Details

sample165.0ms

Algorithm

intervals

Results

69.0ms	1501×	body	80	nan
14.0ms	257×	body	80	valid

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune11.0ms

Pruning

2 alts after pruning (2 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))
0.5b	(+ (log (+ x y)) (log z))

rewrite87.0ms

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:

69.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
13.0ms	(+ (log (+ x y)) (log z))

series349.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(- (+ (log (+ x y)) (log z)) t)
97.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
72.0ms	(+ (log (+ x y)) (log z))

simplify51.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

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

prune339.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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:

39.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
4.0ms	(cbrt (+ x y))
4.0ms	(cbrt (+ x y))
5.0ms	(cbrt (+ x y))

series602.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
142.0ms	(cbrt (+ x y))
137.0ms	(cbrt (+ x y))
140.0ms	(cbrt (+ x y))

simplify164.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	255	701
1	926	660
2	4357	610
3	5001	610

prune558.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

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

16.0ms	(* (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))
13.0ms	(+ (log (+ x y)) (log z))

series1.1s

Counts

4 → 12

Calls

4 calls:

829.0ms	(* (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))))
77.0ms	(+ (log (+ x y)) (log z))
80.0ms	(+ (log (+ x y)) (log z))
73.0ms	(+ (log (+ x y)) (log z))

simplify100.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (83.0ms)

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

prune688.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
28×	`log-prod`
24×	`pow1`
20×	`log-pow` `distribute-lft-out`
16×	`add-sqr-sqrt` `add-cube-cbrt` `associate-+l+` `fma-def`
12×	`associate-+r+`
8×	`associate-+l-` `log-div` `flip3-+` `flip-+`
4×	`add-exp-log` `+-commutative` `expm1-log1p-u` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 120

Calls

4 calls:

12.0ms	(+ (log (+ x y)) (log z))
13.0ms	(+ (log (+ x y)) (log z))
13.0ms	(+ (log (+ x y)) (log z))
18.0ms	(+ (log (+ x y)) (log z))

series294.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (log (+ x y)) (log z))
75.0ms	(+ (log (+ x y)) (log z))
71.0ms	(+ (log (+ x y)) (log z))
76.0ms	(+ (log (+ x y)) (log z))

simplify82.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	158	688
1	328	624
2	858	608
3	2691	604
4	5002	604

prune753.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes704.0ms

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

sample5.8s

Algorithm

intervals

Results

2.6s	56893×	body	80	nan
450.0ms	8032×	body	80	valid