Details

analyze848.0ms

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

sample24.0ms

Algorithm

intervals

Results

12.0ms	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

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5100	23

prune2.0ms

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

series847.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
354.0ms	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
79.0ms	(tanh.f64 (/.f64 t y))
200.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

simplify88.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4973	2920
1	4973	2920

prune99.0ms

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)))))

rewrite38.0ms

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:

4.0ms	(+.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))))
16.0ms	(.f64 y (.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

series880.0ms

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))))))
81.0ms	(tanh.f64 (/.f64 t y))
252.0ms	(*.f64 z (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
195.0ms	(.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 (55.0ms)

Iter	Nodes	Cost
0	5008	2869

prune97.0ms

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

localize15.0ms

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))))

rewrite61.0ms

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)
13.0ms	(*.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z))
21.0ms	(.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))))

series837.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt.f64 z)
263.0ms	(*.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z))
274.0ms	(.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) (cbrt.f64 z)))
215.0ms	(.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))))

simplify95.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5156	3588

prune126.0ms

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

localize21.0ms

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))))

rewrite234.0ms

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)))))
52.0ms	(.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)))))
24.0ms	(.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))))))
70.0ms	(/.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))))

series6.8s

Counts

4 → 12

Calls

4 calls:

2.1s	(.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)))))
868.0ms	(.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))))))
2.3s	(/.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))))

simplify370.0ms

Algorithm

egg-herbie

Counts

599 → 599

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4907	46311
1	4907	46311

prune2.6s

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

bsearch29.0ms

Steps

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

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	39
1	43	39

end0.0ms

sample723.0ms

Algorithm

intervals

Results

404.0ms	7731×	body	80	valid
31.0ms	549×	body	80	invalid
17.0ms	85×	body	640	valid
15.0ms	54×	body	1280	valid
11.0ms	78×	body	320	valid
5.0ms	52×	body	160	valid

Details

analyze848.0ms

sample24.0ms

simplify56.0ms

prune2.0ms

localize11.0ms

rewrite28.0ms

series847.0ms

simplify88.0ms

prune99.0ms

localize11.0ms

rewrite38.0ms

series880.0ms

simplify84.0ms

prune97.0ms

localize15.0ms

rewrite61.0ms

series837.0ms

simplify95.0ms

prune126.0ms

localize21.0ms

rewrite234.0ms

series6.8s

simplify370.0ms

prune2.6s

regimes83.0ms

bsearch29.0ms

simplify3.0ms

end0.0ms

sample723.0ms

Profiling