Details

Time bar (total: 4.2m)

sample23.0ms

Algorithm
intervals
Results
13.0ms300×body80valid

simplify1.7s

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)))

rewrite99.0ms

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:
21.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
3.0ms
(- (* b b) (* a a))
65.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms
(/ 1.0 (- (* b b) (* a a)))
37.0ms
(- (* b b) (* a a))
90.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.3s

Counts
165 → 165
Iterations

Useful iterations: 2 (621.0ms)

IterNodesCost
02583239
18023164
235182682
done50012682

prune430.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.9b

localize15.0ms

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)))

rewrite332.0ms

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:
7.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
58.0ms
(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
22.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
232.0ms
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series630.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
118.0ms
(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
224.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
154.0ms
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify471.0ms

Counts
259 → 259
Iterations

Useful iterations: 1 (139.0ms)

IterNodesCost
03987317
113937077
done50017077

prune634.0ms

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

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
98×add-exp-log
76×add-cbrt-cube
50×prod-exp cbrt-unprod
28×add-sqr-sqrt
26×*-un-lft-identity
22×cbrt-undiv div-exp associate-*r*
20×times-frac
17×associate-*r/
15×pow1
12×add-cube-cbrt
10×associate-*l/
7×pow-prod-down associate-/l/
6×frac-times associate-/r/
5×flip3-- associate-/r* flip-- div-inv distribute-lft-out--
4×associate-*l* frac-sub add-log-exp difference-of-squares
3×distribute-lft-out
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in flip3-+ clear-num *-commutative flip-+ associate-/l* unswap-sqr
Counts
4 → 147
Calls
4 calls:
7.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
176.0ms
(/ (* (* (* PI (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
193.0ms
(* (* (* PI (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
18.0ms
(* PI (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))

series638.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
150.0ms
(/ (* (* (* PI (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
162.0ms
(* (* (* PI (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
189.0ms
(* PI (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))

simplify1.7s

Counts
159 → 159
Iterations

Useful iterations: 2 (791.0ms)

IterNodesCost
02514107
18513997
246212737
done50002737

prune394.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ PI (/ (/ 2.0 (- (/ 1.0 a) (/ 1.0 b))) (/ (pow (cbrt 1.0) 3) (+ b a)))) (- b a))
0.2b
(/ 2.0 (- (/ 1.0 a) (/ 1.0 b)))
0.2b
(/ (/ 2.0 (- (/ 1.0 a) (/ 1.0 b))) (/ (pow (cbrt 1.0) 3) (+ b a)))
0.6b
(/ PI (/ (/ 2.0 (- (/ 1.0 a) (/ 1.0 b))) (/ (pow (cbrt 1.0) 3) (+ b a))))

rewrite21.7s

Algorithm
rewrite-expression-head
Rules
387917×times-frac
210672×*-un-lft-identity
196588×add-sqr-sqrt
111754×add-cube-cbrt
37028×distribute-lft-out--
31639×difference-of-squares
23760×cbrt-prod unpow-prod-down cube-prod
17820×distribute-lft-out
13595×div-inv
10131×associate-/l*
7400×associate-/r/
3960×cube-mult unpow3 sqr-pow
3454×associate-/r*
1797×flip3-- flip--
1796×frac-sub
990×flip3-+ flip-+
109×add-exp-log
83×div-exp
61×add-cbrt-cube
41×cbrt-undiv
6×pow-to-exp pow-exp
4×pow1 frac-2neg clear-num add-log-exp
2×associate-/l/
Counts
4 → 77555
Calls
4 calls:
3.4s
(/ (/ PI (/ (/ 2.0 (- (/ 1.0 a) (/ 1.0 b))) (/ (pow (cbrt 1.0) 3) (+ b a)))) (- b a))
33.0ms
(/ 2.0 (- (/ 1.0 a) (/ 1.0 b)))
131.0ms
(/ (/ 2.0 (- (/ 1.0 a) (/ 1.0 b))) (/ (pow (cbrt 1.0) 3) (+ b a)))
642.0ms
(/ PI (/ (/ 2.0 (- (/ 1.0 a) (/ 1.0 b))) (/ (pow (cbrt 1.0) 3) (+ b a))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (/ PI (/ (/ 2.0 (- (/ 1.0 a) (/ 1.0 b))) (/ (pow (cbrt 1.0) 3) (+ b a)))) (- b a))
50.0ms
(/ 2.0 (- (/ 1.0 a) (/ 1.0 b)))
79.0ms
(/ (/ 2.0 (- (/ 1.0 a) (/ 1.0 b))) (/ (pow (cbrt 1.0) 3) (+ b a)))
101.0ms
(/ PI (/ (/ 2.0 (- (/ 1.0 a) (/ 1.0 b))) (/ (pow (cbrt 1.0) 3) (+ b a))))

simplify25.1s

Counts
77567 → 77567
Iterations

Useful iterations: 0 (7.2s)

IterNodesCost
0510023959100
done510023959100

prune3.3m

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes71.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01824
11924
done1924

end0.0ms

sample526.0ms

Algorithm
intervals
Results
383.0ms9545×body80valid