Details

sample60.0ms

Algorithm

intervals

Results

20.0ms	381×	body	80	valid
17.0ms	375×	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

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 5.7b

Counts

2 → 1

localize17.0ms

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)
5.3b	(/ (+ (* (- (* (+ 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:

17.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(* (- x 0.5) (log x))
12.0ms	(- (* (- x 0.5) (log x)) x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

437.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
276.0ms	(* (- x 0.5) (log x))
429.0ms	(- (* (- x 0.5) (log x)) x)
91.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (43.0ms)

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

prune337.0ms

Filtered

138 candidates to 87 candidates (37.0%)

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: 4.5b

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)
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite30.0ms

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)

series658.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
191.0ms	(cbrt x)
185.0ms	(cbrt x)
100.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify105.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (96.0ms)

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

prune322.0ms

Filtered

94 candidates to 62 candidates (34.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 4.5b

Counts

105 → 10

localize22.0ms

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)
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

123×	`*-un-lft-identity`
44×	`associate-l`
41×	`distribute-lft-out`
39×	`add-sqr-sqrt`
38×	`associate-r`
36×	`log-prod`
35×	`add-cube-cbrt`
30×	`distribute-rgt-in` `distribute-lft-in`
24×	`cbrt-prod` `associate-+l+` `times-frac`
18×	`distribute-lft-out--`
13×	`distribute-rgt-out`
12×	`pow1` `associate-+r+`
10×	`log-pow`
8×	`associate-l/` `associate-/l`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`flip3--` `pow1/3` `frac-add` `flip--`
3×	`associate-/r*`
2×	`flip3-+` `*-commutative` `flip-+` `associate-/l/` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 152

Calls

4 calls:

43.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
23.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.5s

Counts

4 → 12

Calls

4 calls:

828.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
372.0ms	(cbrt x)
193.0ms	(cbrt x)
93.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify110.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	711	1402
1	3294	1196
2	5002	1158

prune555.0ms

Filtered

164 candidates to 113 candidates (31.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	164	10	174

Merged error: 4.5b

Counts

174 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.1b	(- (sqrt (* (- x 0.5) (log x))) (sqrt x))
0.5b	(* (+ (sqrt (* (- x 0.5) (log x))) (sqrt x)) (- (sqrt (* (- x 0.5) (log x))) (sqrt x)))
5.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

8.0ms	(* (- x 0.5) (log x))
15.0ms	(- (sqrt (* (- x 0.5) (log x))) (sqrt x))
36.0ms	(* (+ (sqrt (* (- x 0.5) (log x))) (sqrt x)) (- (sqrt (* (- x 0.5) (log x))) (sqrt x)))
27.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series882.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(* (- x 0.5) (log x))
122.0ms	(- (sqrt (* (- x 0.5) (log x))) (sqrt x))
405.0ms	(* (+ (sqrt (* (- x 0.5) (log x))) (sqrt x)) (- (sqrt (* (- x 0.5) (log x))) (sqrt x)))
95.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1264	2137
1	5002	1911

prune487.0ms

Filtered

156 candidates to 94 candidates (39.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	156	10	166

Merged error: 4.5b

Counts

166 → 10

regimes323.0ms

Accuracy

66.2% (0.4b remaining)

Error of 5.1b against oracle of 4.6b and baseline of 5.9b

bsearch102.0ms

Steps

Iters	Range		Point
9	6.6320067326423015e+100	6.571327383332508e+105	5.015654428537482e+105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	43
1	63	43

end0.0ms

sample1.7s

Algorithm

intervals

Results

607.0ms	11690×	body	80	valid
549.0ms	11791×	body	80	nan