Details

sample41.0ms

Algorithm

intervals

Results

31.0ms

306×

body

valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	90	10
2	384	10
3	1828	10
4	5001	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
2.3b	(- (* b b) (* a a))
10.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

515×	`times-frac`
419×	`add-sqr-sqrt`
403×	`*-un-lft-identity`
395×	`add-cube-cbrt`
339×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
57×	`div-inv`
36×	`add-exp-log` `add-cbrt-cube`
30×	`associate-r`
14×	`frac-times` `associate-l`
13×	`prod-exp` `cbrt-unprod`
12×	`difference-of-squares`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `clear-num`

Counts

4 → 501

Calls

4 calls:

23.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
100.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
36.0ms	(- (* b b) (* a a))
92.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify161.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune908.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 1.0) (- b a))
0.2b	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.4b	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
10.2b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

578×	`times-frac`
486×	`add-sqr-sqrt`
475×	`*-un-lft-identity`
429×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
112×	`add-exp-log` `add-cbrt-cube`
78×	`associate-r`
58×	`div-inv`
51×	`prod-exp` `cbrt-unprod`
47×	`frac-times` `sqrt-prod`
33×	`associate-*l/`
31×	`cbrt-undiv` `div-exp`
20×	`pow1`
19×	`associate-*r/`
18×	`distribute-lft-out--`
17×	`difference-of-squares`
15×	`associate-l`
10×	`flip3--` `pow-prod-down` `flip--`
8×	`frac-sub`
6×	`associate-/r/` `distribute-lft-out` `associate-/l*` `unswap-sqr`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`sub-neg`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+`

Counts

4 → 625

Calls

4 calls:

7.0ms	(/ (sqrt 1.0) (- b a))
48.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
27.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
217.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series717.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (sqrt 1.0) (- b a))
203.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
149.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
286.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify208.0ms

Algorithm

egg-herbie

Counts

637 → 637

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	3013	18547
1	5001	17719

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* (/ PI 2.0) 1.0) (- b a))) (+ b a))
0.2b	(/ (* (/ PI 2.0) 1.0) (- b a))
0.3b	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* (/ PI 2.0) 1.0) (- b a)))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

277×	`times-frac`
236×	`add-sqr-sqrt`
230×	`*-un-lft-identity`
204×	`add-cube-cbrt`
169×	`prod-diff`
47×	`add-exp-log` `add-cbrt-cube`
34×	`div-inv`
17×	`cbrt-undiv` `div-exp`
14×	`prod-exp` `cbrt-unprod`
13×	`fma-neg` `distribute-lft-out--`
12×	`associate-l`
11×	`associate-r` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-/l/`
7×	`flip3--` `associate-*l/` `flip--`
6×	`pow1` `frac-times` `associate-/r/` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `associate-r/` `clear-num` `distribute-lft-out` `associate-/l`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 328

Calls

4 calls:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
55.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* (/ PI 2.0) 1.0) (- b a))) (+ b a))
18.0ms	(/ (* (/ PI 2.0) 1.0) (- b a))
84.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* (/ PI 2.0) 1.0) (- b a)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
230.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* (/ PI 2.0) 1.0) (- b a))) (+ b a))
54.0ms	(/ (* (/ PI 2.0) 1.0) (- b a))
76.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* (/ PI 2.0) 1.0) (- b a)))

simplify76.0ms

Algorithm

egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1246	5817
1	5001	4204

prune668.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* 0.5 (/ PI (* a b))) (+ b a))
0.8b	(/ PI (* a b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log` `add-cbrt-cube`
10×	`*-un-lft-identity`
8×	`cbrt-undiv` `div-exp`
7×	`times-frac`
6×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`prod-exp` `associate-/r*` `cbrt-unprod`
4×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r/` `log1p-expm1-u` `div-inv` `distribute-lft-out` `add-log-exp`
1×	`flip3-+` `associate-*r/` `flip-+` `associate-/l/`

Counts

2 → 55

Calls

2 calls:

11.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
3.0ms	(/ PI (* a b))

series86.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
20.0ms	(/ PI (* a b))

simplify38.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	300	334
1	1490	268
2	5001	268

prune101.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes62.0ms

Accuracy

0% (0.3b 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	6
1	16	6

end0.0ms

sample1.1s

Algorithm

intervals

Results

969.0ms

9618×

body

valid