Details

sample67.0ms

Algorithm

intervals

Results

24.0ms	375×	body	80	valid
20.0ms	359×	body	80	nan

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	12
1	84	12
2	245	12
3	581	12
4	1280	12
5	2462	12
6	5001	12

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 5.2b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (- x 0.5) (log x)) x)
0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(* (- x 0.5) (log x))
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite44.0ms

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:

7.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
8.0ms	(* (- x 0.5) (log x))
16.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

420.0ms	(- (* (- x 0.5) (log x)) x)
607.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
253.0ms	(* (- x 0.5) (log x))
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	501	839
1	1642	776
2	5001	763

prune365.0ms

Filtered

110 candidates to 84 candidates (76.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	97	13	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 4.2b

Counts

111 → 13

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)
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite35.0ms

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

series1.2s

Counts

4 → 12

Calls

4 calls:

777.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
177.0ms	(cbrt x)
180.0ms	(cbrt x)
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify75.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	624	1080
1	2446	943
2	5001	919

prune530.0ms

Filtered

115 candidates to 104 candidates (90.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	115	13	128

Merged error: 4.2b

Counts

128 → 13

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite22.0ms

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

series616.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt x)
181.0ms	(cbrt x)
182.0ms	(cbrt x)
79.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify107.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	212	462
1	697	420
2	3321	413
3	5001	410

prune419.0ms

Filtered

74 candidates to 62 candidates (83.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	74	13	87

Merged error: 4.2b

Counts

87 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 0.5) (log (sqrt x)))
0.2b	(- (* (log (sqrt x)) (- x 0.5)) x)
0.3b	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

9.0ms	(* (- x 0.5) (log (sqrt x)))
11.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
18.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
13.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series525.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (- x 0.5) (log (sqrt x)))
160.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
178.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify77.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	729	1414
1	2783	1316
2	5002	1289

prune414.0ms

Filtered

125 candidates to 91 candidates (72.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	125	13	138

Merged error: 4.2b

Counts

138 → 13

regimes389.0ms

Accuracy

0% (1.2b remaining)

Error of 6.0b against oracle of 4.7b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	26
1	41	26

end0.0ms

sample2.0s

Algorithm

intervals

Results

790.0ms	11779×	body	80	valid
697.0ms	11764×	body	80	nan

Details

sample67.0ms

simplify50.0ms

prune3.0ms

localize16.0ms

rewrite44.0ms

series1.4s

simplify50.0ms

prune365.0ms

localize21.0ms

rewrite35.0ms

series1.2s

simplify75.0ms

prune530.0ms

localize31.0ms

rewrite22.0ms

series616.0ms

simplify107.0ms

prune419.0ms

localize19.0ms

rewrite55.0ms

series525.0ms

simplify77.0ms

prune414.0ms

regimes389.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.0s

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