Details

Time bar (total: 14.3s)

sample33.0ms

Algorithm
intervals
Results
19.0ms318×body80valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01521
13021
28921
337821
4178921
done500021

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b
(/ 1.0 (- (* b b) (* a a)))
5.6b
(- (* b b) (* a a))
7.3b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite287.0ms

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:
67.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
26.0ms
(/ 1.0 (- (* b b) (* a a)))
16.0ms
(- (* b b) (* a a))
172.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
66.0ms
(/ 1.0 (- (* b b) (* a a)))
51.0ms
(- (* b b) (* a a))
134.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify517.0ms

Counts
165 → 165
Iterations

Useful iterations: done (511.0ms)

IterNodesCost
02583239
18733170
done50002752

prune703.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (cbrt 1.0) (- b a))
0.1b
(* (/ PI 2.0) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)) (/ (cbrt 1.0) (- b a))))
0.3b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)) (/ (cbrt 1.0) (- b a)))
7.3b
(* (* (/ PI 2.0) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)) (/ (cbrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite878.0ms

Algorithm
rewrite-expression-head
Rules
173×add-exp-log
137×add-cbrt-cube
106×add-sqr-sqrt
90×times-frac
88×*-un-lft-identity
83×prod-exp cbrt-unprod
52×add-cube-cbrt
50×cbrt-undiv div-exp
49×associate-*r*
47×frac-times
35×cbrt-prod
29×associate-*r/
24×associate-*l*
23×associate-*l/
20×pow1
18×distribute-lft-out--
17×difference-of-squares
10×flip3-- pow-prod-down flip--
8×frac-sub
6×associate-/r/ div-inv associate-/l* unswap-sqr
5×associate-/r*
4×add-log-exp
3×*-commutative
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-2neg flip3-+ clear-num flip-+ distribute-lft-out
Counts
4 → 279
Calls
4 calls:
13.0ms
(/ (cbrt 1.0) (- b a))
163.0ms
(* (/ PI 2.0) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)) (/ (cbrt 1.0) (- b a))))
97.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)) (/ (cbrt 1.0) (- b a)))
588.0ms
(* (* (/ PI 2.0) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)) (/ (cbrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

series701.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (cbrt 1.0) (- b a))
192.0ms
(* (/ PI 2.0) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)) (/ (cbrt 1.0) (- b a))))
148.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)) (/ (cbrt 1.0) (- b a)))
209.0ms
(* (* (/ PI 2.0) (* (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)) (/ (cbrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify930.0ms

Counts
291 → 291
Iterations

Useful iterations: done (904.0ms)

IterNodesCost
04147855
115077608
done50006150

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (cbrt 1.0) (- b a))
0.1b
(/ (* (* (/ PI 2.0) (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.3b
(* (* (/ PI 2.0) (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))
0.3b
(* (/ PI 2.0) (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (- b a))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
166×add-exp-log
129×add-cbrt-cube
88×prod-exp cbrt-unprod
61×add-sqr-sqrt *-un-lft-identity
53×times-frac
40×cbrt-undiv div-exp
35×add-cube-cbrt
33×associate-*r/
27×pow1 frac-times
18×cbrt-prod
16×pow-prod-down
15×associate-*l/ associate-/l/
14×associate-*l*
13×associate-*r*
12×distribute-lft-out--
11×difference-of-squares
9×flip3-- associate-/r* flip--
8×frac-sub
7×associate-/l*
5×div-inv
4×associate-/r/ add-log-exp
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in clear-num *-commutative distribute-lft-out
1×flip3-+ flip-+
Counts
4 → 229
Calls
4 calls:
22.0ms
(/ (cbrt 1.0) (- b a))
520.0ms
(/ (* (* (/ PI 2.0) (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
548.0ms
(* (* (/ PI 2.0) (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))
172.0ms
(* (/ PI 2.0) (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (- b a))))

series618.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ (cbrt 1.0) (- b a))
170.0ms
(/ (* (* (/ PI 2.0) (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
224.0ms
(* (* (/ PI 2.0) (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))
143.0ms
(* (/ PI 2.0) (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (- b a))))

simplify627.0ms

Counts
241 → 241
Iterations

Useful iterations: done (611.0ms)

IterNodesCost
03616441
111796232
done50004852

prune891.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (* 0.5 (/ PI (* a b))) (+ b a))
0.4b
(/ PI (* a b))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log add-cbrt-cube
10×*-un-lft-identity
8×cbrt-undiv div-exp
7×times-frac
6×add-sqr-sqrt add-cube-cbrt
5×prod-exp associate-/r* cbrt-unprod
4×associate-/l*
2×pow1 frac-2neg clear-num associate-/r/ div-inv distribute-lft-out add-log-exp
1×flip3-+ associate-*r/ flip-+ associate-/l/
Counts
2 → 51
Calls
2 calls:
35.0ms
(/ (* 0.5 (/ PI (* a b))) (+ b a))
8.0ms
(/ PI (* a b))

series118.0ms

Counts
2 → 6
Calls
2 calls:
96.0ms
(/ (* 0.5 (/ PI (* a b))) (+ b a))
22.0ms
(/ PI (* a b))

simplify798.0ms

Counts
57 → 57
Iterations

Useful iterations: done (796.0ms)

IterNodesCost
0107688
1299659
21629541
done5000527

prune151.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes74.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11211
done1211

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.4s9580×body80valid