Details

sample184.0ms

Algorithm

intervals

Results

81.0ms	1794×	body	80	nan
14.0ms	256×	body	80	valid

simplify65.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.1b	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.5b	(+ (log (+ x y)) (log z))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
48×	`pow1`
43×	`add-sqr-sqrt`
42×	`prod-diff` `log-pow`
41×	`distribute-lft-out`
35×	`add-cube-cbrt`
28×	`associate-+l+`
19×	`log-prod`
14×	`add-log-exp`
13×	`fma-def`
11×	`distribute-lft-out--`
9×	`associate-+r+`
7×	`fma-neg`
6×	`add-exp-log` `distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*l/` `sum-log` `add-cbrt-cube` `flip--`
5×	`associate-+l-` `associate-l`
4×	`expm1-log1p-u` `log-div` `flip3-+` `diff-log` `associate-r` `frac-add` `flip-+` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`+-commutative` `associate--l-` `sub-neg` `associate--l+`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 172

Calls

4 calls:

63.0ms	(- (+ (log (+ x y)) (log z)) t)
211.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
24.0ms	(* (- a 0.5) (log t))
12.0ms	(+ (log (+ x y)) (log z))

series442.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(- (+ (log (+ x y)) (log z)) t)
176.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
52.0ms	(* (- a 0.5) (log t))
64.0ms	(+ (log (+ x y)) (log z))

simplify76.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	706	1592
1	2722	1253
2	5001	1237

prune481.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log z) t)
0.1b	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
0.2b	(fma (log t) (- a 0.5) (- (log z) t))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`prod-diff`
10×	`pow1`
7×	`log-prod` `log-pow`
5×	`add-log-exp`
4×	`associate-+l+` `fma-def` `fma-neg`
3×	`add-exp-log` `expm1-log1p-u` `associate--l+` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
2×	`associate-+l-` `log-div` `flip3-+` `flip-+` `fma-udef` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `diff-log` `sum-log` `flip--` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

9.0ms	(- (log z) t)
11.0ms	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
0.0ms	(fma (log t) (- a 0.5) (- (log z) t))

series244.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(- (log z) t)
137.0ms	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
52.0ms	(fma (log t) (- a 0.5) (- (log z) t))

simplify38.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	393	634
1	1179	513
2	5001	502

prune254.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log z) t)
0.1b	(+ (fma (- a 0.5) (log t) (log (+ x y))) (- (log z) t))
0.4b	(fma (- a 0.5) (log t) (log (+ x y)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
24×	`prod-diff`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
17×	`associate-+r+`
12×	`pow1`
9×	`log-pow`
8×	`add-log-exp`
6×	`log-prod` `associate--l+`
4×	`fma-neg` `distribute-lft-out--`
3×	`add-exp-log` `expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
2×	`sub-neg` `diff-log` `sum-log` `fma-udef`
1×	`+-commutative` `associate-+r-` `associate-+l+` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 85

Calls

3 calls:

11.0ms	(- (log z) t)
20.0ms	(+ (fma (- a 0.5) (log t) (log (+ x y))) (- (log z) t))
0.0ms	(fma (- a 0.5) (log t) (log (+ x y)))

series216.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(- (log z) t)
76.0ms	(+ (fma (- a 0.5) (log t) (log (+ x y))) (- (log z) t))
85.0ms	(fma (- a 0.5) (log t) (log (+ x y)))

simplify40.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	393	802
1	1233	642
2	5001	611

prune273.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt t) (cbrt t))
0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

10.0ms	(* (cbrt t) (cbrt t))
1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series688.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (cbrt t) (cbrt t))
174.0ms	(cbrt t)
162.0ms	(cbrt t)
163.0ms	(cbrt t)

simplify88.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune383.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes403.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	8
1	16	8

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.4s	55234×	body	80	nan
437.0ms	8030×	body	80	valid