Details

sample75.0ms

Algorithm

intervals

Results

26.0ms	387×	body	80	valid
25.0ms	368×	body	80	nan

simplify57.0ms

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

prune10.0ms

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: 7.7b

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)))
7.2b	(/ (+ (* (- (* (+ 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:

6.0ms	(* (+ 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)

series282.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ y 0.0007936500793651) z)
39.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
130.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (42.0ms)

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

prune350.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 4.8b

Counts

100 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778)
0.1b	(* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
7.2b	(/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

4.0ms	(- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778)
7.0ms	(* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z)
1.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
10.0ms	(/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x)

series280.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778)
40.0ms	(* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z)
129.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
83.0ms	(/ (+ (* (- (fma z y (* 0.0007936500793651 z)) 0.0027777777777778) z) 0.083333333333333) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	440	952
1	1582	803
2	5003	794

prune318.0ms

Filtered

106 candidates to 77 candidates (72.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	106	8	114

Merged error: 4.8b

Counts

114 → 8

localize20.0ms

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)) x)
0.2b	(* (- x 0.5) (log x))
7.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite42.0ms

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)) x)
8.0ms	(* (- x 0.5) (log x))
12.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

432.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
612.0ms	(- (* (- x 0.5) (log x)) x)
258.0ms	(* (- x 0.5) (log x))
88.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify69.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (57.0ms)

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

prune410.0ms

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	1	5	6
Picked	1	0	1
Done	0	1	1
Total	126	10	136

Merged error: 4.7b

Counts

136 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
7.2b	(/ (+ (* (- (* (+ 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)

series625.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt x)
178.0ms	(cbrt x)
177.0ms	(cbrt x)
85.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify105.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (98.0ms)

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

prune346.0ms

Filtered

82 candidates to 72 candidates (87.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	83	9	92

Merged error: 4.7b

Counts

92 → 9

regimes388.0ms

Accuracy

79.2% (0.4b remaining)

Error of 4.5b against oracle of 4.1b and baseline of 6.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	29
1	51	29

end0.0ms

sample2.0s

Algorithm

intervals

Results

782.0ms	11709×	body	80	valid
726.0ms	12059×	body	80	nan