Details

sample149.0ms

Algorithm

intervals

Results

72.0ms	1563×	body	80	nan
17.0ms	256×	body	80	valid

simplify70.0ms

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

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.6b	(+ (log (+ x y)) (log z))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
28×	`associate-+l+`
27×	`pow1`
23×	`add-cube-cbrt`
22×	`log-pow`
21×	`prod-diff` `distribute-lft-out`
19×	`log-prod`
13×	`fma-def`
10×	`add-log-exp`
9×	`associate-+r+`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `distribute-lft-out--`
5×	`add-exp-log` `flip3--` `associate-l` `sum-log` `add-cbrt-cube` `flip--`
4×	`associate-r` `frac-add`
3×	`expm1-log1p-u` `associate-+l-` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `log-div` `diff-log` `difference-of-squares`
1×	`sub-neg` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 120

Calls

3 calls:

124.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
11.0ms	(* (- a 0.5) (log t))
7.0ms	(+ (log (+ x y)) (log z))

series341.0ms

Counts

3 → 9

Calls

3 calls:

206.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
63.0ms	(* (- a 0.5) (log t))
72.0ms	(+ (log (+ x y)) (log z))

simplify73.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	642	1079
1	2528	880
2	5001	863

prune443.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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))

series582.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
136.0ms	(cbrt (+ x y))
133.0ms	(cbrt (+ x y))
136.0ms	(cbrt (+ x y))

simplify143.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (31.0ms)

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

prune507.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.4b	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
0.5b	(+ (log (+ x y)) (log (sqrt z)))

rewrite982.0ms

Algorithm

rewrite-expression-head

Rules

133×	`*-un-lft-identity`
99×	`distribute-lft-out`
81×	`pow1`
75×	`log-pow`
47×	`associate-+l+`
40×	`add-sqr-sqrt`
39×	`prod-diff`
34×	`add-cube-cbrt`
28×	`log-prod`
26×	`fma-def`
18×	`associate-+r+`
15×	`add-log-exp`
12×	`distribute-lft-out--`
11×	`sum-log`
7×	`associate-+l-`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sqrt-prod` `add-cbrt-cube`
5×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
4×	`expm1-log1p-u` `log-div` `associate-r` `frac-add` `log1p-expm1-u`
3×	`+-commutative` `diff-log`
2×	`difference-of-squares`
1×	`sub-neg` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 188

Calls

4 calls:

916.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
12.0ms	(* (- a 0.5) (log t))
34.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
8.0ms	(+ (log (+ x y)) (log (sqrt z)))

series673.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
60.0ms	(* (- a 0.5) (log t))
172.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
148.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify91.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	828	1873
1	3206	1496
2	5002	1431

prune605.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt t)
0.5b	(cbrt t)
0.5b	(* (cbrt t) (cbrt t))
0.6b	(+ (log (+ x y)) (log z))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`cbrt-prod`
17×	`add-cube-cbrt`
16×	`pow1`
8×	`pow1/3`
7×	`log-prod`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
5×	`log-pow` `distribute-lft-out`
4×	`expm1-log1p-u` `associate-+l+` `fma-def` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-+r+`
2×	`associate-+l-` `log-div` `flip3-+` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip-+`
1×	`+-commutative` `pow2` `pow-plus` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

0.0ms	(cbrt t)
0.0ms	(cbrt t)
6.0ms	(* (cbrt t) (cbrt t))
7.0ms	(+ (log (+ x y)) (log z))

series630.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt t)
175.0ms	(cbrt t)
201.0ms	(* (cbrt t) (cbrt t))
76.0ms	(+ (log (+ x y)) (log z))

simplify115.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	272	437
1	831	397
2	4082	373
3	5002	372

prune472.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes633.0ms

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	24	17
1	24	17

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.7s	57153×	body	80	nan
472.0ms	8042×	body	80	valid