Details

sample169.0ms

Algorithm

intervals

Results

85.0ms	1799×	body	80	nan
14.0ms	256×	body	80	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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)

Merged error: 0.2b

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))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
6.0ms	(+ (log (+ x y)) (log z))

series170.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
75.0ms	(+ (log (+ x y)) (log z))

simplify60.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	262	323
1	662	288
2	2590	282
3	5001	278

prune197.0ms

Filtered

46 candidates to 38 candidates (82.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

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)))
0.5b	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

1.0ms	(log (sqrt z))
0.0ms	(fma (log t) (- a 0.5) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
7.0ms	(+ (log (+ x y)) (log (sqrt z)))
33.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(log (sqrt z))
115.0ms	(fma (log t) (- a 0.5) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
335.0ms	(+ (log (+ x y)) (log (sqrt z)))
169.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))

simplify43.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	474	868
1	1342	778
2	5001	721

prune443.0ms

Filtered

114 candidates to 83 candidates (72.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.5b	(fma 2 (log (cbrt z)) (log (+ x y)))
0.6b	(cbrt z)
0.6b	(cbrt z)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

4.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
1.0ms	(cbrt z)
1.0ms	(cbrt z)

series669.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
135.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
177.0ms	(cbrt z)
180.0ms	(cbrt z)

simplify67.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	203	445
1	573	409
2	2204	368
3	5002	358

prune384.0ms

Filtered

73 candidates to 67 candidates (91.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y))))
0.5b	(cbrt (pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3))
0.6b	(fma 2/3 (log z) (log (+ x y)))
0.7b	(pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

0.0ms	(fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y))))
1.0ms	(cbrt (pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3))
0.0ms	(fma 2/3 (log z) (log (+ x y)))
1.0ms	(pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3)

series623.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y))))
107.0ms	(cbrt (pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3))
91.0ms	(fma 2/3 (log z) (log (+ x y)))
315.0ms	(pow (fma 1/3 (log z) (fma 2/3 (log z) (log (+ x y)))) 3)

simplify178.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (169.0ms)

Iter	Nodes	Cost
0	204	707
1	686	652
2	4621	632
3	5001	625

prune323.0ms

Filtered

80 candidates to 59 candidates (73.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes426.0ms

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	21	12
1	21	12

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.6s	56338×	body	80	nan
447.0ms	8023×	body	80	valid