Details

sample63.0ms

Algorithm

intervals

Results

21.0ms	376×	body	80	valid
18.0ms	368×	body	80	nan

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 5.8b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

18.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(* (- x 0.5) (log x))
13.0ms	(- (* (- x 0.5) (log x)) x)
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

463.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
281.0ms	(* (- x 0.5) (log x))
473.0ms	(- (* (- x 0.5) (log x)) x)
99.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	505	1052
1	1641	989
2	5002	976

prune345.0ms

Filtered

138 candidates to 87 candidates (63.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	127	11	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	11	139

Merged error: 4.2b

Counts

139 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
24.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series681.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(cbrt x)
203.0ms	(cbrt x)
188.0ms	(cbrt x)
96.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify114.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	212	622
1	697	575
2	3316	568
3	5001	565

prune514.0ms

Filtered

94 candidates to 62 candidates (66.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	94	11	105

Merged error: 4.2b

Counts

105 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.4b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`frac-times`
14×	`associate-l`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
10×	`flip3-+` `flip-+` `associate-/l*`
9×	`cbrt-prod` `associate-r/` `associate-/r` `add-cbrt-cube`
6×	`pow1` `distribute-lft-out`
4×	`prod-exp` `clear-num` `add-log-exp`
3×	`frac-2neg` `pow1/3` `un-div-inv` `distribute-lft-out--` `unswap-sqr`
2×	`div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
30.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series641.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt x)
188.0ms	(cbrt x)
177.0ms	(cbrt x)
89.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify67.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	401	1013
1	2012	930
2	5001	890

prune428.0ms

Filtered

116 candidates to 77 candidates (66.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	116	11	127

Merged error: 4.2b

Counts

127 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.2b	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
21.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

series680.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt x)
189.0ms	(cbrt x)
180.0ms	(cbrt x)
127.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

simplify133.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	237	593
1	853	543
2	4142	529
3	5002	526

prune295.0ms

Filtered

94 candidates to 62 candidates (66.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	95	10	105

Merged error: 3.3b

Counts

105 → 10

regimes426.0ms

Accuracy

88.8% (0.4b remaining)

Error of 3.3b against oracle of 2.9b and baseline of 6.3b

bsearch109.0ms

Steps

Iters	Range		Point
9	2.325493406994118e+132	2.366852198527526e+141	1.7594265253874347e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	43
1	61	43

end0.0ms

sample1.7s

Algorithm

intervals

Results

619.0ms	11614×	body	80	valid
525.0ms	11479×	body	80	nan