Details

analyze445.0ms

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

sample34.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
3.0ms	38×	body	80	invalid
1.0ms	16×	body	80	nan

simplify131.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (127.0ms)

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: 5.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x) 0.91893853320467)
0.1b	(-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x)
0.2b	(*.f64 (-.f64 x 0.5) (log.f64 x))
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) 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:

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

series108.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x) 0.91893853320467)
29.0ms	(-.f64 (*.f64 (-.f64 x 0.5) (log.f64 x)) x)
19.0ms	(*.f64 (-.f64 x 0.5) (log.f64 x))
27.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify49.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5016	1424

prune201.0ms

Filtered

86 candidates to 108 candidates (-25.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	96	12	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	12	109

Merged error: 4.8b

Counts

109 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite18.0ms

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)

series84.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt.f64 x)
18.0ms	(cbrt.f64 x)
19.0ms	(cbrt.f64 x)
28.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify30.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4949	763
1	4949	763

prune136.0ms

Filtered

64 candidates to 74 candidates (-15.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	74	12	86

Merged error: 4.8b

Counts

86 → 12

localize23.0ms

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)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite39.0ms

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)
16.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series171.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+.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)
18.0ms	(cbrt.f64 x)
28.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5880	1434

prune218.0ms

Filtered

106 candidates to 115 candidates (-8.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	115	12	127

Merged error: 4.8b

Counts

127 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (log.f64 x) (-.f64 x 0.5))
0.2b	(*.f64 (log.f64 x) (-.f64 x 0.5))
0.5b	(.f64 (sqrt.f64 (-.f64 (.f64 (log.f64 x) (-.f64 x 0.5)) x)) (sqrt.f64 (-.f64 (*.f64 (log.f64 x) (-.f64 x 0.5)) x)))
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
25×	`pow1_binary64`
24×	`add-cube-cbrt_binary64`
18×	`sqrt-prod_binary64`
16×	`associate-r_binary64`
14×	`associate-l_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
9×	`times-frac_binary64`
8×	`pow1/2_binary64` `flip3--_binary64` `swap-sqr_binary64` `sqrt-pow1_binary64` `flip--_binary64`
6×	`associate-*r/_binary64` `unswap-sqr_binary64`
5×	`pow-prod-down_binary64` `pow-prod-up_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `frac-times_binary64`
3×	`associate-/r_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l_binary64` `pow-sqr_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64` `log-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-*l/_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow2_binary64`

Counts

4 → 136

Calls

4 calls:

7.0ms	(*.f64 (log.f64 x) (-.f64 x 0.5))
7.0ms	(*.f64 (log.f64 x) (-.f64 x 0.5))
19.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 (log.f64 x) (-.f64 x 0.5)) x)) (sqrt.f64 (-.f64 (*.f64 (log.f64 x) (-.f64 x 0.5)) x)))
12.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series96.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(*.f64 (log.f64 x) (-.f64 x 0.5))
19.0ms	(*.f64 (log.f64 x) (-.f64 x 0.5))
32.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 (log.f64 x) (-.f64 x 0.5)) x)) (sqrt.f64 (-.f64 (*.f64 (log.f64 x) (-.f64 x 0.5)) x)))
27.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5017	1854

prune162.0ms

Filtered

91 candidates to 148 candidates (-62.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	148	12	160

Merged error: 4.8b

Counts

160 → 12

regimes443.0ms

Accuracy

0% (2.3b remaining)

Error of 6.3b against oracle of 4.0b and baseline of 6.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	36
1	60	36

end0.0ms

sample942.0ms

Algorithm

intervals

Results

576.0ms	8000×	body	80	valid
83.0ms	1183×	body	80	invalid
51.0ms	741×	body	80	nan

Details

analyze445.0ms

sample34.0ms

simplify131.0ms

prune7.0ms

localize18.0ms

rewrite45.0ms

series108.0ms

simplify49.0ms

prune201.0ms

localize25.0ms

rewrite18.0ms

series84.0ms

simplify30.0ms

prune136.0ms

localize23.0ms

rewrite39.0ms

series171.0ms

simplify55.0ms

prune218.0ms

localize21.0ms

rewrite50.0ms

series96.0ms

simplify59.0ms

prune162.0ms

regimes443.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample942.0ms

Profiling