Details

Time bar (total: 4.4s)

sample27.0ms

Algorithm
intervals
Results
17.0ms315×body80valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03010
18910
237710
3177910
4500110

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b
(/ 1.0 (- (* b b) (* a a)))
3.9b
(- (* b b) (* a a))
8.5b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite52.0ms

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:
12.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
3.0ms
(- (* b b) (* a a))
22.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
40.0ms
(/ 1.0 (- (* b b) (* a a)))
30.0ms
(- (* b b) (* a a))
88.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify107.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08041567
145031342
250021342

prune382.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
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)))
8.5b
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
171×add-exp-log
137×add-cbrt-cube
83×prod-exp cbrt-unprod
81×add-sqr-sqrt
67×times-frac
65×*-un-lft-identity
58×associate-*r*
49×cbrt-undiv div-exp
47×frac-times
35×add-cube-cbrt
33×associate-*l/
20×pow1
19×associate-*r/
16×distribute-lft-out--
15×cbrt-prod associate-*l*
14×difference-of-squares
10×flip3-- pow-prod-down flip--
9×frac-sub
7×div-inv
6×add-log-exp
4×associate-/r/ unswap-sqr
3×sub-neg *-commutative
2×distribute-rgt-in distribute-lft-in
1×flip3-+ diff-log flip-+ distribute-lft-out
Counts
4 → 244
Calls
4 calls:
11.0ms
(- (/ 1.0 a) (/ 1.0 b))
20.0ms
(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
13.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
37.0ms
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (/ 1.0 a) (/ 1.0 b))
120.0ms
(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
226.0ms
(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
151.0ms
(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify60.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014133876
150013230

prune672.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
138×add-exp-log
110×add-cbrt-cube
77×prod-exp cbrt-unprod
62×add-sqr-sqrt
54×*-un-lft-identity
51×times-frac
48×associate-*r*
28×cbrt-undiv div-exp
27×pow1
26×add-cube-cbrt
17×associate-*r/
16×pow-prod-down distribute-lft-out--
15×cbrt-prod
14×difference-of-squares
7×associate-/l/
6×frac-times flip3-- flip-- div-inv add-log-exp
5×frac-sub
4×associate-/r/
3×sub-neg
2×distribute-rgt-in distribute-lft-in associate-*l* associate-*l/ *-commutative
1×frac-2neg flip3-+ diff-log clear-num associate-/r* flip-+ associate-/l*
Counts
4 → 187
Calls
4 calls:
12.0ms
(- (/ 1.0 a) (/ 1.0 b))
36.0ms
(/ (* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
28.0ms
(* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
16.0ms
(* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a)))

series556.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (/ 1.0 a) (/ 1.0 b))
148.0ms
(/ (* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
261.0ms
(* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
116.0ms
(* (* PI (* (cbrt 1.0) (cbrt 1.0))) (/ (cbrt 1.0) (- b a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010932909
150012435

prune559.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
0.5b
(/ PI (* a b))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log add-cbrt-cube
14×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/l*
3×associate-*r/
2×pow1 frac-2neg clear-num associate-/r* associate-/r/ div-inv add-log-exp
1×flip3-+ flip-+ associate-/l/
Counts
2 → 53
Calls
2 calls:
10.0ms
(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
4.0ms
(/ PI (* a b))

series86.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
20.0ms
(/ PI (* a b))

simplify50.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0390416
12377290
25003290

prune85.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0146
1146

end0.0ms

sample579.0ms

Algorithm
intervals
Results
429.0ms9606×body80valid