Details

analyze463.0ms

Algorithm: search

sample33.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
3.0ms	44×	body	80	invalid
1.0ms	22×	body	80	nan

simplify54.0ms

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

prune4.0ms

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: 6.2b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite38.0ms

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:

10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(* (- x 0.5) (log x))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series121.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
40.0ms	(- (* (- x 0.5) (log x)) x)
22.0ms	(* (- x 0.5) (log x))
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	543	875
1	1816	820
2	5001	763

prune219.0ms

Filtered

83 candidates to 110 candidates (-32.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	12	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	12	111

Merged error: 5.2b

Counts

111 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (sqrt x)) (- x 0.5))
0.2b	(* (- x 0.5) (log (sqrt x)))
0.2b	(- (* (log (sqrt x)) (- x 0.5)) x)
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

7.0ms	(* (log (sqrt x)) (- x 0.5))
9.0ms	(* (- x 0.5) (log (sqrt x)))
7.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series50.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (log (sqrt x)) (- x 0.5))
8.0ms	(* (- x 0.5) (log (sqrt x)))
13.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify60.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	539	1044
1	2197	978
2	5001	964

prune235.0ms

Filtered

89 candidates to 123 candidates (-38.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	123	12	135

Merged error: 5.2b

Counts

135 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite16.0ms

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)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series92.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
22.0ms	(cbrt x)
25.0ms	(cbrt x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify95.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	231	498
1	697	460
2	3102	429
3	5001	426

prune154.0ms

Filtered

59 candidates to 74 candidates (-25.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	9	10
Picked	1	0	1
Done	1	0	1
Total	76	10	86

Merged error: 5.2b

Counts

86 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
5.1b	(pow x 1/3)
5.7b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log`
6×	`cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-/r` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(pow x 1/3)
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series93.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
27.0ms	(cbrt x)
21.0ms	(pow x 1/3)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify37.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	283	499
1	1126	444
2	5001	409

prune155.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 5.2b

Counts

91 → 9

regimes425.0ms

Accuracy

0% (1.2b remaining)

Error of 5.9b against oracle of 4.7b and baseline of 5.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	19
1	35	19

end0.0ms

analyze452.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

780.0ms	8000×	body	80	valid
88.0ms	1247×	body	80	invalid
46.0ms	734×	body	80	nan

Details

analyze463.0ms

sample33.0ms

simplify54.0ms

prune4.0ms

localize20.0ms

rewrite38.0ms

series121.0ms

simplify53.0ms

prune219.0ms

localize20.0ms

rewrite38.0ms

series50.0ms

simplify60.0ms

prune235.0ms

localize26.0ms

rewrite16.0ms

series92.0ms

simplify95.0ms

prune154.0ms

localize33.0ms

rewrite18.0ms

series93.0ms

simplify37.0ms

prune155.0ms

regimes425.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze452.0ms

sample1.1s

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