Details

Time bar (total: 13.6s)

sample59.0ms

Algorithm
intervals
Results
35.0ms315×body80valid

simplify741.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b
(/ 1.0 (- (* b b) (* a a)))
4.8b
(- (* b b) (* a a))
7.9b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite307.0ms

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:
63.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
27.0ms
(/ 1.0 (- (* b b) (* a a)))
17.0ms
(- (* b b) (* a a))
194.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
64.0ms
(/ 1.0 (- (* b b) (* a a)))
41.0ms
(- (* b b) (* a a))
129.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.7s

Counts
165 → 165

prune551.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.4b

localize24.0ms

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)))
7.9b
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite428.0ms

Algorithm
rewrite-expression-head
Rules
352×times-frac
305×*-un-lft-identity
256×add-sqr-sqrt
149×add-cube-cbrt
108×associate-*r*
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
17×div-inv
14×frac-times associate-*l*
12×flip3-+ flip-+
11×pow1
9×associate-/r*
8×associate-*r/ associate-*l/
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 clear-num *-commutative
1×associate-/l/
Counts
4 → 358
Calls
4 calls:
20.0ms
(/ 1.0 (+ b a))
35.0ms
(/ (/ 1.0 (+ b a)) (- b a))
112.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
210.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ 1.0 (+ b a))
85.0ms
(/ (/ 1.0 (+ b a)) (- b a))
86.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
131.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify811.0ms

Counts
370 → 370

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))
0.4b
(* (/ PI 2.0) (/ 1.0 (+ b a)))
0.6b
(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite437.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-sqr-sqrt add-cbrt-cube
59×*-un-lft-identity
52×times-frac
33×add-cube-cbrt
30×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*
11×pow1
9×flip3-- associate-/r* flip--
8×frac-sub
7×distribute-lft-out distribute-lft-out--
6×associate-/r/ div-inv difference-of-squares
4×pow-prod-down associate-/l* add-log-exp unswap-sqr
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in flip3-+ clear-num *-commutative flip-+
Counts
4 → 190
Calls
4 calls:
12.0ms
(/ 1.0 (+ b a))
139.0ms
(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
78.0ms
(* (/ PI 2.0) (/ 1.0 (+ b a)))
197.0ms
(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ 1.0 (+ b a))
133.0ms
(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
83.0ms
(* (/ PI 2.0) (/ 1.0 (+ b a)))
151.0ms
(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify617.0ms

Counts
202 → 202

prune722.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
0.2b
(/ (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
0.4b
(* (/ PI 2.0) (/ 1.0 (+ b a)))
0.5b
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))

rewrite292.0ms

Algorithm
rewrite-expression-head
Rules
444×times-frac
393×add-sqr-sqrt
331×*-un-lft-identity
117×distribute-lft-out--
115×add-cube-cbrt
101×difference-of-squares
83×associate-/r*
61×add-exp-log add-cbrt-cube
39×div-inv
29×cbrt-undiv div-exp
18×associate-*r*
14×associate-/r/
13×associate-*l*
12×prod-exp cbrt-unprod
9×associate-/l*
7×distribute-lft-out
6×pow1
5×associate-/l/
4×flip3-- flip-- add-log-exp unswap-sqr
3×frac-2neg clear-num frac-sub
2×frac-times flip3-+ associate-*r/ associate-*l/ flip-+
1×div-sub pow-prod-down *-commutative
Counts
4 → 352
Calls
4 calls:
23.0ms
(/ 1.0 (+ b a))
124.0ms
(/ (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
47.0ms
(* (/ PI 2.0) (/ 1.0 (+ b a)))
74.0ms
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ 1.0 (+ b a))
152.0ms
(/ (* (/ PI 2.0) (/ 1.0 (+ b a))) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
79.0ms
(* (/ PI 2.0) (/ 1.0 (+ b a)))
72.0ms
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))

simplify735.0ms

Counts
364 → 364

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes74.0ms

Accuracy

32.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify613.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
990.0ms9611×body80valid