Details

sample24.0ms

Algorithm

intervals

Results

13.0ms

307×

body

valid

simplify39.0ms

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: 12.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
2.9b	(- (* b b) (* a a))
8.9b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite245.0ms

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:

42.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
12.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
140.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
91.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify151.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune872.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.9b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

1061×	`times-frac`
851×	`*-un-lft-identity`
814×	`add-sqr-sqrt`
695×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
108×	`associate-r`
97×	`div-inv`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`associate-/l*`
14×	`frac-times` `associate-l`
13×	`fma-neg`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
2×	`*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 875

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
26.0ms	(/ (/ 1.0 (+ b a)) (- b a))
81.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
170.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
48.0ms	(/ (/ 1.0 (+ b a)) (- b a))
65.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
98.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify215.0ms

Algorithm

egg-herbie

Counts

887 → 887

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	3156	21276
1	5003	19725

prune1.6s

Pruning

10 alts after pruning (10 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	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* PI (/ 1.0 (+ b a)))
0.4b	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite522.0ms

Algorithm

rewrite-expression-head

Rules

745×	`times-frac`
600×	`add-sqr-sqrt`
593×	`*-un-lft-identity`
571×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
85×	`div-inv`
50×	`add-exp-log` `add-cbrt-cube`
30×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
17×	`associate-*r/`
13×	`fma-neg`
12×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`distribute-lft-out--`
8×	`difference-of-squares`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg` `distribute-lft-out`
2×	`associate-l/` `-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r` `flip-+` `associate-/l`

Counts

4 → 665

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
136.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
25.0ms	(* PI (/ 1.0 (+ b a)))
272.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
92.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
52.0ms	(* PI (/ 1.0 (+ b a)))
103.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify171.0ms

Algorithm

egg-herbie

Counts

677 → 677

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2418	17086
1	5001	14779

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

361×	`times-frac`
283×	`add-sqr-sqrt`
264×	`*-un-lft-identity`
218×	`add-cube-cbrt`
169×	`prod-diff`
50×	`add-exp-log` `add-cbrt-cube`
42×	`div-inv`
31×	`associate-/r*`
25×	`distribute-lft-out--`
21×	`cbrt-undiv` `div-exp`
20×	`difference-of-squares`
18×	`associate-r`
13×	`fma-neg`
12×	`prod-exp` `associate-/r/` `cbrt-unprod`
6×	`pow1` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `associate-*r/` `frac-sub` `log1p-expm1-u`
3×	`associate-l` `associate-/l/` `distribute-lft-out`
2×	`frac-2neg` `clear-num` `associate-/l*` `unswap-sqr`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 362

Calls

4 calls:

30.0ms	(- (/ 1.0 a) (/ 1.0 b))
57.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
52.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
28.0ms	(* PI (/ 1.0 (+ b a)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
95.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
59.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
50.0ms	(* PI (/ 1.0 (+ b a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

374 → 374

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1438	6138
1	5001	4750

prune727.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample630.0ms

Algorithm

intervals

Results

411.0ms

9598×

body

valid