Details

sample227.0ms

Algorithm

intervals

Results

136.0ms	1738×	body	80	nan
24.0ms	257×	body	80	valid

simplify69.0ms

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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))
0.6b	(+ (log (+ x y)) (log z))

rewrite179.0ms

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:

34.0ms	(- (+ (log (+ x y)) (log z)) t)
120.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
11.0ms	(* (- a 0.5) (log t))
6.0ms	(+ (log (+ x y)) (log z))

series486.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(- (+ (log (+ x y)) (log z)) t)
192.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
57.0ms	(* (- a 0.5) (log t))
73.0ms	(+ (log (+ x y)) (log z))

simplify79.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (64.0ms)

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

prune529.0ms

Pruning

9 alts after pruning (9 fresh and 0 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))
0.5b	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
0.5b	(+ (log (+ x y)) (log (sqrt z)))

rewrite731.0ms

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:

670.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
11.0ms	(* (- a 0.5) (log t))
32.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
8.0ms	(+ (log (+ x y)) (log (sqrt z)))

series652.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
58.0ms	(* (- a 0.5) (log t))
163.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
144.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify85.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	828	1873
1	3206	1496
2	5002	1437

prune649.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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))

rewrite13.0ms

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:

4.0ms	(- (log z) t)
6.0ms	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
0.0ms	(fma (log t) (- a 0.5) (- (log z) t))

series277.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(- (log z) t)
157.0ms	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
58.0ms	(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

prune299.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma 2 (log (cbrt (sqrt z))) (+ (log (+ x y)) (log (sqrt z))))
0.5b	(+ (log (+ x y)) (log (sqrt z)))
0.5b	(cbrt (sqrt z))
0.5b	(cbrt (sqrt z))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
10×	`log-prod`
9×	`pow1` `sqrt-prod`
6×	`associate-+r+`
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`
2×	`associate-+l-` `log-div` `flip3-+` `pow1/3` `flip-+`
1×	`+-commutative` `sum-log` `fma-udef`

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma 2 (log (cbrt (sqrt z))) (+ (log (+ x y)) (log (sqrt z))))
10.0ms	(+ (log (+ x y)) (log (sqrt z)))
1.0ms	(cbrt (sqrt z))
1.0ms	(cbrt (sqrt z))

series699.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(fma 2 (log (cbrt (sqrt z))) (+ (log (+ x y)) (log (sqrt z))))
147.0ms	(+ (log (+ x y)) (log (sqrt z)))
146.0ms	(cbrt (sqrt z))
151.0ms	(cbrt (sqrt z))

simplify93.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	334	584
1	897	530
2	3592	501
3	5001	497

prune478.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes524.0ms

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

sample7.1s

Algorithm

intervals

Results

4.4s	56411×	body	80	nan
754.0ms	8034×	body	80	valid