Details

analyze821.0ms

Algorithm

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

sample28.0ms

Algorithm

intervals

Results

17.0ms	251×	body	80	valid
1.0ms	20×	body	80	invalid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5100	23

prune1.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 4.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
0.0b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
0.0b	(tanh.f64 (/.f64 t y))
4.1b	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

18×	`frac-sub_binary64`
13×	`tanh-def-a_binary64` `tanh-def-b_binary64` `tanh-def-c_binary64`
11×	`associate-*r/_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
5×	`sub-neg_binary64` `associate-r_binary64` `add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate-+r+_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `associate-l_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

7.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
4.0ms	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
2.0ms	(tanh.f64 (/.f64 t y))
12.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series834.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
351.0ms	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
83.0ms	(tanh.f64 (/.f64 t y))
186.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

simplify86.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4973	2920
1	4973	2920

prune96.0ms

Filtered

73 candidates to 90 candidates (-23.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	6	91

Merged error: 1.0b

Counts

91 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
0.0b	(tanh.f64 (/.f64 t y))
1.1b	(*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
2.7b	(.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

33×	`associate-*r/_binary64`
18×	`frac-sub_binary64`
13×	`tanh-def-a_binary64` `tanh-def-b_binary64` `tanh-def-c_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
10×	`sub-neg_binary64`
9×	`*-un-lft-identity_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate-+r+_binary64`
2×	`flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(+.f64 x (.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
2.0ms	(tanh.f64 (/.f64 t y))
11.0ms	(*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
13.0ms	(.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

series873.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(+.f64 x (.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
77.0ms	(tanh.f64 (/.f64 t y))
249.0ms	(*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
194.0ms	(.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5008	2869

prune101.0ms

Filtered

78 candidates to 103 candidates (-32.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	101	8	109

Merged error: 1.0b

Counts

109 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 z)
0.6b	(*.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z))
0.7b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z)))
2.7b	(.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1_binary64` `add-exp-log_binary64`
33×	`associate-r/_binary64` `associate-l/_binary64`
27×	`frac-sub_binary64`
23×	`add-cbrt-cube_binary64`
22×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
18×	`tanh-def-a_binary64` `tanh-def-b_binary64` `tanh-def-c_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64` `associate-l_binary64`
8×	`associate-r_binary64`
7×	`cbrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`pow1/3_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`

Counts

4 → 117

Calls

4 calls:

1.0ms	(cbrt.f64 z)
12.0ms	(*.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z))
17.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z)))
21.0ms	(.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z))))

series827.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cbrt.f64 z)
261.0ms	(*.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z))
273.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z)))
210.0ms	(.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z))))

simplify93.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5156	3588

prune125.0ms

Filtered

94 candidates to 129 candidates (-37.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	128	9	137

Merged error: 1.0b

Counts

137 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (*.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
1.4b	(.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (*.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y)))))
2.7b	(.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
6.9b	(/.f64 (.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (*.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

637×	`associate-*r/_binary64`
540×	`frac-times_binary64`
492×	`tanh-def-a_binary64` `tanh-def-b_binary64` `tanh-def-c_binary64`
450×	`frac-sub_binary64`
227×	`associate-/l/_binary64`
180×	`associate-*l/_binary64`
61×	`add-exp-log_binary64`
43×	`add-cbrt-cube_binary64`
31×	`cbrt-unprod_binary64` `prod-exp_binary64`
24×	`associate-r_binary64`
22×	`associate-/r/_binary64`
20×	`pow1_binary64`
18×	`*-un-lft-identity_binary64` `frac-add_binary64`
17×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
8×	`times-frac_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-prod_binary64`
3×	`distribute-lft-out_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l*_binary64`

Counts

4 → 587

Calls

4 calls:

21.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (*.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
47.0ms	(.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (*.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y)))))
21.0ms	(.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
62.0ms	(/.f64 (.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (*.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series7.0s

Counts

4 → 12

Calls

4 calls:

2.2s	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (*.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
942.0ms	(.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (*.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y)))))
1.6s	(.f64 y (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (/.f64 (.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
2.2s	(/.f64 (.f64 (cbrt.f64 z) (-.f64 (.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y))) (*.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 x y))))) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

simplify375.0ms

Algorithm

egg-herbie

Counts

599 → 599

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4907	46311
1	4907	46311

prune2.5s

Filtered

484 candidates to 599 candidates (-23.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	597	2	599
Fresh	4	1	5
Picked	1	0	1
Done	2	1	3
Total	604	4	608

Merged error: 0b

Counts

608 → 4

regimes83.0ms

Accuracy

19.4% (1.6b remaining)

Error of 1.6b against oracle of 0.0b and baseline of 2.0b

bsearch30.0ms

Steps

Iters	Range		Point
10	-1.2905149889371164e+179	-3.305112858858447e+163	-1.1428028320336448e+179

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	39
1	43	39

end0.0ms

sample697.0ms

Algorithm

intervals

Results

388.0ms	7731×	body	80	valid
35.0ms	549×	body	80	invalid
16.0ms	85×	body	640	valid
15.0ms	54×	body	1280	valid
13.0ms	78×	body	320	valid
5.0ms	52×	body	160	valid

Details

analyze821.0ms

sample28.0ms

simplify55.0ms

prune1.0ms

localize11.0ms

rewrite28.0ms

series834.0ms

simplify86.0ms

prune96.0ms

localize11.0ms

rewrite35.0ms

series873.0ms

simplify84.0ms

prune101.0ms

localize16.0ms

rewrite60.0ms

series827.0ms

simplify93.0ms

prune125.0ms

localize20.0ms

rewrite222.0ms

series7.0s

simplify375.0ms

prune2.5s

regimes83.0ms

bsearch30.0ms

simplify4.0ms

end0.0ms

sample697.0ms

Profiling