Details

Time bar (total: 20.9s)

sample62.0ms

Algorithm
intervals
Results
37.0ms318×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01521
13121
29021
338521
4186021
done500121

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize26.0ms

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)))

rewrite407.0ms

Algorithm
rewrite-expression-head
Rules
515×times-frac
419×add-sqr-sqrt
403×*-un-lft-identity
395×add-cube-cbrt
339×prod-diff
171×distribute-rgt-in distribute-lft-in
57×div-inv
36×add-exp-log add-cbrt-cube
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×distribute-lft-out--
4×expm1-log1p-u pow-prod-down associate-/r* associate-/r/ frac-sub log1p-expm1-u unswap-sqr
3×sub-neg associate-/l*
2×*-commutative
1×frac-2neg fma-neg diff-log clear-num
Counts
4 → 501
Calls
4 calls:
75.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
19.0ms
(/ 1.0 (- (* b b) (* a a)))
14.0ms
(- (* b b) (* a a))
221.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
87.0ms
(/ 1.0 (- (* b b) (* a a)))
36.0ms
(- (* b b) (* a a))
174.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.3s

Counts
513 → 513
Iterations

Useful iterations: done (2.3s)

IterNodesCost
088627857
1291425859
done500223272

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- b a))
0.2b
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b
(/ (/ PI 2.0) (+ b a))
7.3b
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite436.0ms

Algorithm
rewrite-expression-head
Rules
702×times-frac
557×*-un-lft-identity
528×add-sqr-sqrt
481×add-cube-cbrt
338×prod-diff
171×distribute-rgt-in distribute-lft-in
67×div-inv
61×add-exp-log add-cbrt-cube
59×associate-*l*
33×associate-*r*
27×distribute-lft-out
22×cbrt-undiv div-exp
19×prod-exp cbrt-unprod
16×associate-/l*
14×frac-times
12×distribute-lft-out--
11×pow1 difference-of-squares
9×associate-/r*
8×associate-*r/ associate-*l/ associate-/r/
6×flip3-- flip-- unswap-sqr
4×expm1-log1p-u pow-prod-down frac-sub log1p-expm1-u add-log-exp
2×sub-neg frac-2neg flip3-+ clear-num *-commutative flip-+
1×associate-/l/
Counts
4 → 634
Calls
4 calls:
12.0ms
(/ 1.0 (- b a))
109.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
20.0ms
(/ (/ PI 2.0) (+ b a))
228.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series331.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1.0 (- b a))
83.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
70.0ms
(/ (/ PI 2.0) (+ b a))
128.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.5s

Counts
646 → 646
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0103129916
1338727807
done500125121

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI (* (+ a b) 2.0)) (* (/ 1.0 (- b a)) (fma (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) a) (- (/ (pow (cbrt 1.0) 3) b)))))
0.3b
(/ PI (* (+ a b) 2.0))
0.3b
(* (/ PI 2.0) (/ 1.0 (- b a)))
0.4b
(* (/ 1.0 (- b a)) (fma (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) a) (- (/ (pow (cbrt 1.0) 3) b))))

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
62×add-exp-log add-cbrt-cube
50×times-frac
46×*-un-lft-identity
43×associate-*l*
34×add-cube-cbrt
25×associate-*r* prod-exp cbrt-unprod
16×cbrt-undiv div-exp
13×pow1
9×associate-*l/
8×associate-/r/
6×fma-udef distribute-lft-out-- difference-of-squares unswap-sqr
5×distribute-rgt-in distribute-lft-in pow-prod-down div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative associate-/l*
2×frac-times flip3-- flip3-+ associate-*r/ flip-- flip-+
1×frac-2neg clear-num associate-/r*
Counts
4 → 176
Calls
4 calls:
109.0ms
(* (/ PI (* (+ a b) 2.0)) (* (/ 1.0 (- b a)) (fma (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) a) (- (/ (pow (cbrt 1.0) 3) b)))))
12.0ms
(/ PI (* (+ a b) 2.0))
66.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))
43.0ms
(* (/ 1.0 (- b a)) (fma (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) a) (- (/ (pow (cbrt 1.0) 3) b))))

series993.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(* (/ PI (* (+ a b) 2.0)) (* (/ 1.0 (- b a)) (fma (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) a) (- (/ (pow (cbrt 1.0) 3) b)))))
75.0ms
(/ PI (* (+ a b) 2.0))
101.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))
584.0ms
(* (/ 1.0 (- b a)) (fma (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) a) (- (/ (pow (cbrt 1.0) 3) b))))

simplify640.0ms

Counts
188 → 188
Iterations

Useful iterations: done (633.0ms)

IterNodesCost
02974496
19494075
done50002757

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt
70×times-frac
63×*-un-lft-identity
53×associate-*r*
49×add-cube-cbrt
46×associate-*l*
40×add-exp-log add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in prod-exp cbrt-unprod
11×cbrt-undiv div-exp
10×pow1
8×associate-/r/
7×div-inv distribute-lft-out-- difference-of-squares unswap-sqr
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×flip3-- associate-*r/ pow-prod-down *-commutative flip-- associate-/l*
2×frac-times distribute-neg-frac
1×distribute-lft-neg-out neg-mul-1 frac-2neg flip3-+ clear-num associate-/r* flip-+
Counts
4 → 192
Calls
4 calls:
49.0ms
(* PI (/ (* 1.0 (/ 1.0 a)) (- b a)))
12.0ms
(/ PI (* (+ a b) 2.0))
97.0ms
(* (- (/ 1.0 b)) (/ 1.0 (- b a)))
92.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(* PI (/ (* 1.0 (/ 1.0 a)) (- b a)))
63.0ms
(/ PI (* (+ a b) 2.0))
61.0ms
(* (- (/ 1.0 b)) (/ 1.0 (- b a)))
75.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify742.0ms

Counts
204 → 204
Iterations

Useful iterations: done (733.0ms)

IterNodesCost
03342478
110932405
done50002136

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes191.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify18.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03265
14665
25565
36165
46465
done6465

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s9580×body80valid