Details

Time bar (total: 7.1s)

sample24.0ms

Algorithm
intervals
Results
14.0ms313×body80valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
19010
238410
3182810
4500110

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b
(/ 1.0 (- (* b b) (* a a)))
4.8b
(- (* b b) (* a a))
8.7b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite177.0ms

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))
102.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
46.0ms
(/ 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)))

simplify161.0ms

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: 8.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
0.1b
(/ (/ 1.0 (+ b a)) (- b a))
0.1b
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.7b
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
820×times-frac
669×*-un-lft-identity
620×add-sqr-sqrt
513×add-cube-cbrt
338×prod-diff
171×distribute-rgt-in distribute-lft-in
108×associate-*r*
69×div-inv
61×add-exp-log add-cbrt-cube
42×distribute-lft-out--
41×difference-of-squares
37×distribute-lft-out
28×associate-/r/
22×cbrt-undiv div-exp
21×associate-/l*
19×prod-exp cbrt-unprod
14×frac-times associate-*l*
12×flip3-+ flip-+
11×pow1
9×associate-/r*
8×associate-*r/ associate-*l/
6×flip3-- flip-- unswap-sqr
4×expm1-log1p-u pow-prod-down frac-sub log1p-expm1-u add-log-exp
2×sub-neg frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 704
Calls
4 calls:
5.0ms
(/ 1.0 (+ b a))
15.0ms
(/ (/ 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)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 1.0 (+ b a))
49.0ms
(/ (/ 1.0 (+ b a)) (- b a))
60.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
101.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify194.0ms

Algorithm
egg-herbie
Counts
716 → 716
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0314416922
1500115938

prune1.3s

Filtered
716 candidates to 335 candidates (46.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
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)))
0.4b
(* PI (/ 1.0 (+ b a)))

rewrite268.0ms

Algorithm
rewrite-expression-head
Rules
504×times-frac
411×*-un-lft-identity
406×add-sqr-sqrt
389×add-cube-cbrt
338×prod-diff
171×distribute-rgt-in distribute-lft-in
57×div-inv
52×add-exp-log add-cbrt-cube
30×associate-*r*
21×prod-exp cbrt-unprod
17×associate-*r/
13×cbrt-undiv div-exp
11×pow1
7×associate-/l/ distribute-lft-out
6×frac-times associate-/r/
5×flip3-- associate-/r* flip-- distribute-lft-out--
4×expm1-log1p-u associate-*l* pow-prod-down frac-sub log1p-expm1-u associate-/l* add-log-exp difference-of-squares
2×sub-neg frac-2neg flip3-+ associate-*l/ clear-num *-commutative flip-+ unswap-sqr
Counts
4 → 494
Calls
4 calls:
5.0ms
(/ 1.0 (+ b a))
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)))
15.0ms
(* PI (/ 1.0 (+ b a)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ 1.0 (+ b a))
91.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
100.0ms
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
56.0ms
(* PI (/ 1.0 (+ b a)))

simplify143.0ms

Algorithm
egg-herbie
Counts
506 → 506
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0240912732
1500111631

prune861.0ms

Filtered
506 candidates to 206 candidates (40.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
275×add-sqr-sqrt
259×times-frac
235×*-un-lft-identity
84×associate-*r*
83×add-cube-cbrt
80×distribute-lft-out--
69×difference-of-squares
45×add-exp-log add-cbrt-cube
27×div-inv
15×cbrt-undiv div-exp associate-/l*
14×prod-exp cbrt-unprod
10×associate-*l*
9×associate-/r*
8×pow1 associate-/r/
7×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- flip-- associate-/l/
2×frac-2neg flip3-+ associate-*r/ pow-prod-down clear-num *-commutative flip-+
1×frac-times div-sub associate-*l/ frac-sub
Counts
4 → 276
Calls
4 calls:
5.0ms
(/ 1.0 (+ b a))
66.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
104.0ms
(* (/ (* PI (/ 1.0 (+ b a))) 2.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
15.0ms
(* PI (/ 1.0 (+ b a)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ 1.0 (+ b a))
45.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
96.0ms
(* (/ (* PI (/ 1.0 (+ b a))) 2.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
55.0ms
(* PI (/ 1.0 (+ b a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
288 → 288
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011142752
150022507

prune656.0ms

Filtered
288 candidates to 193 candidates (67.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes60.0ms

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
01810
11810

end0.0ms

sample584.0ms

Algorithm
intervals
Results
428.0ms9632×body80valid