Details

analyze474.0ms

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
0%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

sample40.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
3.0ms	38×	body	80	invalid
1.0ms	18×	body	80	nan

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4954	36
1	4954	36

prune14.0ms

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: 6.5b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.2b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
6.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_5068` `add-sqr-sqrt_binary64_5053`
20×	`add-cube-cbrt_binary64_5039`
18×	`log-prod_binary64_4986`
12×	`associate--l+_binary64_5124`
11×	`add-log-exp_binary64_5033`
9×	`distribute-lft-in_binary64_5110` `times-frac_binary64_5063` `distribute-rgt-in_binary64_5111`
8×	`add-cbrt-cube_binary64_5040` `add-exp-log_binary64_5032`
7×	`pow1_binary64_5014` `associate-+l+_binary64_5120`
5×	`associate-l_binary64_5128`
4×	`associate-r_binary64_5127`
3×	`associate-/l_binary64_5132` `associate-/r_binary64_5131`
2×	`associate-/l/_binary64_5134` `associate-*l/_binary64_5130` `diff-log_binary64_4984` `flip3-+_binary64_5066` `flip-+_binary64_5093` `flip3--_binary64_5067` `flip--_binary64_5094` `sum-log_binary64_4983` `sub-neg_binary64_5072`
1×	`pow-prod-down_binary64_4995` `log-pow_binary64_4989` `associate-+l-_binary64_5122` `cbrt-undiv_binary64_5038` `frac-2neg_binary64_5061` `distribute-lft-out_binary64_5112` `clear-num_binary64_5071` `distribute-lft-out--_binary64_5113` `prod-exp_binary64_5019` `unswap-sqr_binary64_5096` `difference-of-squares_binary64_5097` `cbrt-unprod_binary64_5037` `div-exp_binary64_5021` `div-inv_binary64_5069` `*-commutative_binary64_5136` `+-commutative_binary64_5135`

Counts

4 → 96

Calls

4 calls:

11.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series492.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
155.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
162.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
77.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify79.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4946	2145
1	4946	2145

prune569.0ms

Filtered

88 candidates to 108 candidates (-22.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	11	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Merged error: 4.3b

Counts

109 → 11

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
6.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_5068` `add-sqr-sqrt_binary64_5053` `add-cube-cbrt_binary64_5039`
9×	`cbrt-prod_binary64_5035` `times-frac_binary64_5063`
6×	`add-cbrt-cube_binary64_5040` `add-exp-log_binary64_5032`
4×	`add-log-exp_binary64_5033` `pow1_binary64_5014`
3×	`associate-/l_binary64_5132` `pow1/3_binary64_5006` `associate-/r_binary64_5131`
2×	`associate-/l/_binary64_5134`
1×	`cbrt-undiv_binary64_5038` `flip3-+_binary64_5066` `frac-2neg_binary64_5061` `flip-+_binary64_5093` `clear-num_binary64_5071` `div-exp_binary64_5021` `div-inv_binary64_5069`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
12.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series333.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt.f64 x)
86.0ms	(cbrt.f64 x)
85.0ms	(cbrt.f64 x)
76.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify72.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5034	1155

prune636.0ms

Filtered

64 candidates to 74 candidates (-15.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	74	11	85

Merged error: 4.3b

Counts

85 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.2b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
6.1b	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_5053`
25×	`*-un-lft-identity_binary64_5068`
20×	`add-cube-cbrt_binary64_5039`
18×	`log-prod_binary64_4986`
17×	`associate-r_binary64_5127`
13×	`add-exp-log_binary64_5032`
12×	`associate--l+_binary64_5124`
11×	`add-cbrt-cube_binary64_5040` `add-log-exp_binary64_5033` `times-frac_binary64_5063`
9×	`distribute-lft-in_binary64_5110` `pow1_binary64_5014` `distribute-rgt-in_binary64_5111`
8×	`associate-l_binary64_5128`
7×	`associate-+l+_binary64_5120`
4×	`associate-*l/_binary64_5130` `prod-exp_binary64_5019` `unswap-sqr_binary64_5096`
3×	`flip3-+_binary64_5066` `flip-+_binary64_5093` `cbrt-unprod_binary64_5037`
2×	`pow-prod-down_binary64_4995` `diff-log_binary64_4984` `flip3--_binary64_5067` `frac-times_binary64_5060` `flip--_binary64_5094` `sum-log_binary64_4983` `sub-neg_binary64_5072` `*-commutative_binary64_5136`
1×	`log-pow_binary64_4989` `associate-+l-_binary64_5122` `cbrt-undiv_binary64_5038` `distribute-lft-out_binary64_5112` `un-div-inv_binary64_5070` `distribute-lft-out--_binary64_5113` `rec-exp_binary64_5020` `difference-of-squares_binary64_5097` `associate-*r/_binary64_5129` `div-exp_binary64_5021` `div-inv_binary64_5069` `+-commutative_binary64_5135`

Counts

4 → 106

Calls

4 calls:

7.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
11.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
17.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

series496.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
154.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
157.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
86.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

simplify58.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5118	2291

prune549.0ms

Filtered

92 candidates to 118 candidates (-28.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Merged error: 4.3b

Counts

129 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) x)
0.2b	(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (log.f64 x) (-.f64 x 1/2)) x)) (sqrt.f64 (-.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) x))) 2069265617858471/2251799813685248)
0.5b	(.f64 (sqrt.f64 (-.f64 (.f64 (log.f64 x) (-.f64 x 1/2)) x)) (sqrt.f64 (-.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) x)))
6.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_5053`
20×	`*-un-lft-identity_binary64_5068` `add-cube-cbrt_binary64_5039`
19×	`pow1_binary64_5014`
18×	`sqrt-prod_binary64_5047`
12×	`sqrt-div_binary64_5048`
9×	`times-frac_binary64_5063`
8×	`add-cbrt-cube_binary64_5040` `swap-sqr_binary64_5095` `add-log-exp_binary64_5033` `pow1/2_binary64_5004` `add-exp-log_binary64_5032` `sqrt-pow1_binary64_5049`
7×	`flip3--_binary64_5067` `flip--_binary64_5094`
6×	`associate-l_binary64_5128` `associate-r_binary64_5127`
5×	`pow-prod-up_binary64_4994`
4×	`unswap-sqr_binary64_5096` `frac-times_binary64_5060`
3×	`pow-prod-down_binary64_4995` `associate-/l_binary64_5132` `associate-/r_binary64_5131` `pow-sqr_binary64_5101` `sub-neg_binary64_5072`
2×	`associate-/l/_binary64_5134` `associate-l/_binary64_5130` `associate--l+_binary64_5124` `flip3-+_binary64_5066` `flip-+_binary64_5093` `associate-r/_binary64_5129`
1×	`sqrt-unprod_binary64_5051` `cbrt-undiv_binary64_5038` `diff-log_binary64_4984` `distribute-lft-in_binary64_5110` `frac-2neg_binary64_5061` `clear-num_binary64_5071` `pow2_binary64_5005` `rem-square-sqrt_binary64_5055` `prod-exp_binary64_5019` `distribute-rgt-in_binary64_5111` `cbrt-unprod_binary64_5037` `div-exp_binary64_5021` `sum-log_binary64_4983` `div-inv_binary64_5069` `pow-plus_binary64_5009` `*-commutative_binary64_5136` `+-commutative_binary64_5135`

Counts

4 → 110

Calls

4 calls:

7.0ms	(-.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) x)
22.0ms	(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (log.f64 x) (-.f64 x 1/2)) x)) (sqrt.f64 (-.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) x))) 2069265617858471/2251799813685248)
19.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 (log.f64 x) (-.f64 x 1/2)) x)) (sqrt.f64 (-.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) x)))
12.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series559.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(-.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) x)
161.0ms	(+.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (log.f64 x) (-.f64 x 1/2)) x)) (sqrt.f64 (-.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) x))) 2069265617858471/2251799813685248)
161.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 (log.f64 x) (-.f64 x 1/2)) x)) (sqrt.f64 (-.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)) x)))
78.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify112.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5517	2815

prune433.0ms

Filtered

79 candidates to 122 candidates (-54.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	122	9	131

Merged error: 4.3b

Counts

131 → 9

regimes873.0ms

Accuracy

89.2% (0.2b remaining)

Error of 4.3b against oracle of 4.0b and baseline of 6.2b

bsearch38.0ms

Steps

Iters	Range		Point
7	6446025310009729/34359738368	5373955542272701/536870912	5706248.294004319

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	115	95
1	115	95

end0.0ms

sample1.0s

Algorithm

intervals

Results

582.0ms	8000×	body	80	valid
87.0ms	1172×	body	80	invalid
44.0ms	714×	body	80	nan

Details

analyze474.0ms

sample40.0ms

simplify113.0ms

prune14.0ms

localize27.0ms

rewrite46.0ms

series492.0ms

simplify79.0ms

prune569.0ms

localize37.0ms

rewrite20.0ms

series333.0ms

simplify72.0ms

prune636.0ms

localize36.0ms

rewrite47.0ms

series496.0ms

simplify58.0ms

prune549.0ms

localize32.0ms

rewrite64.0ms

series559.0ms

simplify112.0ms

prune433.0ms

regimes873.0ms

bsearch38.0ms

simplify4.0ms

end0.0ms

sample1.0s

Profiling