Details

Time bar (total: 8.8s)

sample23.0ms

Algorithm
intervals
Results
13.0ms310×body80valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
19010
238410
3182810
4500110

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b
(/ 1.0 (- (* b b) (* a a)))
4.0b
(- (* b b) (* a a))
9.9b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite173.0ms

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))
99.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
49.0ms
(/ 1.0 (- (* b b) (* a a)))
29.0ms
(- (* b b) (* a a))
89.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify153.0ms

Algorithm
egg-herbie
Counts
513 → 513
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0248115016
1500213008

prune1.0s

Filtered
513 candidates to 220 candidates (42.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(/ (/ 1.0 (+ b a)) (- b a))
0.2b
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
9.9b
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite311.0ms

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))
18.0ms
(/ (/ 1.0 (+ b a)) (- b a))
63.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
129.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (/ 1.0 a) (/ 1.0 b))
49.0ms
(/ (/ 1.0 (+ b a)) (- b a))
62.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
97.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify225.0ms

Algorithm
egg-herbie
Counts
887 → 887
Iterations

Useful iterations: 1 (56.0ms)

IterNodesCost
0315621276
1500319725

prune1.7s

Filtered
887 candidates to 414 candidates (46.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (* (* 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)))

rewrite298.0ms

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:
23.0ms
(- (/ 1.0 a) (/ 1.0 b))
108.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
91.0ms
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
15.0ms
(* PI (/ 1.0 (+ b a)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (/ 1.0 a) (/ 1.0 b))
94.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
102.0ms
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
57.0ms
(* PI (/ 1.0 (+ b a)))

simplify170.0ms

Algorithm
egg-herbie
Counts
677 → 677
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0241817086
1500115039

prune1.3s

Filtered
677 candidates to 285 candidates (42.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
0.2b
(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.4b
(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite287.0ms

Algorithm
rewrite-expression-head
Rules
753×times-frac
592×add-sqr-sqrt *-un-lft-identity
568×add-cube-cbrt
507×prod-diff
171×distribute-rgt-in distribute-lft-in
87×div-inv
50×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp
16×prod-exp cbrt-unprod
13×fma-neg
12×associate-*r*
11×associate-/l*
10×distribute-lft-out--
9×pow1
8×associate-*r/ associate-/r/ difference-of-squares
6×add-log-exp
5×associate-/r*
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/ distribute-lft-out
3×sub-neg flip3-+ pow-prod-down frac-sub flip-+
2×frac-2neg clear-num
1×diff-log associate-*l* *-commutative
Counts
4 → 664
Calls
4 calls:
23.0ms
(- (/ 1.0 a) (/ 1.0 b))
33.0ms
(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
94.0ms
(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
78.0ms
(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (/ 1.0 a) (/ 1.0 b))
93.0ms
(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
100.0ms
(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
68.0ms
(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify158.0ms

Algorithm
egg-herbie
Counts
676 → 676
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0238115859
1500112851

prune1.2s

Filtered
676 candidates to 285 candidates (42.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes90.0ms

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)

IterNodesCost
0179
1179

end0.0ms

sample572.0ms

Algorithm
intervals
Results
417.0ms9614×body80valid