Details

analyze2.0s

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

sample39.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
2.0ms	18×	body	80	invalid

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	5461	37

prune10.0ms

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: 29.4b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
0.1b	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
2.8b	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
28.5b	(/.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))

rewrite75.0ms

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:

14.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
8.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
18.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
33.0ms	(/.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))

series223.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
6.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
56.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
154.0ms	(/.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))

simplify63.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5007	2034

prune187.0ms

Filtered

78 candidates to 99 candidates (-26.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	5	100

Merged error: 0.2b

Counts

100 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)
0.0b	(+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)))
0.0b	(+.f64 x (+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))))
1.7b	(*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

7.0ms	(+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)
6.0ms	(+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)))
7.0ms	(+.f64 x (+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))))
15.0ms	(*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))

series48.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)
12.0ms	(+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688)))
22.0ms	(+.f64 x (+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))))
11.0ms	(*.f64 (/.f64 y z) (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5018	1153

prune109.0ms

Filtered

66 candidates to 90 candidates (-36.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	89	6	95

Merged error: 0.0b

Counts

95 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)))
0.0b	(+.f64 x (+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))))
0.2b	(/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)
3.2b	(*.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:

6.0ms	(+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)))
8.0ms	(+.f64 x (+.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)
13.0ms	(*.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))

series59.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)))
27.0ms	(+.f64 x (+.f64 (.f64 y 7049496828096731/2251799813685248) (.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))))
7.0ms	(/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z)
12.0ms	(*.f64 y (/.f64 (+.f64 (/.f64 t z) -23151763167026757919721122556003/633825300114114700748351602688) z))

simplify55.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4965	1297
1	4965	1297

prune110.0ms

Filtered

75 candidates to 106 candidates (-41.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	106	6	112

Merged error: 0.0b

Counts

112 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (.f64 y (+.f64 (/.f64 t (.f64 z z)) 7049496828096731/2251799813685248)))
3.1b	(.f64 y (+.f64 (/.f64 t (.f64 z z)) 7049496828096731/2251799813685248))
7.5b	(/.f64 t (*.f64 z z))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-r_binary64`
3×	`associate-l_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64` `div-exp_binary64` `flip-+_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 57

Calls

3 calls:

4.0ms	(+.f64 x (.f64 y (+.f64 (/.f64 t (.f64 z z)) 7049496828096731/2251799813685248)))
10.0ms	(.f64 y (+.f64 (/.f64 t (.f64 z z)) 7049496828096731/2251799813685248))
5.0ms	(/.f64 t (*.f64 z z))

series39.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(+.f64 x (.f64 y (+.f64 (/.f64 t (.f64 z z)) 7049496828096731/2251799813685248)))
16.0ms	(.f64 y (+.f64 (/.f64 t (.f64 z z)) 7049496828096731/2251799813685248))
6.0ms	(/.f64 t (*.f64 z z))

simplify58.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5174	638

prune53.0ms

Filtered

45 candidates to 66 candidates (-46.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	65	7	72

Merged error: 0.0b

Counts

72 → 7

regimes962.0ms

Accuracy

97.2% (0.8b remaining)

Error of 1.2b against oracle of 0.5b and baseline of 27.2b

bsearch65.0ms

Steps

Iters	Range		Point
9	137284757703.7726	1.8557257387315294e+19	1.7772195073898476e+19
8	-1.6569392546423388e+52	-1.7461598756475075e+48	-1.7838082981782328e+48

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	71
1	73	71

end0.0ms

sample1.1s

Algorithm

intervals

Results

704.0ms	8000×	body	80	valid
72.0ms	859×	body	80	invalid

Details

analyze2.0s

sample39.0ms

simplify118.0ms

prune10.0ms

localize26.0ms

rewrite75.0ms

series223.0ms

simplify63.0ms

prune187.0ms

localize11.0ms

rewrite37.0ms

series48.0ms

simplify40.0ms

prune109.0ms

localize11.0ms

rewrite39.0ms

series59.0ms

simplify55.0ms

prune110.0ms

localize8.0ms

rewrite20.0ms

series39.0ms

simplify58.0ms

prune53.0ms

regimes962.0ms

bsearch65.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling