Details

analyze2.2s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0.8%	98.9%	0.3%	13
1.2%	98.5%	0.3%	14

sample42.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
2.0ms	26×	body	80	invalid

simplify119.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4956	55
1	4956	55

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 31.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
4.1b	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
28.7b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `associate-l/_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `unswap-sqr_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 87

Calls

4 calls:

7.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
11.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
20.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
32.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))

series703.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
21.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
171.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
474.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))

simplify118.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4966	3033
1	4966	3033

prune195.0ms

Filtered

78 candidates to 99 candidates (-26.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	6	100

Merged error: 0.5b

Counts

100 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b

(+.f64 x (+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))))

0.0b

(+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)))

1.6b

(*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`associate-l_binary64`
11×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `associate-r_binary64` `flip-+_binary64` `sum-log_binary64`
3×	`associate-+r+_binary64`
2×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

3 → 66

Calls

3 calls:

7.0ms

(+.f64 x (+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))))

8.0ms

(+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)))

12.0ms

(*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))

series161.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms

(+.f64 x (+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))))

43.0ms

(+.f64 (*.f64 y 7049496828096731/2251799813685248) (*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)))

47.0ms

(*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))

simplify61.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5147	1553

prune77.0ms

Filtered

56 candidates to 75 candidates (-33.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	73	8	81

Merged error: 0.5b

Counts

81 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))))
0.0b	(+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)))
0.1b	(/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)
4.4b	(*.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`
11×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`distribute-lft-out_binary64`
6×	`pow1_binary64`
4×	`associate-/l*_binary64` `sum-log_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-l*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-+r+_binary64` `-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

7.0ms	(+.f64 x (+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))))
5.0ms	(+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)))
9.0ms	(/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)
15.0ms	(*.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))

series191.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+.f64 x (+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))))
43.0ms	(+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)))
24.0ms	(/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)
45.0ms	(*.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))

simplify87.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4970	1931
1	4970	1931

prune88.0ms

Filtered

74 candidates to 106 candidates (-43.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	106	8	114

Merged error: 0.5b

Counts

114 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.3b	(*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248))
11.6b	(cbrt.f64 (+.f64 (*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248)) x))
11.6b	(cbrt.f64 (+.f64 (*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248)) x))
11.6b	(cbrt.f64 (+.f64 (*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248)) x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `cbrt-prod_binary64`
6×	`cbrt-div_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate-r_binary64` `flip-+_binary64`
3×	`pow1/3_binary64` `associate-l_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

16.0ms	(*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248))
15.0ms	(cbrt.f64 (+.f64 (*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248)) x))
17.0ms	(cbrt.f64 (+.f64 (*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248)) x))
15.0ms	(cbrt.f64 (+.f64 (*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248)) x))

series1.2s

Counts

4 → 12

Calls

4 calls:

53.0ms	(*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248))
380.0ms	(cbrt.f64 (+.f64 (*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248)) x))
373.0ms	(cbrt.f64 (+.f64 (*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248)) x))
374.0ms	(cbrt.f64 (+.f64 (*.f64 y (+.f64 (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z) 7049496828096731/2251799813685248)) x))

simplify127.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4914	2054
1	4914	2054

prune134.0ms

Filtered

61 candidates to 74 candidates (-21.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	74	8	82

Merged error: 0.5b

Counts

82 → 8

regimes469.0ms

Accuracy

97.8% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 27.3b

bsearch74.0ms

Steps

Iters	Range		Point
9	7.198143132141369e+34	1.444077661436546e+41	1.4262767847954125e+41
8	-1.720245396752578e+42	-2.693119961739492e+37	-1.5029013782256487e+42

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	91
1	71	91

end0.0ms

sample1.1s

Algorithm

intervals

Results

720.0ms	8000×	body	80	valid
86.0ms	903×	body	80	invalid

Details

analyze2.2s

sample42.0ms

simplify119.0ms

prune4.0ms

localize25.0ms

rewrite72.0ms

series703.0ms

simplify118.0ms

prune195.0ms

localize11.0ms

rewrite29.0ms

series161.0ms

simplify61.0ms

prune77.0ms

localize11.0ms

rewrite39.0ms

series191.0ms

simplify87.0ms

prune88.0ms

localize16.0ms

rewrite65.0ms

series1.2s

simplify127.0ms

prune134.0ms

regimes469.0ms

bsearch74.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling