Details

analyze1.2s (20.7%)

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)

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms	250×	body	128	valid
1.0ms	16×	body	128	invalid
1.0ms	2×	body	1024	valid
0.0ms	2×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 43 to 29 computations (32.6% saved)

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

441×	`div-sub_binary64`
396×	`distribute-rgt-in_binary64`
366×	`distribute-lft-in_binary64`
260×	`associate-l_binary64`
256×	`associate-r_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	55	23
2	148	23
3	349	23
4	1247	23
5	4605	23
6	4879	23
7	5155	23

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

4.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	4.9b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

Compiler

Compiled 38 to 24 computations (36.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(tanh.f64 (/.f64 t y))
0.0b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
0.2b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
4.8b	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

rewrite129.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

18×	`frac-sub_binary64`
15×	`cancel-sign-sub-inv_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`tanh-def-a_binary64`

Counts

4 → 93

Calls

4 calls:

9.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
6.0ms	(+.f64 x (.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))

Compiler

Compiled 3049 to 811 computations (73.4% saved)

series590.0ms (10.1%)

Error

0.1b

Counts

4 → 58

Calls

4 calls:

248.0ms	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
208.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
71.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
31.0ms	(tanh.f64 (/.f64 t y))

Compiler

Compiled 5735 to 3739 computations (34.8% saved)

simplify179.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

308×	`times-frac_binary64`
238×	`associate-l_binary64`
229×	`distribute-rgt-in_binary64`
223×	`distribute-lft-in_binary64`
211×	`associate-r_binary64`

Counts

151 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	6113
1	887	5617
2	3171	5611
3	4814	5611
4	4981	5611

prune50.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	3	100

Error

0.0b

Counts

100 → 3

Alt Table

Status	Error	Program
	39.6b	(+.f64 x (/.f64 (.f64 (.f64 y z) (-.f64 (.f64 (-.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 1 (exp.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 -1 (exp.f64 (.f64 (/.f64 x y) 2)))))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 (exp.f64 (*.f64 2 (/.f64 x y))) 1))))
▶	29.0b	(+.f64 x (*.f64 z (-.f64 t x)))
✓	4.9b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

Compiler

Compiled 2521 to 1121 computations (55.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 z (-.f64 t x))
0.0b	(+.f64 x (*.f64 z (-.f64 t x)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`cancel-sign-sub-inv_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`distribute-lft-in_binary64`
8×	`associate-+r+_binary64`

Counts

2 → 49

Calls

2 calls:

5.0ms	(*.f64 z (-.f64 t x))
3.0ms	(+.f64 x (*.f64 z (-.f64 t x)))

Compiler

Compiled 659 to 183 computations (72.2% saved)

series49.0ms (0.8%)

Error

0.0b

Counts

2 → 33

Calls

2 calls:

24.0ms	(+.f64 x (*.f64 z (-.f64 t x)))
18.0ms	(*.f64 z (-.f64 t x))

Compiler

Compiled 665 to 409 computations (38.5% saved)

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

538×	`neg-mul-1_binary64`
485×	`associate-r_binary64`
361×	`exp-prod_binary64`
340×	`distribute-rgt-neg-out_binary64`
336×	`cancel-sign-sub-inv_binary64`

Counts

82 → 54

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	100	812
1	248	764
2	675	764
3	2186	764
4	4224	764
5	5115	764

prune15.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	54	3	57

Error

0.0b

Counts

57 → 3

Alt Table

Status	Error	Program
▶	39.6b	(+.f64 x (/.f64 (.f64 (.f64 y z) (-.f64 (.f64 (-.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 1 (exp.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 -1 (exp.f64 (.f64 (/.f64 x y) 2)))))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 (exp.f64 (*.f64 2 (/.f64 x y))) 1))))
✓	29.0b	(+.f64 x (*.f64 z (-.f64 t x)))
✓	4.9b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

Compiler

Compiled 434 to 199 computations (54.1% saved)

localize32.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (.f64 y z) (-.f64 (.f64 (-.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 1 (exp.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 -1 (exp.f64 (.f64 (/.f64 x y) 2)))))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 (exp.f64 (*.f64 2 (/.f64 x y))) 1)))
2.5b	(+.f64 -1 (exp.f64 (*.f64 (/.f64 x y) 2)))
4.9b	(-.f64 1 (exp.f64 (*.f64 -2 (/.f64 t y))))
5.4b	(.f64 (.f64 y z) (-.f64 (.f64 (-.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 1 (exp.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 -1 (exp.f64 (.f64 (/.f64 x y) 2))))))

rewrite606.0ms (10.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

198×	`associate-*r/_binary64`
151×	`flip-+_binary64`
151×	`flip3-+_binary64`
132×	`frac-times_binary64`
128×	`frac-sub_binary64`

Counts

4 → 220

Calls

4 calls:

31.0ms	(/.f64 (.f64 (.f64 y z) (-.f64 (.f64 (-.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 1 (exp.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 -1 (exp.f64 (.f64 (/.f64 x y) 2)))))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 (exp.f64 (*.f64 2 (/.f64 x y))) 1)))
20.0ms	(.f64 (.f64 y z) (-.f64 (.f64 (-.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 1 (exp.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 -1 (exp.f64 (.f64 (/.f64 x y) 2))))))
4.0ms	(+.f64 -1 (exp.f64 (*.f64 (/.f64 x y) 2)))
3.0ms	(-.f64 1 (exp.f64 (*.f64 -2 (/.f64 t y))))

Compiler

Compiled 31617 to 20826 computations (34.1% saved)

series467.0ms (8%)

Error

0.0b

Counts

4 → 47

Calls

4 calls:

304.0ms	(/.f64 (.f64 (.f64 y z) (-.f64 (.f64 (-.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 1 (exp.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 -1 (exp.f64 (.f64 (/.f64 x y) 2)))))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 (exp.f64 (*.f64 2 (/.f64 x y))) 1)))
85.0ms	(.f64 (.f64 y z) (-.f64 (.f64 (-.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 1 (exp.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 -1 (exp.f64 (.f64 (/.f64 x y) 2))))))
23.0ms	(-.f64 1 (exp.f64 (*.f64 -2 (/.f64 t y))))
17.0ms	(+.f64 -1 (exp.f64 (*.f64 (/.f64 x y) 2)))

Compiler

Compiled 7890 to 5359 computations (32.1% saved)

simplify331.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

582×	`times-frac_binary64`
456×	`*-commutative_binary64`
312×	`cancel-sign-sub-inv_binary64`
296×	`associate-l_binary64`
244×	`associate-r_binary64`

Counts

267 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	798	23677
1	3160	21735
2	4979	21735

prune450.0ms (7.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	236	3	239

Error

0.0b

Counts

239 → 3

Alt Table

Status	Error	Program
	39.6b	(+.f64 x (/.f64 (.f64 (.f64 y z) (-.f64 (.f64 (-.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 1 (exp.f64 (.f64 (/.f64 x y) 2)))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 -1 (exp.f64 (.f64 (/.f64 x y) 2)))))) (.f64 (+.f64 1 (exp.f64 (.f64 -2 (/.f64 t y)))) (+.f64 (exp.f64 (*.f64 2 (/.f64 x y))) 1))))
	29.0b	(+.f64 x (*.f64 z (-.f64 t x)))
	4.9b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

Compiler

Compiled 26856 to 17424 computations (35.1% saved)

regimes548.0ms (9.4%)

Accuracy

Total 1.2b remaining (90.5%)

Threshold costs 0b (0%)

Compiler

Compiled 12096 to 7442 computations (38.5% saved)

bsearch6.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`+-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	22	58
1	33	58
2	41	58
3	45	58
4	47	58
5	47	58

end1.0ms (0%)

Compiler: Compiled 42 to 20 computations (52.4% saved)

sample960.0ms (16.4%)

Algorithm

1×

intervals

Results

490.0ms	7784×	body	128	valid
40.0ms	597×	body	128	invalid
19.0ms	80×	body	1024	valid
13.0ms	60×	body	256	valid
13.0ms	75×	body	512	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 159 to 100 computations (37.1% saved)

Details

analyze1.2s (20.7%)

sample30.0ms (0.5%)

simplify54.0ms (0.9%)

prune1.0ms (0%)

localize11.0ms (0.2%)

rewrite129.0ms (2.2%)

series590.0ms (10.1%)

simplify179.0ms (3.1%)

prune50.0ms (0.9%)

localize6.0ms (0.1%)

rewrite30.0ms (0.5%)

series49.0ms (0.8%)

simplify82.0ms (1.4%)

prune15.0ms (0.3%)

localize32.0ms (0.5%)

rewrite606.0ms (10.4%)

series467.0ms (8%)

simplify331.0ms (5.7%)

prune450.0ms (7.7%)

regimes548.0ms (9.4%)

bsearch6.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample960.0ms (16.4%)

Profiling