Details

sample83.0ms

Algorithm

intervals

Results

28.0ms	376×	body	80	valid
24.0ms	405×	body	80	nan

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5251	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: 5.3b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
4.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `associate-+l+` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

12.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(* (- x 0.5) (log x))
7.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series115.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
23.0ms	(* (- x 0.5) (log x))
35.0ms	(- (* (- x 0.5) (log x)) x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify60.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5013	1429

prune239.0ms

Filtered

88 candidates to 110 candidates (-25.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	95	15	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	15	111

Merged error: 0.0b

Counts

111 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
13.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series89.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt x)
22.0ms	(cbrt x)
21.0ms	(cbrt x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify52.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4975	772
1	4975	772

prune158.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	75	14	89

Merged error: 0.0b

Counts

89 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
4.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-prod` `associate-+l+`
12×	`associate-+r+`
9×	`times-frac`
8×	`associate-*l/`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

15.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series172.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
21.0ms	(cbrt x)
21.0ms	(cbrt x)
21.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify68.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4948	1461
1	4948	1461

prune240.0ms

Filtered

97 candidates to 115 candidates (-18.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	117	12	129

Merged error: 0.0b

Counts

129 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (log (* (cbrt -1) (cbrt (/ 1 (/ -1 x))))) (- (* x 3) 1.5)) x)
0.4b	(* (log (* (cbrt -1) (cbrt (/ 1 (/ -1 x))))) (- (* x 3) 1.5))
0.6b	(cbrt (/ 1 (/ -1 x)))
4.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
51×	`add-sqr-sqrt`
49×	`add-cube-cbrt` `*-un-lft-identity`
44×	`cbrt-prod`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `add-log-exp`
5×	`sub-neg` `div-inv`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
3×	`pow1/3` `associate-r` `pow-prod-down` `associate-/r` `log-pow` `associate-/l`
2×	`flip3--` `associate-*r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `cbrt-div` `frac-2neg` `flip3-+` `diff-log` `div-exp` `prod-exp` `clear-num` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

14.0ms	(- (* (log (* (cbrt -1) (cbrt (/ 1 (/ -1 x))))) (- (* x 3) 1.5)) x)
16.0ms	(* (log (* (cbrt -1) (cbrt (/ 1 (/ -1 x))))) (- (* x 3) 1.5))
5.0ms	(cbrt (/ 1 (/ -1 x)))
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series293.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(- (* (log (* (cbrt -1) (cbrt (/ 1 (/ -1 x))))) (- (* x 3) 1.5)) x)
87.0ms	(* (log (* (cbrt -1) (cbrt (/ 1 (/ -1 x))))) (- (* x 3) 1.5))
24.0ms	(cbrt (/ 1 (/ -1 x)))
26.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify66.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5036	1919

prune236.0ms

Filtered

85 candidates to 137 candidates (-61.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	137	12	149

Merged error: 0.0b

Counts

149 → 12

regimes676.0ms

Accuracy

95.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 6.0b

bsearch19.0ms

Steps

Iters	Range		Point
5	7.438075474013355e+18	1.901336874005294e+19	1.607373441556529e+19

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	64
1	60	64

end0.0ms

sample2.3s

Algorithm

intervals

Results

797.0ms	11696×	body	80	valid
701.0ms	11591×	body	80	nan

Details

sample83.0ms

simplify76.0ms

prune7.0ms

localize16.0ms

rewrite40.0ms

series115.0ms

simplify60.0ms

prune239.0ms

localize24.0ms

rewrite18.0ms

series89.0ms

simplify52.0ms

prune158.0ms

localize21.0ms

rewrite32.0ms

series172.0ms

simplify68.0ms

prune240.0ms

localize27.0ms

rewrite51.0ms

series293.0ms

simplify66.0ms

prune236.0ms

regimes676.0ms

bsearch19.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling