Details

analyze627.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

sample44.0ms

Algorithm

intervals

Results

8.0ms	171×	body	80	valid
7.0ms	35×	body	1280	nan
6.0ms	26×	body	1280	valid
5.0ms	31×	body	640	valid
3.0ms	23×	body	640	nan
3.0ms	20×	body	320	valid
1.0ms	9×	body	320	nan
1.0ms	8×	body	160	valid
0.0ms	14×	body	80	nan
0.0ms	6×	body	160	nan

simplify176.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (173.0ms)

Iter	Nodes	Cost
0	4867	12
1	4867	12

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: 20.8b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 1 y))
2.3b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
4.1b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
27×	`difference-of-squares_binary64`
17×	`add-cube-cbrt_binary64`
15×	`distribute-lft-out--_binary64`
8×	`log-prod_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64`
5×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
4×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `div-sub_binary64` `log-div_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `associate--r-_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 94

Calls

3 calls:

9.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))
17.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
21.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

series31.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))
10.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
14.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

simplify39.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4993	1400
1	4993	1400

prune99.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	4	104

Merged error: 0.1b

Counts

104 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 y))
0.1b	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))
4.1b	(log.f64 (-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))))
4.9b	(-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
38×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`
18×	`add-exp-log_binary64`
15×	`difference-of-squares_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `distribute-lft-out--_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
5×	`associate-l_binary64`
4×	`associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`log-prod_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `log-div_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `log-pow_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 123

Calls

4 calls:

7.0ms	(/.f64 1 (-.f64 1 y))
16.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))
4.0ms	(log.f64 (-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))))
5.0ms	(-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 1 (-.f64 1 y))
7.0ms	(*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))
14.0ms	(log.f64 (-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y)))))
11.0ms	(-.f64 1 (*.f64 (-.f64 x y) (/.f64 1 (-.f64 1 y))))

simplify51.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4965	1364
1	4965	1364

prune77.0ms

Filtered

91 candidates to 135 candidates (-48.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	135	4	139

Merged error: 0.1b

Counts

139 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (log.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) 3))) (log.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))))
2.2b	(-.f64 1 (pow.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) 3))
11.4b	(log.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))))
12.9b	(log.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) 3)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64`
38×	`log-prod_binary64`
37×	`difference-of-squares_binary64`
36×	`*-un-lft-identity_binary64`
16×	`associate--l+_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64` `times-frac_binary64`
10×	`pow1_binary64`
8×	`add-cube-cbrt_binary64` `log-div_binary64`
7×	`distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `log-pow_binary64` `sqr-pow_binary64` `add-exp-log_binary64`
4×	`flip3--_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`associate--r+_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `associate--l-_binary64` `diff-log_binary64` `associate--r-_binary64` `rem-log-exp_binary64` `flip-+_binary64`

Counts

4 → 104

Calls

4 calls:

40.0ms	(-.f64 (log.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) 3))) (log.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))))
30.0ms	(-.f64 1 (pow.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) 3))
3.0ms	(log.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))))
33.0ms	(log.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) 3)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(-.f64 (log.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) 3))) (log.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))))
51.0ms	(-.f64 1 (pow.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) 3))
40.0ms	(log.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))))
64.0ms	(log.f64 (-.f64 1 (pow.f64 (/.f64 (-.f64 x y) (-.f64 1 y)) 3)))

simplify71.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5072	3178

prune129.0ms

Filtered

80 candidates to 116 candidates (-45.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Merged error: 0.1b

Counts

120 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 -1 y) (+.f64 (/.f64 x y) (/.f64 x (*.f64 y y))))
2.7b	(log.f64 (+.f64 (/.f64 -1 y) (+.f64 (/.f64 x y) (/.f64 x (*.f64 y y)))))
3.0b	(+.f64 (/.f64 x y) (/.f64 x (*.f64 y y)))
7.5b	(/.f64 x (*.f64 y y))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
11×	`add-log-exp_binary64` `times-frac_binary64`
10×	`add-exp-log_binary64`
9×	`frac-add_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
8×	`distribute-lft-out_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `log-prod_binary64` `log-div_binary64` `flip-+_binary64`
4×	`distribute-rgt-out_binary64` `sum-log_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `+-commutative_binary64`
1×	`associate-/r*_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `log-pow_binary64` `distribute-rgt1-in_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-+r+_binary64`

Counts

4 → 77

Calls

4 calls:

19.0ms	(+.f64 (/.f64 -1 y) (+.f64 (/.f64 x y) (/.f64 x (*.f64 y y))))
18.0ms	(log.f64 (+.f64 (/.f64 -1 y) (+.f64 (/.f64 x y) (/.f64 x (*.f64 y y)))))
12.0ms	(+.f64 (/.f64 x y) (/.f64 x (*.f64 y y)))
5.0ms	(/.f64 x (*.f64 y y))

series29.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 (/.f64 -1 y) (+.f64 (/.f64 x y) (/.f64 x (*.f64 y y))))
9.0ms	(log.f64 (+.f64 (/.f64 -1 y) (+.f64 (/.f64 x y) (/.f64 x (*.f64 y y)))))
8.0ms	(+.f64 (/.f64 x y) (/.f64 x (*.f64 y y)))
6.0ms	(/.f64 x (*.f64 y y))

simplify74.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4956	1266
1	4956	1266

prune67.0ms

Filtered

67 candidates to 89 candidates (-32.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	88	5	93

Merged error: 0.1b

Counts

93 → 5

regimes169.0ms

Accuracy

96% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 17.9b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	158	40
1	158	40

end0.0ms

sample1.3s

Algorithm

intervals

Results

279.0ms	5683×	body	80	valid
215.0ms	859×	body	1280	valid
144.0ms	752×	body	1280	nan
140.0ms	767×	body	640	valid
118.0ms	813×	body	640	nan
62.0ms	463×	body	320	valid
50.0ms	447×	body	320	nan
20.0ms	228×	body	160	valid
18.0ms	243×	body	160	nan
15.0ms	377×	body	80	nan

Details

analyze627.0ms

sample44.0ms

simplify176.0ms

prune2.0ms

localize8.0ms

rewrite50.0ms

series31.0ms

simplify39.0ms

prune99.0ms

localize10.0ms

rewrite37.0ms

series34.0ms

simplify51.0ms

prune77.0ms

localize16.0ms

rewrite110.0ms

series279.0ms

simplify71.0ms

prune129.0ms

localize10.0ms

rewrite57.0ms

series29.0ms

simplify74.0ms

prune67.0ms

regimes169.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample1.3s

Profiling