Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

311×

body

valid

simplify40.0ms

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: 13.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b	(/ 1.0 (- (* b b) (* a a)))
3.1b	(- (* b b) (* a a))
9.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite170.0ms

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:

22.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
97.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
42.0ms	(/ 1.0 (- (* b b) (* a a)))
35.0ms	(- (* b b) (* a a))
93.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify162.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune923.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.7b

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)))
9.8b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite305.0ms

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:

23.0ms	(- (/ 1.0 a) (/ 1.0 b))
15.0ms	(/ (/ 1.0 (+ b a)) (- b a))
61.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
128.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
53.0ms	(/ (/ 1.0 (+ b a)) (- b a))
61.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
96.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify233.0ms

Algorithm

egg-herbie

Counts

887 → 887

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	3156	21276
1	5003	19725

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

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))) (- (/ 1.0 a) (/ 1.0 b)))
0.3b	(* PI (/ 1.0 (+ b a)))

rewrite304.0ms

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:

25.0ms	(- (/ 1.0 a) (/ 1.0 b))
108.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
93.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
16.0ms	(* PI (/ 1.0 (+ b a)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
103.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
51.0ms	(* PI (/ 1.0 (+ b a)))

simplify189.0ms

Algorithm

egg-herbie

Counts

677 → 677

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2418	17086
1	5001	15039

prune1.3s

Pruning

11 alts after pruning (11 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))
0.3b	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 662

Calls

4 calls:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
6.0ms	(/ (* PI 1.0) (+ b a))
103.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
100.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
56.0ms	(/ (* PI 1.0) (+ b a))
106.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify177.0ms

Algorithm

egg-herbie

Counts

674 → 674

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2400	17101
1	5002	14141

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes82.0ms

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	18	10
1	18	10

end0.0ms

sample557.0ms

Algorithm

intervals

Results

404.0ms

9574×

body

valid