Details

Time bar (total: 15.2s)

sample40.0ms

Algorithm
intervals
Results
27.0ms302×body80valid

simplify750.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize31.0ms

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)))
6.0b
(- (* b b) (* a a))
9.3b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite293.0ms

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:
56.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms
(/ 1.0 (- (* b b) (* a a)))
12.0ms
(- (* b b) (* a a))
198.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
52.0ms
(/ 1.0 (- (* b b) (* a a)))
39.0ms
(- (* b b) (* a a))
145.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.8s

Counts
165 → 165

prune579.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.2b

localize27.0ms

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))
9.3b
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite380.0ms

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:
15.0ms
(/ 1.0 (- b a))
95.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
26.0ms
(/ (/ PI 2.0) (+ b a))
227.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series331.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1.0 (- b a))
80.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
68.0ms
(/ (/ PI 2.0) (+ b a))
128.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify626.0ms

Counts
300 → 300

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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

rewrite429.0ms

Algorithm
rewrite-expression-head
Rules
122×times-frac
108×*-un-lft-identity
88×add-sqr-sqrt
60×add-cube-cbrt
43×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp prod-exp cbrt-unprod distribute-lft-out associate-/l*
12×associate-*r* distribute-lft-out--
11×div-inv
10×associate-*l/ difference-of-squares
9×pow1 associate-/r*
8×associate-/l/
6×frac-times flip3-- associate-*r/ flip-- add-log-exp
5×frac-sub
4×associate-/r/
3×sub-neg pow-prod-down
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num
1×flip3-+ diff-log associate-*l* *-commutative flip-+
Counts
4 → 190
Calls
4 calls:
53.0ms
(- (/ 1.0 a) (/ 1.0 b))
138.0ms
(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
18.0ms
(/ (/ PI 2.0) (+ b a))
200.0ms
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (/ 1.0 a) (/ 1.0 b))
143.0ms
(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
65.0ms
(/ (/ PI 2.0) (+ b a))
159.0ms
(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.8s

Counts
202 → 202

prune753.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
514×times-frac
420×add-sqr-sqrt
380×*-un-lft-identity
142×add-cube-cbrt
122×distribute-lft-out--
105×difference-of-squares
83×associate-/r*
44×div-inv
43×add-exp-log add-cbrt-cube
22×cbrt-undiv div-exp
19×associate-/l*
14×distribute-lft-out
12×associate-/r/
6×prod-exp cbrt-unprod add-log-exp
5×flip3-- flip--
4×pow1 frac-sub associate-/l/
3×frac-2neg clear-num
1×sub-neg flip3-+ diff-log div-sub associate-*l/ flip-+
Counts
4 → 366
Calls
4 calls:
27.0ms
(- (/ 1.0 a) (/ 1.0 b))
84.0ms
(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
67.0ms
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
34.0ms
(/ (/ PI 2.0) (+ b a))

series388.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (/ 1.0 a) (/ 1.0 b))
159.0ms
(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
69.0ms
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
103.0ms
(/ (/ PI 2.0) (+ b a))

simplify836.0ms

Counts
378 → 378

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes112.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify661.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.4s9537×body80valid