Details

analyze469.0ms

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

sample33.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
3.0ms	43×	body	80	invalid
1.0ms	21×	body	80	nan

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4926	24
1	4926	24

prune7.0ms

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: 6.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
5.7b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
12×	`associate--l+_binary64`
11×	`add-log-exp_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64` `associate-+l+_binary64`
5×	`associate-l_binary64`
4×	`associate-r_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 96

Calls

4 calls:

12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
9.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series98.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
16.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
29.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
26.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4891	1411
1	4891	1411

prune153.0ms

Filtered

87 candidates to 108 candidates (-24.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 4.3b

Counts

109 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.3b	(+.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 2069265617858471/2251799813685248 x))
5.7b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `pow1_binary64` `times-frac_binary64`
8×	`associate-l_binary64` `associate-*l/_binary64`
7×	`associate-r_binary64`
6×	`flip3--_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`
4×	`frac-add_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `associate-+r-_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64`

Counts

4 → 102

Calls

4 calls:

10.0ms	(.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)
10.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
11.0ms	(+.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 2069265617858471/2251799813685248 x))
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series77.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)
16.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
26.0ms	(+.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 2069265617858471/2251799813685248 x))
25.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5256	1586

prune120.0ms

Filtered

89 candidates to 114 candidates (-28.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	114	10	124

Merged error: 4.3b

Counts

124 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
5.7b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64` `cbrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `pow1/3_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series76.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt.f64 x)
16.0ms	(cbrt.f64 x)
16.0ms	(cbrt.f64 x)
25.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify60.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4921	761
1	4921	761

prune94.0ms

Filtered

64 candidates to 74 candidates (-15.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	74	10	84

Merged error: 4.3b

Counts

84 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
5.9b	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
17×	`associate-r_binary64`
15×	`add-exp-log_binary64`
12×	`associate--l+_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
9×	`pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
8×	`associate-l_binary64`
7×	`associate-+l+_binary64`
5×	`prod-exp_binary64`
4×	`unswap-sqr_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `cbrt-unprod_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `log-pow_binary64` `associate-+l-_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
11.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
19.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

series97.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
16.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
26.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
26.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

simplify55.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5171	1520

prune99.0ms

Filtered

90 candidates to 119 candidates (-32.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	119	10	129

Merged error: 4.3b

Counts

129 → 10

regimes414.0ms

Accuracy

80.9% (0.4b remaining)

Error of 4.3b against oracle of 3.8b and baseline of 6.0b

bsearch23.0ms

Steps

Iters	Range		Point
7	5.446931646166542e+66	1.026543643267144e+68	7.878993829516815e+66

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	106	66
1	106	66

end0.0ms

sample1.1s

Algorithm

intervals

Results

669.0ms	8000×	body	80	valid
104.0ms	1255×	body	80	invalid
60.0ms	780×	body	80	nan

Details

analyze469.0ms

sample33.0ms

simplify89.0ms

prune7.0ms

localize16.0ms

rewrite45.0ms

series98.0ms

simplify53.0ms

prune153.0ms

localize17.0ms

rewrite48.0ms

series77.0ms

simplify55.0ms

prune120.0ms

localize26.0ms

rewrite19.0ms

series76.0ms

simplify60.0ms

prune94.0ms

localize19.0ms

rewrite55.0ms

series97.0ms

simplify55.0ms

prune99.0ms

regimes414.0ms

bsearch23.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling