.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y))) x)

series536.0ms (2%)

Counts

3 → 108

Calls

3 calls:

277.0ms

(fma.f64 (*.f64 y z) (-.f64 (/.f64 (expm1.f64 (*.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y))) x)

191.0ms

(-.f64 (/.f64 (expm1.f64 (*.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y)))

68.0ms

(/.f64 (expm1.f64 (*.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2)))

rewrite39.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`*-un-lft-identity_binary64`
68×	`add-sqr-sqrt_binary64`
63×	`add-cube-cbrt_binary64`
61×	`times-frac_binary64`
54×	`prod-diff_binary64`

Counts

3 → 141

Calls

3 calls:

12.0ms

(-.f64 (/.f64 (expm1.f64 (*.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y)))

6.0ms

(/.f64 (expm1.f64 (*.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2)))

0.0ms

(fma.f64 (*.f64 y z) (-.f64 (/.f64 (expm1.f64 (*.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y))) x)

simplify247.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

942×	`times-frac_binary64`
229×	`fma-neg_binary64`
177×	`fma-def_binary64`
176×	`+-commutative_binary64`
143×	`associate--l+_binary64`

Counts

249 → 249

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	374	15756
1	983	12285
2	3326	12102
3	5190	12102

prune257.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	273	4	277

Error

Counts

277 → 4

Alt Table

Status	Error	Program
✓	4.8b	(fma.f64 (.f64 y z) (-.f64 (.f64 (*.f64 (cbrt.f64 (tanh.f64 (/.f64 t y))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (cbrt.f64 (tanh.f64 (/.f64 t y)))) (tanh.f64 (/.f64 x y))) x)
✓	19.7b	(fma.f64 (.f64 y z) (-.f64 (/.f64 (expm1.f64 (.f64 (/.f64 t y) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) 2))) (tanh.f64 (/.f64 x y))) x)
✓	5.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
	29.2b	(+.f64 x (*.f64 z (-.f64 t x)))

Compiler

Compiled 13008 to 5701 computations (56.2% saved)

regimes456.0ms (1.7%)

Accuracy

Total 0.6b remaining (76.2%)

Threshold costs 0.6b (76.2%)

Counts

69 → 3

Compiler

Compiled 9058 to 5331 computations (41.1% saved)

bsearch3.0ms (0%)

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

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	89
1	41	89
2	48	89
3	52	89
4	54	89
5	53	89

end1.0ms (0%)

Compiler: Compiled 62 to 23 computations (62.9% saved)

sample977.0ms (3.7%)

Algorithm

1×

intervals

Results

501.0ms	7781×	body	128	valid
38.0ms	556×	body	128	invalid
18.0ms	72×	body	1024	valid
16.0ms	94×	body	512	valid
6.0ms	53×	body	256	valid

Compiler

Compiled 208 to 94 computations (54.8% saved)

Details

analyze1.2s (4.7%)

sample34.0ms (0.1%)

simplify41.0ms (0.2%)

prune3.0ms (0%)

localize10.0ms (0%)

series818.0ms (3.1%)

rewrite7.0ms (0%)

simplify248.0ms (0.9%)

prune125.0ms (0.5%)

localize34.0ms (0.1%)

series3.1s (11.6%)

rewrite52.0ms (0.2%)

simplify323.0ms (1.2%)

prune358.0ms (1.3%)

localize13.0ms (0%)

series14.2s (53.1%)

rewrite40.0ms (0.1%)

simplify1.2s (4.4%)

prune2.3s (8.8%)

localize17.0ms (0.1%)

series536.0ms (2%)

rewrite39.0ms (0.1%)

simplify247.0ms (0.9%)

prune257.0ms (1%)

regimes456.0ms (1.7%)

bsearch3.0ms (0%)

simplify5.0ms (0%)

end1.0ms (0%)

sample977.0ms (3.7%)

Profiling