Details

analyze1.6s (3.5%)

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)

sample69.0ms (0.1%)

Algorithm

1×

intervals

Results

16.0ms	248×	body	128	valid
1.0ms	5×	body	1024	valid
1.0ms	17×	body	128	invalid
0.0ms	2×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 43 to 29 computations (32.6% saved)

simplify38.0ms (0.1%)

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

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

5.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.0b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
▶	5.0b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

Compiler

Compiled 107 to 59 computations (44.9% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	0.0b	(tanh.f64 (/.f64 x y))
✓	0.1b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	5.9b	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series579.0ms (1.3%)

Counts

4 → 132

Calls

4 calls:

303.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
165.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
56.0ms	(tanh.f64 (/.f64 t y))
55.0ms	(tanh.f64 (/.f64 x y))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
27×	`prod-diff_binary64`
27×	`add-cube-cbrt_binary64`
18×	`frac-sub_binary64`

Counts

4 → 122

Calls

4 calls:

11.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
5.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
1.0ms	(tanh.f64 (/.f64 t y))
1.0ms	(tanh.f64 (/.f64 x y))

simplify251.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

930×	`times-frac_binary64`
285×	`associate-l_binary64`
258×	`associate-r_binary64`
257×	`*-commutative_binary64`
255×	`fma-neg_binary64`

Counts

254 → 240

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	391	16922
1	1158	7478
2	4280	7478
3	6238	7478

prune219.0ms (0.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	235	5	240
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	237	5	242

Error

0.0b

Counts

242 → 5

Alt Table

Status	Error	Program
	32.8b	(+.f64 x (.f64 (.f64 y z) (/.f64 (-.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 x y)) 2)) (-.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2))) (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2)) (expm1.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 x y)) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2))))))
	28.6b	(+.f64 x (*.f64 (-.f64 t x) z))
	7.4b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))))
	12.1b	(+.f64 x (/.f64 (.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3))) (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (+.f64 (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))) (*.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
▶	1.8b	(+.f64 x (.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))

Compiler

Compiled 9902 to 3116 computations (68.5% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(tanh.f64 (/.f64 x y))
	0.1b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	0.7b	(*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
✓	4.2b	(.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

series588.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

309.0ms	(.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
279.0ms	(*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

rewrite43.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 142

Calls

2 calls:

13.0ms	(*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
10.0ms	(.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

simplify287.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

330×	`associate-r_binary64`
328×	`fma-neg_binary64`
325×	`associate-l_binary64`
303×	`sub-neg_binary64`
256×	`*-commutative_binary64`

Counts

238 → 230

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	15492
1	1086	10229
2	4168	9601
3	4822	9601
4	4985	9601

prune405.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	338	0	338
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	338	5	343

Error

0.0b

Counts

343 → 5

Alt Table

Status	Error	Program
	32.8b	(+.f64 x (.f64 (.f64 y z) (/.f64 (-.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 x y)) 2)) (-.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2))) (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2)) (expm1.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 x y)) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2))))))
	28.6b	(+.f64 x (*.f64 (-.f64 t x) z))
▶	7.4b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))))
	12.1b	(+.f64 x (/.f64 (.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3))) (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (+.f64 (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))) (*.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
✓	1.8b	(+.f64 x (.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))

Compiler

Compiled 14828 to 4571 computations (69.2% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(tanh.f64 (/.f64 x y))
✓	0.1b	(-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))
✓	3.4b	(log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))
✓	6.6b	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))))

series524.0ms (1.1%)

Counts

3 → 108

Calls

3 calls:

310.0ms

(*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))))

159.0ms

(-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))

55.0ms

(log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))

rewrite36.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`prod-diff_binary64`
59×	`*-un-lft-identity_binary64`
57×	`add-sqr-sqrt_binary64`
54×	`log-pow_binary64`
53×	`add-cube-cbrt_binary64`

Counts

3 → 150

Calls

3 calls:

10.0ms

(*.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))))

7.0ms

(-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))

1.0ms

(log.f64 (exp.f64 (tanh.f64 (/.f64 x y))))

simplify259.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

771×	`times-frac_binary64`
285×	`associate-l_binary64`
271×	`fma-neg_binary64`
253×	`associate-r_binary64`
197×	`*-commutative_binary64`

Counts

258 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	390	20518
1	899	7072
2	3273	7039
3	4985	7039
4	4960	7039

prune281.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	268	5	273

Error

0.0b

Counts

273 → 5

Alt Table

Status	Error	Program
	32.8b	(+.f64 x (.f64 (.f64 y z) (/.f64 (-.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 x y)) 2)) (-.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2))) (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2)) (expm1.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 x y)) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2))))))
	28.6b	(+.f64 x (*.f64 (-.f64 t x) z))
✓	7.4b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))))
▶	12.1b	(+.f64 x (/.f64 (.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3))) (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (+.f64 (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))) (*.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
✓	1.8b	(+.f64 x (.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))

Compiler

Compiled 10628 to 2620 computations (75.3% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (tanh.f64 (/.f64 x y)) 3)
✓	0.1b	(pow.f64 (tanh.f64 (/.f64 t y)) 3)
✓	5.8b	(.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)))
✓	9.6b	(/.f64 (.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3))) (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (+.f64 (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))) (*.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))

series9.2s (20%)

Counts

4 → 144

Calls

4 calls:

8.0s	(/.f64 (.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3))) (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (+.f64 (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))) (*.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
1.1s	(.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)))
88.0ms	(pow.f64 (tanh.f64 (/.f64 x y)) 3)
88.0ms	(pow.f64 (tanh.f64 (/.f64 t y)) 3)

rewrite4.3s (9.2%)

Algorithm

1×	rewrite-expression-head

Rules

6780×	`frac-add_binary64`
6093×	`frac-times_binary64`
5430×	`tanh-def-a_binary64`
5430×	`tanh-def-b_binary64`
5430×	`tanh-def-c_binary64`

Counts

4 → 3866

Calls

4 calls:

229.0ms	(/.f64 (.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3))) (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (+.f64 (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))) (*.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
27.0ms	(.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)))
2.0ms	(pow.f64 (tanh.f64 (/.f64 x y)) 3)
2.0ms	(pow.f64 (tanh.f64 (/.f64 t y)) 3)

simplify15.4s (33.4%)

Algorithm

1×	egg-herbie

Counts

4010 → 3802

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14827	890965

prune10.3s (22.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	3802	0	3802
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	3802	5	3807

Error

0.0b

Counts

3807 → 5

Alt Table

Status	Error	Program
	32.8b	(+.f64 x (.f64 (.f64 y z) (/.f64 (-.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 x y)) 2)) (-.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2))) (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2)) (expm1.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (pow.f64 (exp.f64 (/.f64 x y)) 2)) (+.f64 1 (pow.f64 (exp.f64 (/.f64 t y)) -2))))))
	28.6b	(+.f64 x (*.f64 (-.f64 t x) z))
✓	7.4b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (log.f64 (exp.f64 (tanh.f64 (/.f64 x y)))))))
✓	12.1b	(+.f64 x (/.f64 (.f64 (.f64 y z) (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3))) (+.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (+.f64 (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))) (*.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))))
✓	1.8b	(+.f64 x (.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))

Compiler

Compiled 716935 to 300309 computations (58.1% saved)

regimes622.0ms (1.3%)

Accuracy

Total 2.0b remaining (99.1%)

Threshold costs 0b (0%)

Counts

93 → 1

Compiler

Compiled 15048 to 8041 computations (46.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	28	31
2	39	29
3	50	29
4	57	29
5	61	29
6	62	29
7	62	29

end1.0ms (0%)

Compiler: Compiled 23 to 14 computations (39.1% saved)

sample1.1s (2.4%)

Algorithm

1×

intervals

Results

575.0ms	7777×	body	128	valid
45.0ms	574×	body	128	invalid
26.0ms	90×	body	1024	valid
16.0ms	81×	body	512	valid
6.0ms	51×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 212 to 125 computations (41% saved)

Details

analyze1.6s (3.5%)

sample69.0ms (0.1%)

simplify38.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0%)

series579.0ms (1.3%)

rewrite30.0ms (0.1%)

simplify251.0ms (0.5%)

prune219.0ms (0.5%)

localize14.0ms (0%)

series588.0ms (1.3%)

rewrite43.0ms (0.1%)

simplify287.0ms (0.6%)

prune405.0ms (0.9%)

localize12.0ms (0%)

series524.0ms (1.1%)

rewrite36.0ms (0.1%)

simplify259.0ms (0.6%)

prune281.0ms (0.6%)

localize20.0ms (0%)

series9.2s (20%)

rewrite4.3s (9.2%)

simplify15.4s (33.4%)

prune10.3s (22.2%)

regimes622.0ms (1.3%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.1s (2.4%)

Profiling