Details

sample68.0ms

Algorithm

intervals

Results

24.0ms	389×	body	80	valid
19.0ms	409×	body	80	nan

simplify56.0ms

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

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: 4.9b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite34.0ms

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)
1.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
15.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series273.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
121.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
38.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify49.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (40.0ms)

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

prune335.0ms

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: 4.0b

Counts

95 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
4.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`associate-l`
7×	`associate-r`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`flip3--` `prod-diff` `associate-/r` `flip--` `associate-/l`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `clear-num` `log-pow` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

9.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
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)

series915.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
537.0ms	(- (* (- x 0.5) (log x)) x)
257.0ms	(* (- x 0.5) (log x))
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	550	878
1	2238	772
2	5001	763

prune412.0ms

Filtered

120 candidates to 90 candidates (75.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 4.0b

Counts

129 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.5b	(/ (+ (* (- (* (+ 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)

series616.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt x)
182.0ms	(cbrt x)
174.0ms	(cbrt x)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify101.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (94.0ms)

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

prune421.0ms

Filtered

82 candidates to 72 candidates (87.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 4.0b

Counts

92 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467))
0.1b	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
4.6b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
21×	`add-cube-cbrt`
16×	`associate-r`
15×	`add-exp-log`
14×	`prod-diff`
12×	`frac-sub`
11×	`times-frac` `add-cbrt-cube` `associate--r+`
9×	`add-log-exp`
8×	`pow1` `flip3--` `associate-*l/` `flip--`
6×	`frac-times` `flip3-+` `associate-l` `flip-+`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`diff-log` `associate-*r/` `un-div-inv` `cbrt-unprod`
2×	`sub-neg` `div-exp` `pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `rec-exp` `fma-neg` `1-exp` `fma-udef` `div-inv` `distribute-lft-out--` `associate--r-` `difference-of-squares`

Counts

4 → 119

Calls

4 calls:

18.0ms	(- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467))
1.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
12.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
15.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467))
128.0ms	(fma (log x) (- x 0.5) (- (* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x)) (- x 0.91893853320467)))
38.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
85.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify118.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	958	1648
1	4070	1431
2	5001	1427

prune455.0ms

Filtered

131 candidates to 100 candidates (76.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	131	9	140

Merged error: 3.4b

Counts

140 → 9

regimes260.0ms

Accuracy

0% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	12
1	28	12

end0.0ms

sample1.8s

Algorithm

intervals

Results

671.0ms	11618×	body	80	valid
597.0ms	11724×	body	80	nan