Details

sample174.0ms

Algorithm

intervals

Results

73.0ms	1658×	body	80	nan
14.0ms	258×	body	80	valid

simplify60.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite14.0ms

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))
13.0ms	(+ (log (+ x y)) (log z))

series170.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
74.0ms	(+ (log (+ x y)) (log z))

simplify52.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (48.0ms)

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

prune187.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite14.0ms

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))
13.0ms	(+ (log (+ x y)) (log z))

series169.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
72.0ms	(+ (log (+ x y)) (log z))

simplify52.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (48.0ms)

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

prune213.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (log (+ x y)) (log z))
0.5b	(* (log z) (log z))
0.8b	(pow (log z) 3)
0.8b	(pow (log (+ x y)) 3)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
35×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
23×	`log-pow`
16×	`prod-diff`
13×	`log-prod`
8×	`add-exp-log` `unpow-prod-down` `cube-prod` `add-cbrt-cube`
6×	`pow-unpow` `swap-sqr`
4×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `associate--l+` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
2×	`associate--l-` `cube-mult` `pow-to-exp` `log-div` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow2` `sub-neg` `flip3--` `flip3-+` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `difference-of-squares` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

14.0ms	(- (log (+ x y)) (log z))
10.0ms	(* (log z) (log z))
3.0ms	(pow (log z) 3)
4.0ms	(pow (log (+ x y)) 3)

series727.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (log (+ x y)) (log z))
156.0ms	(* (log z) (log z))
176.0ms	(pow (log z) 3)
314.0ms	(pow (log (+ x y)) 3)

simplify78.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	393	728
1	1983	622
2	5002	535

prune522.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))) (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))))
0.6b	(+ (log (+ x y)) (log z))
0.6b	(+ (log (+ x y)) (log z))
0.6b	(+ (log (+ x y)) (log z))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`pow1`
21×	`add-cube-cbrt` `log-prod`
16×	`cbrt-prod`
15×	`log-pow` `distribute-lft-out`
12×	`associate-+l+` `fma-def`
9×	`associate-+r+`
6×	`add-exp-log` `associate-+l-` `log-div` `flip3-+` `pow1/3` `swap-sqr` `associate-r` `associate-l` `flip-+`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`+-commutative` `sum-log`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 132

Calls

4 calls:

12.0ms	(* (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))) (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))))
13.0ms	(+ (log (+ x y)) (log z))
13.0ms	(+ (log (+ x y)) (log z))
17.0ms	(+ (log (+ x y)) (log z))

series1.0s

Counts

4 → 12

Calls

4 calls:

809.0ms	(* (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))) (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))))
79.0ms	(+ (log (+ x y)) (log z))
78.0ms	(+ (log (+ x y)) (log z))
78.0ms	(+ (log (+ x y)) (log z))

simplify89.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	706	1687
1	2773	1534
2	5002	1423

prune656.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes758.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	8
1	23	8
2	23	8

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.8s	56887×	body	80	nan
441.0ms	8030×	body	80	valid