Details

sample29.0ms

Algorithm

intervals

Results

17.0ms

315×

body

valid

simplify42.0ms

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: 17.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
4.5b	(- (* b b) (* a a))
11.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite250.0ms

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:

43.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
12.0ms	(/ 1.0 (- (* b b) (* a a)))
10.0ms	(- (* b b) (* a a))
146.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
39.0ms	(/ 1.0 (- (* b b) (* a a)))
33.0ms	(- (* b b) (* a a))
86.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify159.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune905.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
11.5b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

940×	`times-frac`
738×	`*-un-lft-identity`
713×	`add-sqr-sqrt`
662×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
95×	`div-inv`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
14×	`frac-times`
13×	`fma-neg` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 801

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
77.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
17.0ms	(/ (/ PI 2.0) (+ b a))
174.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- (/ 1.0 a) (/ 1.0 b))
61.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
51.0ms	(/ (/ PI 2.0) (+ b a))
92.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify214.0ms

Algorithm

egg-herbie

Counts

813 → 813

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2928	20392
1	5001	18352

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite572.0ms

Algorithm

rewrite-expression-head

Rules

763×	`times-frac`
622×	`add-sqr-sqrt`
606×	`*-un-lft-identity`
580×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
86×	`div-inv`
59×	`add-exp-log` `add-cbrt-cube`
33×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
13×	`fma-neg` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`frac-sub`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg`
2×	`*-commutative` `distribute-lft-out`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 708

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
296.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
137.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
41.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- (/ 1.0 a) (/ 1.0 b))
85.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
66.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
50.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify193.0ms

Algorithm

egg-herbie

Counts

720 → 720

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2631	18209
1	5001	16146

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (/ PI (* a b)))
0.2b	(/ (* 0.5 (/ PI (* a b))) (+ b a))
0.9b	(/ PI (* a b))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `add-cube-cbrt` `times-frac` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-*r/` `clear-num` `associate-/r/` `distribute-lft-out`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

23.0ms	(* 0.5 (/ PI (* a b)))
24.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
7.0ms	(/ PI (* a b))

series118.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* 0.5 (/ PI (* a b)))
67.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
19.0ms	(/ PI (* a b))

simplify48.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	340	481
1	1769	389
2	5001	389

prune144.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes43.0ms

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	17	6
1	17	6

end0.0ms

sample647.0ms

Algorithm

intervals

Results

418.0ms

9556×

body

valid