Details

sample165.0ms

Algorithm

intervals

Results

84.0ms	1745×	body	80	nan
14.0ms	257×	body	80	valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	61	8
2	161	8
3	393	8
4	984	8
5	2256	8
6	4095	8
7	5001	8

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.3b

Counts

2 → 1

localize15.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.5b	(+ (log (+ x y)) (log z))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
7×	`pow1` `log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `log-pow` `distribute-lft-out`
4×	`associate-+l+` `fma-def` `sum-log`
3×	`associate-+r+`
2×	`add-exp-log` `expm1-log1p-u` `associate-+l-` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `fma-udef`

Counts

2 → 43

Calls

2 calls:

1.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
7.0ms	(+ (log (+ x y)) (log z))

series166.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
73.0ms	(+ (log (+ x y)) (log z))

simplify57.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	265	326
1	671	294
2	2572	288
3	5001	284

prune148.0ms

Filtered

49 candidates to 38 candidates (77.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Merged error: 0.1b

Counts

50 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt z))
0.2b	(fma (log t) (- a 0.5) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
0.4b	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
0.5b	(+ (log (+ x y)) (log (sqrt z)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
32×	`log-prod`
28×	`pow1` `distribute-lft-out`
25×	`log-pow`
23×	`add-log-exp`
22×	`sum-log`
20×	`associate-+l+`
18×	`associate-+r+`
16×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`sqrt-prod`
11×	`fma-def`
6×	`associate-+l-`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`+-commutative`
1×	`sqrt-pow1` `pow1/2` `rem-log-exp` `fma-udef`

Counts

4 → 124

Calls

4 calls:

2.0ms	(log (sqrt z))
1.0ms	(fma (log t) (- a 0.5) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
15.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
8.0ms	(+ (log (+ x y)) (log (sqrt z)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(log (sqrt z))
120.0ms	(fma (log t) (- a 0.5) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
171.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
155.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify42.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	514	969
1	1368	864
2	5001	795

prune366.0ms

Filtered

136 candidates to 91 candidates (66.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	136	8	144

Merged error: 0.1b

Counts

144 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log t) (- a 0.5) (- (+ (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt (sqrt z)))) (log (sqrt (sqrt z)))) t))
0.3b	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt (sqrt z))))
0.3b	(+ (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt (sqrt z)))) (log (sqrt (sqrt z))))
0.5b	(+ (log (+ x y)) (log (sqrt z)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

112×	`*-un-lft-identity`
105×	`distribute-lft-out`
80×	`sum-log`
76×	`pow1`
72×	`log-pow`
66×	`add-log-exp`
59×	`associate-+l+`
57×	`log-prod`
45×	`associate-+r+`
36×	`sqrt-prod`
25×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`fma-def`
12×	`associate-+l-`
6×	`+-commutative` `log-div` `flip3-+` `flip-+`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`fma-udef`

Counts

4 → 211

Calls

4 calls:

1.0ms	(fma (log t) (- a 0.5) (- (+ (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt (sqrt z)))) (log (sqrt (sqrt z)))) t))
16.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt (sqrt z))))
31.0ms	(+ (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt (sqrt z)))) (log (sqrt (sqrt z))))
8.0ms	(+ (log (+ x y)) (log (sqrt z)))

series999.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(fma (log t) (- a 0.5) (- (+ (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt (sqrt z)))) (log (sqrt (sqrt z)))) t))
327.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt (sqrt z))))
350.0ms	(+ (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt (sqrt z)))) (log (sqrt (sqrt z))))
155.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify70.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	828	2147
1	2523	1927
2	5001	1815

prune595.0ms

Filtered

223 candidates to 120 candidates (53.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	224	7	231

Merged error: 0.1b

Counts

231 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.4b	(fma 2 (log (cbrt z)) (log (+ x y)))
0.6b	(cbrt z)
0.6b	(cbrt z)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
7×	`add-log-exp`
6×	`associate-+r+` `log-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def`
2×	`pow1/3` `sum-log` `fma-udef` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `log-pow` `flip-+`

Counts

4 → 62

Calls

4 calls:

5.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
1.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
1.0ms	(cbrt z)
1.0ms	(cbrt z)

series895.0ms

Counts

4 → 12

Calls

4 calls:

386.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
139.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
187.0ms	(cbrt z)
183.0ms	(cbrt z)

simplify68.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	203	452
1	567	417
2	2190	374
3	5001	362

prune278.0ms

Filtered

74 candidates to 67 candidates (90.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	74	7	81

Merged error: 0.1b

Counts

81 → 7

regimes486.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.6s	56471×	body	80	nan
445.0ms	8026×	body	80	valid