Details

sample187.0ms

Algorithm

intervals

Results

95.0ms	1840×	body	80	nan
16.0ms	257×	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

prune11.0ms

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))
0.5b	(+ (log (+ x y)) (log z))

rewrite335.0ms

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:

78.0ms	(- (+ (log (+ x y)) (log z)) t)
207.0ms	(+ (- (+ (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))

series445.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (+ (log (+ x y)) (log z)) t)
168.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
49.0ms	(* (- a 0.5) (log t))
82.0ms	(+ (log (+ x y)) (log z))

simplify83.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (68.0ms)

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

prune882.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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))

rewrite27.0ms

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:

10.0ms	(- (log z) t)
15.0ms	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
0.0ms	(fma (log t) (- a 0.5) (- (log z) t))

series249.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(- (log z) t)
148.0ms	(+ (log (+ x y)) (fma (log t) (- a 0.5) (- (log z) t)))
49.0ms	(fma (log t) (- a 0.5) (- (log z) t))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (33.0ms)

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

prune408.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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))
0.5b	(fma (- a 0.5) (log t) (log (+ x y)))

rewrite33.0ms

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:

9.0ms	(- (log z) t)
21.0ms	(+ (fma (- a 0.5) (log t) (log (+ x y))) (- (log z) t))
0.0ms	(fma (- a 0.5) (log t) (log (+ x y)))

series231.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(- (log z) t)
83.0ms	(+ (fma (- a 0.5) (log t) (log (+ x y))) (- (log z) t))
87.0ms	(fma (- a 0.5) (log t) (log (+ x y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (36.0ms)

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

prune448.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
0.5b	(+ (log (+ x y)) (log z))
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

43×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
28×	`associate-+l+`
27×	`*-un-lft-identity`
24×	`cbrt-prod`
21×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`associate-+r+`
9×	`pow1`
8×	`associate-*l/`
6×	`distribute-lft-out` `add-log-exp`
5×	`fma-def` `log-pow`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `frac-add` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `associate-+l-` `log-div` `pow1/3` `sum-log`

Counts

4 → 111

Calls

4 calls:

36.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
13.0ms	(+ (log (+ x y)) (log z))
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series580.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(+ (* (- a 0.5) (* 2 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
70.0ms	(+ (log (+ x y)) (log z))
176.0ms	(cbrt t)
181.0ms	(cbrt t)

simplify72.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	653	918
1	2378	778
2	5003	742

prune943.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes585.0ms

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	15
1	24	15

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.0s	56770×	body	80	nan
503.0ms	8040×	body	80	valid