Details

sample77.0ms

Algorithm

intervals

Results

28.0ms	377×	body	80	valid
24.0ms	406×	body	80	nan

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (18.0ms)

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

prune9.0ms

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: 6.4b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ y 0.0007936500793651) z)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

7.0ms	(* (+ y 0.0007936500793651) z)
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)

series260.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ y 0.0007936500793651) z)
37.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
117.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	446	778
1	1546	696
2	5002	694

prune331.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	91	9	100

Merged error: 4.0b

Counts

100 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ y 0.0007936500793651) z)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
6.2b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`-un-lft-identity` `associate-r*`
17×	`add-exp-log`
16×	`add-cube-cbrt`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`pow1` `associate-l`
6×	`associate-*l/` `prod-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`
2×	`frac-times` `div-exp`
1×	`cbrt-undiv` `rec-exp` `flip3--` `1-exp` `associate-*r/` `un-div-inv` `flip--` `fma-udef` `div-inv` `distribute-lft-out`

Counts

4 → 97

Calls

4 calls:

6.0ms	(* (+ y 0.0007936500793651) z)
8.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
18.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series260.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (+ y 0.0007936500793651) z)
36.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
115.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
80.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify65.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	555	864
1	2213	758
2	5001	738

prune319.0ms

Filtered

109 candidates to 83 candidates (76.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	109	9	118

Merged error: 4.0b

Counts

118 → 9

localize17.0ms

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))
0.2b	(- (* (- x 0.5) (log x)) x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite43.0ms

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:

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

series1.2s

Counts

4 → 12

Calls

4 calls:

468.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
263.0ms	(* (- x 0.5) (log x))
419.0ms	(- (* (- x 0.5) (log x)) x)
81.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify69.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (58.0ms)

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

prune387.0ms

Filtered

128 candidates to 102 candidates (79.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	127	10	137

Merged error: 4.0b

Counts

137 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.0b	(/ (+ (* (- (* (+ 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` `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)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series611.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt x)
171.0ms	(cbrt x)
175.0ms	(cbrt x)
81.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify109.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (101.0ms)

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

prune336.0ms

Filtered

82 candidates to 72 candidates (87.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	82	10	92

Merged error: 4.0b

Counts

92 → 10

regimes384.0ms

Accuracy

86.7% (0.3b remaining)

Error of 4.0b against oracle of 3.7b and baseline of 5.9b

bsearch99.0ms

Steps

Iters	Range		Point
10	3002406562115.273	1.7961853507280167e+24	9.26678330514666e+17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	29
1	47	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

809.0ms	11678×	body	80	valid
708.0ms	11687×	body	80	nan