Details

sample25.0ms

Algorithm

intervals

Results

13.0ms

307×

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: 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)))

rewrite264.0ms

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:

45.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms	(/ 1.0 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))
154.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
91.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify146.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune889.0ms

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)))

rewrite405.0ms

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:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
28.0ms	(/ (/ 1.0 (+ b a)) (- b a))
86.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
182.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ 1.0 a) (/ 1.0 b))
48.0ms	(/ (/ 1.0 (+ b a)) (- b a))
69.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
102.0ms	(* (* (/ 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

prune1.8s

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 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b	(* (/ PI 2.0) (/ 1.0 (+ b a)))
0.4b	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

761×	`times-frac`
619×	`add-sqr-sqrt`
605×	`*-un-lft-identity`
579×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
86×	`div-inv`
59×	`add-exp-log` `add-cbrt-cube`
30×	`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`
12×	`distribute-lft-out--`
11×	`pow1`
10×	`flip3--` `flip--` `difference-of-squares`
9×	`frac-sub`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `distribute-lft-out`
2×	`*-commutative`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 707

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
162.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
36.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
145.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (/ 1.0 a) (/ 1.0 b))
99.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
51.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))
106.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify177.0ms

Algorithm

egg-herbie

Counts

719 → 719

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2643	18215
1	5001	16153

prune1.3s

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

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

685×	`times-frac`
587×	`add-sqr-sqrt`
513×	`*-un-lft-identity`
297×	`add-cube-cbrt`
169×	`prod-diff`
122×	`distribute-lft-out--`
105×	`difference-of-squares`
79×	`associate-/r*`
67×	`div-inv`
59×	`add-exp-log` `add-cbrt-cube`
28×	`cbrt-undiv` `div-exp`
18×	`associate-r`
13×	`fma-neg` `associate-l`
12×	`prod-exp` `associate-/r/` `cbrt-unprod`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`flip3--` `flip--` `associate-/l/`
4×	`expm1-log1p-u` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`distribute-lft-out`
2×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 531

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
71.0ms	(/ (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
52.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
39.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(/ (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
48.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
60.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify99.0ms

Algorithm

egg-herbie

Counts

543 → 543

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2141	8470
1	5001	7240

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes68.0ms

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	22	12
1	22	12

end0.0ms

sample620.0ms

Algorithm

intervals

Results

409.0ms

9598×

body

valid