Details

sample173.0ms

Algorithm

intervals

Results

87.0ms	1737×	body	80	nan
15.0ms	257×	body	80	valid

simplify63.0ms

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

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.2b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite42.0ms

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:

32.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
6.0ms	(+ (log (+ x y)) (log z))

series321.0ms

Counts

3 → 9

Calls

3 calls:

163.0ms	(- (+ (log (+ x y)) (log z)) t)
87.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
71.0ms	(+ (log (+ x y)) (log z))

simplify43.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (34.0ms)

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

prune286.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.2b	(fma (log t) (- a 0.5) (pow (- (+ (log (+ x y)) (log z)) t) 1))
0.6b	(+ (log (+ x y)) (log z))

rewrite42.0ms

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:

32.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (pow (- (+ (log (+ x y)) (log z)) t) 1))
6.0ms	(+ (log (+ x y)) (log z))

series327.0ms

Counts

3 → 9

Calls

3 calls:

165.0ms	(- (+ (log (+ x y)) (log z)) t)
91.0ms	(fma (log t) (- a 0.5) (pow (- (+ (log (+ x y)) (log z)) t) 1))
71.0ms	(+ (log (+ x y)) (log z))

simplify43.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	393	878
1	1248	670
2	5001	658

prune305.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (log (+ x y)))
0.6b	(cbrt (log (+ x y)))
0.6b	(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))

series1.9s

Counts

4 → 12

Calls

4 calls:

464.0ms	(cbrt (log (+ x y)))
464.0ms	(cbrt (log (+ x y)))
450.0ms	(cbrt (log (+ x y)))
552.0ms	(fma (* (cbrt (log (+ x y))) (cbrt (log (+ x y)))) (cbrt (log (+ x y))) (log z))

simplify65.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (53.0ms)

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

prune315.0ms

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) (pow (- (+ (log (+ x y)) (log z)) t) 1))) (cbrt (fma (log t) (- a 0.5) (pow (- (+ (log (+ x y)) (log z)) t) 1))))
0.6b	(+ (log (+ x y)) (log z))
0.6b	(+ (log (+ x y)) (log z))
0.6b	(+ (log (+ x y)) (log z))

rewrite31.0ms

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) (pow (- (+ (log (+ x y)) (log z)) t) 1))) (cbrt (fma (log t) (- a 0.5) (pow (- (+ (log (+ x y)) (log z)) t) 1))))
6.0ms	(+ (log (+ x y)) (log z))
9.0ms	(+ (log (+ x y)) (log z))
6.0ms	(+ (log (+ x y)) (log z))

series951.0ms

Counts

4 → 12

Calls

4 calls:

726.0ms	(* (cbrt (fma (log t) (- a 0.5) (pow (- (+ (log (+ x y)) (log z)) t) 1))) (cbrt (fma (log t) (- a 0.5) (pow (- (+ (log (+ x y)) (log z)) t) 1))))
80.0ms	(+ (log (+ x y)) (log z))
69.0ms	(+ (log (+ x y)) (log z))
75.0ms	(+ (log (+ x y)) (log z))

simplify85.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	710	1775
1	2790	1614
2	5002	1491

prune690.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.0b

regimes805.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.5s	55312×	body	80	nan
445.0ms	8035×	body	80	valid