Details

sample73.0ms

Algorithm

intervals

Results

26.0ms	375×	body	80	valid
24.0ms	359×	body	80	nan

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (20.0ms)

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: 5.2b

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)
0.1b	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite32.0ms

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)))
14.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series272.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
38.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
123.0ms	(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
83.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (46.0ms)

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

prune314.0ms

Filtered

93 candidates to 73 candidates (78.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	87	8	95

Merged error: 2.8b

Counts

95 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467))
0.1b	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b	(fma (log x) (- x 0.5) (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467)))
4.8b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt` `*-un-lft-identity`
74×	`prod-diff`
73×	`add-cube-cbrt`
64×	`times-frac`
16×	`distribute-lft-out--`
15×	`difference-of-squares`
13×	`fma-neg`
11×	`associate--r+`
9×	`add-log-exp`
7×	`div-inv`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log` `associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `frac-sub` `flip--` `fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate--r-`

Counts

4 → 160

Calls

4 calls:

13.0ms	(- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467))
1.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
1.0ms	(fma (log x) (- x 0.5) (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467)))
3.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series320.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467))
35.0ms	(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
129.0ms	(fma (log x) (- x 0.5) (- (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x) (- x 0.91893853320467)))
76.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify74.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	614	2804
1	1854	2265
2	5001	1958

prune423.0ms

Filtered

172 candidates to 95 candidates (55.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	166	6	172
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	172	8	180

Merged error: 2.0b

Counts

180 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.8b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite8.0ms

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`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
3.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series789.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
172.0ms	(cbrt x)
172.0ms	(cbrt x)
268.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify66.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	170	423
1	480	383
2	2100	377
3	5001	370

prune410.0ms

Filtered

80 candidates to 68 candidates (85.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	80	8	88

Merged error: 2.0b

Counts

88 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.6b	(expm1 (log1p (cbrt x)))
4.8b	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1/3`
1×	`cbrt-undiv` `expm1-log1p` `frac-2neg` `div-exp` `clear-num` `div-inv` `expm1-udef`

Counts

4 → 66

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(expm1 (log1p (cbrt x)))
3.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series725.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
173.0ms	(cbrt x)
295.0ms	(expm1 (log1p (cbrt x)))
75.0ms	(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify66.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	182	414
1	493	372
2	2113	366
3	5001	360

prune402.0ms

Filtered

78 candidates to 63 candidates (80.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	78	8	86

Merged error: 2.0b

Counts

86 → 8

regimes327.0ms

Accuracy

67.1% (0.9b remaining)

Error of 4.0b against oracle of 3.0b and baseline of 5.9b

bsearch98.0ms

Steps

Iters	Range		Point
8	506179501895.91473	576140799423863.1	564945614527036.0

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	32
1	56	32
2	56	32

end0.0ms

sample2.0s

Algorithm

intervals

Results

801.0ms	11779×	body	80	valid
699.0ms	11764×	body	80	nan

Details

sample73.0ms

simplify61.0ms

prune10.0ms

localize16.0ms

rewrite32.0ms

series272.0ms

simplify56.0ms

prune314.0ms

localize15.0ms

rewrite24.0ms

series320.0ms

simplify74.0ms

prune423.0ms

localize29.0ms

rewrite8.0ms

series789.0ms

simplify66.0ms

prune410.0ms

localize30.0ms

rewrite8.0ms

series725.0ms

simplify66.0ms

prune402.0ms

regimes327.0ms

bsearch98.0ms

simplify2.0ms

end0.0ms

sample2.0s

Profiling