Details

Time bar (total: 11.5s)

sample23.0ms

Algorithm
intervals
Results
13.0ms300×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01521
13021
28621
335221
4141621
done500021

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b
(/ 1.0 (- (* b b) (* a a)))
3.6b
(- (* b b) (* a a))
9.1b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite111.0ms

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:
23.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
3.0ms
(- (* b b) (* a a))
73.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms
(/ 1.0 (- (* b b) (* a a)))
35.0ms
(- (* b b) (* a a))
88.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.3s

Counts
165 → 165
Iterations

Useful iterations: 2 (606.0ms)

IterNodesCost
02583239
18023164
235182682
done50012682

prune430.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
0.2b
(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
0.3b
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
9.1b
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
176×add-exp-log
140×add-cbrt-cube
84×prod-exp cbrt-unprod
69×add-sqr-sqrt
61×*-un-lft-identity times-frac
58×associate-*r*
51×cbrt-undiv div-exp
47×frac-times
35×add-cube-cbrt
33×associate-*l/
20×pow1
19×associate-*r/
15×cbrt-prod associate-*l*
11×distribute-lft-out--
10×pow-prod-down difference-of-squares
9×flip3-- flip--
8×frac-sub
6×associate-/r/ div-inv
4×associate-/r* add-log-exp unswap-sqr
3×*-commutative distribute-lft-out
2×distribute-rgt-in sub-neg distribute-lft-in flip3-+ flip-+
1×frac-2neg clear-num associate-/l*
Counts
4 → 247
Calls
4 calls:
8.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
66.0ms
(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
25.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
263.0ms
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series652.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
122.0ms
(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
235.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
160.0ms
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify661.0ms

Counts
259 → 259
Iterations

Useful iterations: 1 (139.0ms)

IterNodesCost
03987317
113937077
done50017077

prune667.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite511.0ms

Algorithm
rewrite-expression-head
Rules
116×add-exp-log
88×add-cbrt-cube
55×prod-exp cbrt-unprod
46×add-sqr-sqrt
39×associate-*l/
38×*-un-lft-identity
36×times-frac
32×cbrt-undiv div-exp
27×frac-times
22×associate-*r*
20×add-cube-cbrt
15×pow1 associate-*r/ associate-/l/
14×associate-*l*
9×flip3-- associate-/r* flip--
8×frac-sub
7×pow-prod-down distribute-lft-out--
6×associate-/r/ div-inv difference-of-squares
4×add-log-exp unswap-sqr
3×distribute-lft-out
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in flip3-+ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 191
Calls
4 calls:
8.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
223.0ms
(/ (* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
242.0ms
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
29.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))

series703.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
160.0ms
(/ (* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
177.0ms
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
234.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))

simplify571.0ms

Counts
203 → 203
Iterations

Useful iterations: done (563.0ms)

IterNodesCost
03275264
110955115
done50015105

prune536.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
428×times-frac
378×add-sqr-sqrt
310×*-un-lft-identity
117×distribute-lft-out--
116×add-exp-log
102×add-cube-cbrt
101×difference-of-squares
88×add-cbrt-cube
83×associate-/r*
48×cbrt-undiv div-exp
39×prod-exp cbrt-unprod div-inv
14×associate-/r/
13×associate-*l*
10×associate-*r*
7×associate-/l*
6×pow1
5×associate-*l/ associate-/l/
4×flip3-- flip-- add-log-exp unswap-sqr
3×frac-2neg clear-num frac-sub distribute-lft-out
2×frac-times flip3-+ associate-*r/ flip-+
1×div-sub pow-prod-down *-commutative
Counts
4 → 352
Calls
4 calls:
8.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
96.0ms
(/ (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
35.0ms
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
28.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))

series580.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
159.0ms
(/ (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
48.0ms
(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
235.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))

simplify494.0ms

Counts
364 → 364
Iterations

Useful iterations: 1 (197.0ms)

IterNodesCost
052110194
116079793
done50009793

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes82.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02033
12333
done2333

end0.0ms

sample586.0ms

Algorithm
intervals
Results
424.0ms9545×body80valid