Details

sample147.0ms

Algorithm

intervals

Results

73.0ms	1563×	body	80	nan
14.0ms	256×	body	80	valid

simplify63.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

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))

rewrite141.0ms

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:

119.0ms	(+ (- (+ (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))

series331.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
58.0ms	(* (- a 0.5) (log t))
75.0ms	(+ (log (+ x y)) (log z))

simplify67.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (57.0ms)

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

prune421.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))

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))

series555.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
128.0ms	(cbrt (+ x y))
132.0ms	(cbrt (+ x y))
129.0ms	(cbrt (+ x y))

simplify141.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (28.0ms)

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

prune505.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

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)))

rewrite738.0ms

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:

673.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
11.0ms	(* (- a 0.5) (log t))
35.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
8.0ms	(+ (log (+ x y)) (log (sqrt z)))

series693.0ms

Counts

4 → 12

Calls

4 calls:

304.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
57.0ms	(* (- a 0.5) (log t))
177.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
155.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify88.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (72.0ms)

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

prune615.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (fma (* (- a 0.5) (* 2 (log (cbrt t)))) 1 (- (+ (log (+ x y)) (* 2 (log (sqrt z)))) t)) (* (log (cbrt t)) (- a 0.5)))
0.5b	(cbrt t)
0.5b	(cbrt t)
0.6b	(+ (log (+ x y)) (* 2 (log (sqrt z))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-+r+`
27×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`prod-diff`
17×	`distribute-rgt-in` `distribute-lft-in`
16×	`log-prod`
7×	`fma-def` `add-log-exp`
6×	`cbrt-prod` `sqrt-prod`
5×	`pow1` `associate-+l+`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `associate-+l-` `sub-neg` `log-div` `pow1/3` `sum-log`
1×	`log-pow` `fma-udef` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

6.0ms	(+ (fma (* (- a 0.5) (* 2 (log (cbrt t)))) 1 (- (+ (log (+ x y)) (* 2 (log (sqrt z)))) t)) (* (log (cbrt t)) (- a 0.5)))
0.0ms	(cbrt t)
0.0ms	(cbrt t)
7.0ms	(+ (log (+ x y)) (* 2 (log (sqrt z))))

series799.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(+ (fma (* (- a 0.5) (* 2 (log (cbrt t)))) 1 (- (+ (log (+ x y)) (* 2 (log (sqrt z)))) t)) (* (log (cbrt t)) (- a 0.5)))
189.0ms	(cbrt t)
182.0ms	(cbrt t)
175.0ms	(+ (log (+ x y)) (* 2 (log (sqrt z))))

simplify56.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	595	1306
1	1847	1140
2	5002	1040

prune600.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes664.0ms

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

sample4.9s

Algorithm

intervals

Results

2.6s	57153×	body	80	nan
438.0ms	8042×	body	80	valid