Details

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
3.1%	46.8%	50%	5
4.7%	45.3%	50%	6
5.5%	44.5%	50%	7
5.9%	44.1%	50%	8
6%	43.9%	50%	9
6.1%	43.8%	50%	10
6.2%	43.8%	50%	11
6.2%	43.7%	50%	12
6.2%	43.7%	50%	13
6.2%	43.7%	50%	14

sample160.0ms

Algorithm

intervals

Results

100.0ms	108×	body	1280	valid
32.0ms	76×	body	640	valid
9.0ms	39×	body	320	valid
7.0ms	256×	pre	80	true
4.0ms	32×	body	160	valid
0.0ms	1×	body	80	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5257	9

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: 61.9b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (log.f64 (-.f64 1.0 x)) (log.f64 (+.f64 1.0 x)))
7.9b	(log.f64 (-.f64 1.0 x))
7.9b	(log.f64 (+.f64 1.0 x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`times-frac_binary64`
15×	`pow1_binary64` `add-cube-cbrt_binary64`
12×	`log-pow_binary64`
9×	`log-prod_binary64`
7×	`add-exp-log_binary64`
6×	`log-div_binary64`
5×	`add-cbrt-cube_binary64`
4×	`associate-/r_binary64` `associate-/l_binary64`
3×	`add-log-exp_binary64`
2×	`flip3--_binary64` `rem-log-exp_binary64` `div-sub_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

3 → 69

Calls

3 calls:

6.0ms	(/.f64 (log.f64 (-.f64 1.0 x)) (log.f64 (+.f64 1.0 x)))
4.0ms	(log.f64 (-.f64 1.0 x))
3.0ms	(log.f64 (+.f64 1.0 x))

series22.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/.f64 (log.f64 (-.f64 1.0 x)) (log.f64 (+.f64 1.0 x)))
3.0ms	(log.f64 (-.f64 1.0 x))
4.0ms	(log.f64 (+.f64 1.0 x))

simplify59.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4962	1012
1	4962	1012

prune94.0ms

Filtered

55 candidates to 78 candidates (-41.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Merged error: 58.9b

Counts

79 → 4

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(.f64 1/2 (/.f64 (.f64 x x) (*.f64 1.0 1.0)))
0.0b	(/.f64 (log.f64 (-.f64 1.0 x)) (-.f64 (+.f64 (.f64 1.0 x) (log.f64 1.0)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
7.9b	(log.f64 (-.f64 1.0 x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
14×	`times-frac_binary64`
10×	`pow1_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`associate-r_binary64` `log-prod_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `div-exp_binary64`
4×	`associate-/r/_binary64` `associate-/l*_binary64` `log-div_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `flip3--_binary64` `associate-r/_binary64` `associate-l_binary64` `flip--_binary64`
2×	`unswap-sqr_binary64` `div-sub_binary64` `div-inv_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 83

Calls

3 calls:

11.0ms	(.f64 1/2 (/.f64 (.f64 x x) (*.f64 1.0 1.0)))
13.0ms	(/.f64 (log.f64 (-.f64 1.0 x)) (-.f64 (+.f64 (.f64 1.0 x) (log.f64 1.0)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
4.0ms	(log.f64 (-.f64 1.0 x))

series20.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(.f64 1/2 (/.f64 (.f64 x x) (*.f64 1.0 1.0)))
12.0ms	(/.f64 (log.f64 (-.f64 1.0 x)) (-.f64 (+.f64 (.f64 1.0 x) (log.f64 1.0)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
4.0ms	(log.f64 (-.f64 1.0 x))

simplify37.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5227	1790

prune114.0ms

Filtered

64 candidates to 92 candidates (-43.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	94	2	96

Merged error: 0.0b

Counts

96 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b

(*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0)))

0.0b

(*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0)))

0.0b

(/.f64 (-.f64 (log.f64 1.0) (+.f64 (*.f64 1.0 x) (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0))))) (-.f64 (+.f64 (*.f64 1.0 x) (log.f64 1.0)) (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
18×	`cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
10×	`associate-r_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`distribute-lft-out--_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64`
4×	`associate-*r/_binary64` `log-pow_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

3 → 106

Calls

3 calls:

9.0ms

(*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0)))

9.0ms

(*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0)))

19.0ms

(/.f64 (-.f64 (log.f64 1.0) (+.f64 (*.f64 1.0 x) (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0))))) (-.f64 (+.f64 (*.f64 1.0 x) (log.f64 1.0)) (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0)))))

series19.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms

(*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0)))

4.0ms

(*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0)))

10.0ms

(/.f64 (-.f64 (log.f64 1.0) (+.f64 (*.f64 1.0 x) (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0))))) (-.f64 (+.f64 (*.f64 1.0 x) (log.f64 1.0)) (*.f64 1/2 (/.f64 (*.f64 x x) (*.f64 1.0 1.0)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4980	2782
1	4980	2782

prune176.0ms

Filtered

72 candidates to 115 candidates (-59.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	113	4	117

Merged error: 0b

Counts

117 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
0.0b	(/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
0.0b	(/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
0.0b	(.f64 (cbrt.f64 (/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))) (cbrt.f64 (/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (*.f64 1.0 1.0)))))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

213×	`*-un-lft-identity_binary64`
168×	`times-frac_binary64`
165×	`add-sqr-sqrt_binary64`
152×	`cbrt-prod_binary64`
93×	`add-cube-cbrt_binary64`
72×	`distribute-lft-out--_binary64`
47×	`pow1_binary64` `swap-sqr_binary64`
36×	`log-pow_binary64`
29×	`associate-r_binary64` `associate-l_binary64`
28×	`associate-/r/_binary64`
24×	`difference-of-squares_binary64`
18×	`associate-/l*_binary64`
15×	`associate-*r/_binary64`
14×	`frac-sub_binary64`
12×	`add-exp-log_binary64`
10×	`flip3--_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
9×	`associate-/r*_binary64` `unswap-sqr_binary64`
7×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
6×	`associate-/l/_binary64` `pow1/3_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 273

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
16.0ms	(/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
18.0ms	(/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
45.0ms	(.f64 (cbrt.f64 (/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))) (cbrt.f64 (/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (*.f64 1.0 1.0)))))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
10.0ms	(/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
15.0ms	(/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))
21.0ms	(.f64 (cbrt.f64 (/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0)))))) (cbrt.f64 (/.f64 (-.f64 (log.f64 1.0) (+.f64 (.f64 1.0 x) (.f64 1/2 (/.f64 (.f64 x x) (.f64 1.0 1.0))))) (-.f64 (+.f64 (log.f64 1.0) (.f64 1.0 x)) (.f64 1/2 (/.f64 (.f64 x x) (*.f64 1.0 1.0)))))))

simplify124.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5182	17314

prune2.5s

Filtered

187 candidates to 285 candidates (-52.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	285	4	289

Merged error: 0b

Counts

289 → 4

regimes38.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	104
1	91	104

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.0s	3416×	body	1280	valid
1.1s	2478×	body	640	valid
280.0ms	1261×	body	320	valid
135.0ms	8000×	pre	80	true
82.0ms	621×	body	160	valid
13.0ms	224×	body	80	valid

Details

analyze1.3s

sample160.0ms

simplify63.0ms

prune2.0ms

localize6.0ms

rewrite15.0ms

series22.0ms

simplify59.0ms

prune94.0ms

localize13.0ms

rewrite31.0ms

series20.0ms

simplify37.0ms

prune114.0ms

localize12.0ms

rewrite42.0ms

series19.0ms

simplify52.0ms

prune176.0ms

localize17.0ms

rewrite111.0ms

series56.0ms

simplify124.0ms

prune2.5s

regimes38.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample4.8s

Profiling