Details

sample151.0ms

Algorithm

intervals

Results

76.0ms	1620×	body	80	nan
14.0ms	256×	body	80	valid

simplify62.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.3b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
28×	`pow1`
25×	`log-pow` `distribute-lft-out`
21×	`prod-diff`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
7×	`log-prod` `fma-neg`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`associate-+l-` `log-div` `associate-+l+` `fma-def`
3×	`add-exp-log` `expm1-log1p-u` `associate-+r+` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate--l-` `diff-log` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--` `fma-udef` `difference-of-squares`

Counts

3 → 92

Calls

3 calls:

38.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
7.0ms	(+ (log (+ x y)) (log z))

series353.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(- (+ (log (+ x y)) (log z)) t)
86.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
72.0ms	(+ (log (+ x y)) (log z))

simplify49.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	388	866
1	1209	661
2	5001	650

prune308.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.6b	(* (cbrt (+ x y)) (cbrt (+ x y)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
20.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (+ x y))
124.0ms	(cbrt (+ x y))
133.0ms	(cbrt (+ x y))
162.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

simplify143.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	255	701
1	933	660
2	4363	610
3	5001	610

prune529.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (log (+ x y)))
0.5b	(cbrt (log (+ x y)))
0.5b	(cbrt (log (+ x y)))
0.7b	(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
7×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `log-pow`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

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

series2.0s

Counts

4 → 12

Calls

4 calls:

465.0ms	(cbrt (log (+ x y)))
464.0ms	(cbrt (log (+ x y)))
468.0ms	(cbrt (log (+ x y)))
572.0ms	(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))

simplify63.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (57.0ms)

Iter	Nodes	Cost
0	97	446
1	173	386
2	488	377
3	1652	351
4	5002	350

prune330.0ms

Pruning

6 alts after pruning (4 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))

rewrite30.0ms

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:

6.0ms	(* (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))))
7.0ms	(+ (log (+ x y)) (log z))
7.0ms	(+ (log (+ x y)) (log z))
7.0ms	(+ (log (+ x y)) (log z))

series976.0ms

Counts

4 → 12

Calls

4 calls:

753.0ms	(* (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))))
74.0ms	(+ (log (+ x y)) (log z))
74.0ms	(+ (log (+ x y)) (log z))
76.0ms	(+ (log (+ x y)) (log z))

simplify90.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (70.0ms)

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

prune675.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.1b

regimes933.0ms

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	16
1	21	16

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	54937×	body	80	nan
437.0ms	8032×	body	80	valid