Details

Time bar (total: 6.4s)

sample30.0ms

Algorithm
intervals
Results
17.0ms300×body80valid

simplify34.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b
(/ 1.0 (- (* b b) (* a a)))
5.0b
(- (* b b) (* a a))
7.5b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
47×times-frac
39×*-un-lft-identity
36×add-exp-log add-cbrt-cube
31×add-cube-cbrt
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×div-inv distribute-lft-out--
4×pow-prod-down associate-/r* associate-/r/ frac-sub unswap-sqr
3×sub-neg associate-/l*
2×distribute-rgt-in distribute-lft-in *-commutative
1×frac-2neg diff-log clear-num
Counts
4 → 153
Calls
4 calls:
46.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
15.0ms
(/ 1.0 (- (* b b) (* a a)))
8.0ms
(- (* b b) (* a a))
135.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms
(/ 1.0 (- (* b b) (* a a)))
38.0ms
(- (* b b) (* a a))
96.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify103.0ms

Counts
165 → 165

prune422.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- b a))
0.2b
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b
(/ (/ PI 2.0) (+ b a))
7.5b
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite277.0ms

Algorithm
rewrite-expression-head
Rules
234×times-frac
193×*-un-lft-identity
164×add-sqr-sqrt
117×add-cube-cbrt
61×add-exp-log add-cbrt-cube
59×associate-*l*
33×associate-*r*
27×distribute-lft-out
22×cbrt-undiv div-exp
19×prod-exp cbrt-unprod
16×associate-/l*
15×div-inv
14×frac-times
12×distribute-lft-out--
11×pow1 difference-of-squares
9×associate-/r*
8×associate-*r/ associate-*l/ associate-/r/
6×flip3-- flip-- unswap-sqr
4×pow-prod-down frac-sub add-log-exp
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in flip3-+ clear-num *-commutative flip-+
1×associate-/l/
Counts
4 → 288
Calls
4 calls:
12.0ms
(/ 1.0 (- b a))
81.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
19.0ms
(/ (/ PI 2.0) (+ b a))
149.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1.0 (- b a))
74.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
59.0ms
(/ (/ PI 2.0) (+ b a))
107.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify48.0ms

Counts
300 → 300

prune753.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
61×add-exp-log *-un-lft-identity add-cbrt-cube
57×times-frac
35×add-cube-cbrt
33×associate-*r*
27×frac-times
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
15×associate-*r/ associate-*l/ associate-/l/
14×associate-*l*
12×distribute-lft-out--
11×pow1 difference-of-squares
10×flip3-- flip--
9×associate-/r*
8×frac-sub
6×associate-/r/ div-inv
4×pow-prod-down associate-/l* add-log-exp unswap-sqr
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in clear-num *-commutative distribute-lft-out
1×flip3-+ flip-+
Counts
4 → 195
Calls
4 calls:
12.0ms
(/ 1.0 (- b a))
94.0ms
(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
117.0ms
(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
40.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ 1.0 (- b a))
106.0ms
(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
82.0ms
(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
65.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify39.0ms

Counts
207 → 207

prune533.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
229×times-frac
219×*-un-lft-identity
217×add-sqr-sqrt
83×add-cube-cbrt
75×associate-*r*
61×add-exp-log add-cbrt-cube
52×distribute-lft-out--
43×difference-of-squares
25×distribute-lft-out
23×div-inv
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
15×associate-/l*
14×associate-*l*
11×pow1
9×associate-/r*
8×associate-/r/
6×frac-times associate-*l/
4×associate-*r/ pow-prod-down add-log-exp unswap-sqr
3×flip3-- flip-- associate-/l/
2×frac-2neg flip3-+ clear-num *-commutative flip-+
1×div-sub frac-sub
Counts
4 → 269
Calls
4 calls:
13.0ms
(/ 1.0 (- b a))
136.0ms
(* (* (/ PI 2.0) (/ 1.0 (- b a))) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a)))
79.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))
46.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ 1.0 (- b a))
115.0ms
(* (* (/ PI 2.0) (/ 1.0 (- b a))) (/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a)))
88.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (+ b a))
59.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify47.0ms

Counts
281 → 281

prune677.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes78.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.1s9496×body80valid