Details

sample57.0ms

Algorithm

intervals

Results

18.0ms	345×	body	80	valid
16.0ms	357×	body	80	nan

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (17.0ms)

Iter	Nodes	Cost
0	40	12
1	92	12
2	269	12
3	669	12
4	1565	11
5	2855	11
6	5001	11

prune13.0ms

Filtered

1 candidates to 1 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: 3.1b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
2.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `prod-diff` `associate-/r` `associate-/l`
2×	`flip3--` `associate-*l/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

7.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series269.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
40.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
121.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	432	812
1	1472	709
2	5003	707

prune342.0ms

Filtered

93 candidates to 73 candidates (78.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 1.8b

Counts

95 → 9

localize17.0ms

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))
2.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`associate-+l+` `add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `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` `fma-neg` `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 → 116

Calls

4 calls:

8.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(* (- x 0.5) (log x))
14.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

416.0ms	(- (* (- x 0.5) (log x)) x)
414.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
248.0ms	(* (- x 0.5) (log x))
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify68.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	576	925
1	2275	825
2	5001	802

prune431.0ms

Filtered

128 candidates to 102 candidates (79.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	125	12	137

Merged error: 1.7b

Counts

137 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite17.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 70

Calls

4 calls:

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

series609.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt x)
178.0ms	(cbrt x)
172.0ms	(cbrt x)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify102.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	223	484
1	699	441
2	3468	432
3	5001	425

prune408.0ms

Filtered

82 candidates to 72 candidates (87.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	82	12	94

Merged error: 1.7b

Counts

94 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 0.5) (log (sqrt x)))
0.3b	(fma (log (sqrt x)) (- x 0.5) (- 0.91893853320467 x))
0.3b	(+ (* (- x 0.5) (log (sqrt x))) (fma (log (sqrt x)) (- x 0.5) (- 0.91893853320467 x)))
2.9b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`log-prod` `*-un-lft-identity`
22×	`add-cube-cbrt`
12×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `sqrt-prod`
9×	`times-frac`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `log-pow` `associate-/l`
2×	`flip3-+` `associate-*l/` `flip-+` `fma-udef` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `flip3--` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

8.0ms	(* (- x 0.5) (log (sqrt x)))
1.0ms	(fma (log (sqrt x)) (- x 0.5) (- 0.91893853320467 x))
9.0ms	(+ (* (- x 0.5) (log (sqrt x))) (fma (log (sqrt x)) (- x 0.5) (- 0.91893853320467 x)))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series573.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (- x 0.5) (log (sqrt x)))
116.0ms	(fma (log (sqrt x)) (- x 0.5) (- 0.91893853320467 x))
261.0ms	(+ (* (- x 0.5) (log (sqrt x))) (fma (log (sqrt x)) (- x 0.5) (- 0.91893853320467 x)))
84.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	578	1122
1	2019	1042
2	5001	1006

prune453.0ms

Filtered

119 candidates to 93 candidates (78.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	119	12	131

Merged error: 1.7b

Counts

131 → 12

regimes379.0ms

Accuracy

83.2% (0.3b remaining)

Error of 4.4b against oracle of 4.0b and baseline of 6.0b

bsearch90.0ms

Steps

Iters	Range		Point
7	1.2751829223193255e+26	4.550222926920082e+27	7.819139136123641e+26

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms

sample1.7s

Algorithm

intervals

Results

630.0ms	11658×	body	80	valid
553.0ms	11696×	body	80	nan