Details

sample183.0ms

Algorithm

intervals

Results

95.0ms	1958×	body	80	nan
15.0ms	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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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))

rewrite45.0ms

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:

35.0ms	(- (+ (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))

series331.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(- (+ (log (+ x y)) (log z)) t)
90.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
71.0ms	(+ (log (+ x y)) (log z))

simplify41.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (33.0ms)

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

prune274.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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))

rewrite30.0ms

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:

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

series531.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
122.0ms	(cbrt (+ x y))
127.0ms	(cbrt (+ x y))
123.0ms	(cbrt (+ x y))

simplify133.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (27.0ms)

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

prune486.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

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))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
27×	`distribute-lft-out`
20×	`pow1`
17×	`log-pow`
11×	`fma-def`
9×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `sum-log`
6×	`associate-+l-`
5×	`associate-+l+` `distribute-rgt-neg-in`
4×	`log-div` `flip3-+` `flip-+`
3×	`add-exp-log` `expm1-log1p-u` `associate-+r+` `add-cbrt-cube` `log1p-expm1-u`
2×	`+-commutative` `neg-log`
1×	`neg-sub0` `associate-+r-` `unsub-neg` `fma-udef`

Counts

3 → 79

Calls

3 calls:

30.0ms	(+ (+ (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))

series319.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(+ (+ (log (+ x y)) (log z)) (- t))
85.0ms	(fma (log t) (- a 0.5) (+ (+ (log (+ x y)) (log z)) (- t)))
73.0ms	(+ (log (+ x y)) (log z))

simplify39.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	378	571
1	1258	506
2	5001	497

prune263.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

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

series2.3s

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (log (+ x y)) (log z))
856.0ms	(cbrt (fma (log t) (- a 0.5) (+ (+ (log (+ x y)) (log z)) (- t))))
671.0ms	(cbrt (fma (log t) (- a 0.5) (+ (+ (log (+ x y)) (log z)) (- t))))
668.0ms	(cbrt (fma (log t) (- a 0.5) (+ (+ (log (+ x y)) (log z)) (- t))))

simplify63.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	602	1600
1	2139	1476
2	5001	1460

prune476.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes491.0ms

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	16
1	21	16

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.8s	56959×	body	80	nan
472.0ms	8027×	body	80	valid