Details

Time bar (total: 8.2s)

sample62.0ms

Algorithm
intervals
Results
38.0ms321×body80valid

simplify44.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.0b
(/ 1.0 (- (* b b) (* a a)))
3.8b
(- (* b b) (* a a))
10.6b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite370.0ms

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:
98.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
26.0ms
(/ 1.0 (- (* b b) (* a a)))
17.0ms
(- (* b b) (* a a))
218.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
46.0ms
(/ 1.0 (- (* b b) (* a a)))
39.0ms
(- (* b b) (* a a))
108.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify95.0ms

Counts
165 → 165

prune553.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
0.1b
(/ (/ 1.0 (+ b a)) (- b a))
0.2b
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
10.6b
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite467.0ms

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:
15.0ms
(/ 1.0 (+ b a))
38.0ms
(/ (/ 1.0 (+ b a)) (- b a))
144.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
222.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series373.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ 1.0 (+ b a))
68.0ms
(/ (/ 1.0 (+ b a)) (- b a))
74.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
168.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify56.0ms

Counts
370 → 370

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
0.2b
(/ (* (* 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)))

rewrite629.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
47×*-un-lft-identity
42×add-sqr-sqrt
36×times-frac
30×associate-*r*
25×add-cube-cbrt
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-- div-inv distribute-lft-out--
4×associate-*l* pow-prod-down frac-sub associate-/l* add-log-exp difference-of-squares
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in flip3-+ associate-*l/ clear-num *-commutative flip-+ unswap-sqr
Counts
4 → 148
Calls
4 calls:
12.0ms
(/ 1.0 (+ b a))
92.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
471.0ms
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
47.0ms
(* PI (/ 1.0 (+ b a)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1.0 (+ b a))
152.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
163.0ms
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
62.0ms
(* PI (/ 1.0 (+ b a)))

simplify133.0ms

Counts
160 → 160

prune507.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite433.0ms

Algorithm
rewrite-expression-head
Rules
272×add-exp-log add-cbrt-cube
129×prod-exp cbrt-unprod
87×cbrt-undiv div-exp
21×*-un-lft-identity times-frac associate-*r/
20×add-sqr-sqrt
19×associate-*r*
18×pow1
15×add-cube-cbrt
9×pow-prod-down
8×distribute-rgt-in distribute-lft-in
6×associate-/l/ associate-/l*
5×flip3-- flip-- div-inv
4×frac-times sub-neg associate-*l* associate-/r/ add-log-exp
3×distribute-lft-out
2×frac-2neg associate-*l/ clear-num associate-/r* *-commutative unswap-sqr
1×flip3-+ flip-+
Counts
4 → 206
Calls
4 calls:
135.0ms
(/ (/ (* (* PI (/ 1.0 (+ b a))) (* 1.0 (- b a))) (* a b)) (* 2.0 (- b a)))
101.0ms
(* (* PI (/ 1.0 (+ b a))) (* 1.0 (- b a)))
34.0ms
(* PI (/ 1.0 (+ b a)))
137.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (* 1.0 (- b a))) (* a b))

series500.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (/ (* (* PI (/ 1.0 (+ b a))) (* 1.0 (- b a))) (* a b)) (* 2.0 (- b a)))
132.0ms
(* (* PI (/ 1.0 (+ b a))) (* 1.0 (- b a)))
79.0ms
(* PI (/ 1.0 (+ b a)))
199.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (* 1.0 (- b a))) (* a b))

simplify42.0ms

Counts
218 → 218

prune290.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes80.0ms

Accuracy

5.8% (0.3b remaining)

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

bsearch0.0ms

simplify33.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s9583×body80valid