Details

sample179.0ms

Algorithm

intervals

Results

74.0ms	1739×	body	80	nan
15.0ms	257×	body	80	valid

simplify61.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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))

rewrite319.0ms

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)
212.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
25.0ms	(* (- a 0.5) (log t))
12.0ms	(+ (log (+ x y)) (log z))

series456.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(- (+ (log (+ x y)) (log z)) t)
182.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
54.0ms	(* (- a 0.5) (log t))
65.0ms	(+ (log (+ x y)) (log z))

simplify89.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (74.0ms)

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

prune486.0ms

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))

rewrite22.0ms

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))

series250.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(- (log z) t)
146.0ms	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
52.0ms	(fma (log t) (- a 0.5) (- (log z) t))

simplify39.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (32.0ms)

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

prune280.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

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)))
0.4b	(+ (log (+ x y)) (log (sqrt z)))

rewrite1.2s

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:

1.1s	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
22.0ms	(* (- a 0.5) (log t))
57.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
18.0ms	(+ (log (+ x y)) (log (sqrt z)))

series620.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
52.0ms	(* (- a 0.5) (log t))
162.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
136.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify83.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (67.0ms)

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

prune560.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt z))
0.1b	(+ (+ (log (+ x y)) (log (sqrt z))) (fma (log t) (- a 0.5) (- (log (sqrt z)) t)))
0.3b	(fma (log t) (- a 0.5) (- (log (sqrt z)) t))
0.4b	(+ (log (+ x y)) (log (sqrt z)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

2.0ms	(log (sqrt z))
54.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (fma (log t) (- a 0.5) (- (log (sqrt z)) t)))
0.0ms	(fma (log t) (- a 0.5) (- (log (sqrt z)) t))
14.0ms	(+ (log (+ x y)) (log (sqrt z)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(log (sqrt z))
274.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (fma (log t) (- a 0.5) (- (log (sqrt z)) t)))
56.0ms	(fma (log t) (- a 0.5) (- (log (sqrt z)) t))
160.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify42.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	482	837
1	1455	790
2	5001	775

prune385.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes332.0ms

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

sample5.6s

Algorithm

intervals

Results

2.4s	55808×	body	80	nan
427.0ms	8028×	body	80	valid