Details

analyze454.0ms

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

sample44.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
5.0ms	21×	body	80	nan
2.0ms	26×	body	80	invalid

simplify138.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	5577	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: 7.5b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x) 0.91893853320467)
0.2b	(*.f64 (-.f64 x 0.5) (log.f64 x))
0.2b	(-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x)
6.9b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite46.0ms

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:

14.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x) 0.91893853320467)
8.0ms	(*.f64 (-.f64 x 0.5) (log.f64 x))
8.0ms	(-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series113.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x) 0.91893853320467)
19.0ms	(*.f64 (-.f64 x 0.5) (log.f64 x))
31.0ms	(-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x)
28.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify54.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5016	1424

prune192.0ms

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

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
6.9b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) 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 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series90.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt.f64 x)
22.0ms	(cbrt.f64 x)
19.0ms	(cbrt.f64 x)
29.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify33.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4949	763
1	4949	763

prune141.0ms

Filtered

64 candidates to 74 candidates (-15.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	74	10	84

Merged error: 4.3b

Counts

84 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (-.f64 x 0.5) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 0.5) (log.f64 (cbrt.f64 x))))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
6.9b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod_binary64`
30×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
24×	`associate-+l+_binary64` `cbrt-prod_binary64`
12×	`associate-+r+_binary64`
9×	`times-frac_binary64`
8×	`associate-*l/_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `flip3--_binary64` `frac-add_binary64` `flip--_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1/3_binary64` `flip-+_binary64`
1×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 103

Calls

4 calls:

16.0ms	(+.f64 (.f64 (-.f64 x 0.5) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 0.5) (log.f64 (cbrt.f64 x))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
14.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series174.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+.f64 (.f64 (-.f64 x 0.5) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 0.5) (log.f64 (cbrt.f64 x))))
19.0ms	(cbrt.f64 x)
19.0ms	(cbrt.f64 x)
31.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify60.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5880	1434

prune224.0ms

Filtered

104 candidates to 115 candidates (-10.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	115	10	125

Merged error: 4.3b

Counts

125 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 (log.f64 (cbrt.f64 x)) (-.f64 (.f64 x 3) 1.5)) x)
0.4b	(.f64 (log.f64 (cbrt.f64 x)) (-.f64 (.f64 x 3) 1.5))
0.6b	(cbrt.f64 x)
6.9b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`sub-neg_binary64` `associate-l_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-/l_binary64` `cbrt-prod_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-*r/_binary64` `pow1/3_binary64` `log-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

8.0ms	(-.f64 (.f64 (log.f64 (cbrt.f64 x)) (-.f64 (.f64 x 3) 1.5)) x)
10.0ms	(.f64 (log.f64 (cbrt.f64 x)) (-.f64 (.f64 x 3) 1.5))
1.0ms	(cbrt.f64 x)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series225.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(-.f64 (.f64 (log.f64 (cbrt.f64 x)) (-.f64 (.f64 x 3) 1.5)) x)
66.0ms	(.f64 (log.f64 (cbrt.f64 x)) (-.f64 (.f64 x 3) 1.5))
19.0ms	(cbrt.f64 x)
29.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4924	1184
1	4924	1184

prune115.0ms

Filtered

71 candidates to 89 candidates (-25.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	89	10	99

Merged error: 4.3b

Counts

99 → 10

regimes546.0ms

Accuracy

86.3% (0.3b remaining)

Error of 4.2b against oracle of 3.9b and baseline of 6.1b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	119	78
1	119	78

end0.0ms

sample886.0ms

Algorithm

intervals

Results

537.0ms	8000×	body	80	valid
84.0ms	1262×	body	80	invalid
43.0ms	718×	body	80	nan

Details

analyze454.0ms

sample44.0ms

simplify138.0ms

prune7.0ms

localize16.0ms

rewrite46.0ms

series113.0ms

simplify54.0ms

prune192.0ms

localize29.0ms

rewrite19.0ms

series90.0ms

simplify33.0ms

prune141.0ms

localize22.0ms

rewrite36.0ms

series174.0ms

simplify60.0ms

prune224.0ms

localize19.0ms

rewrite35.0ms

series225.0ms

simplify61.0ms

prune115.0ms

regimes546.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample886.0ms

Profiling