Details

Time bar (total: 2.5m)

sample84.0ms

Algorithm
intervals
Results
67.0ms308×body80valid

simplify677.0ms

Calls
1 calls:
Slowest
677.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize52.0ms

Local error

Found 4 expressions with local error:

9.3b
(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
3.9b
(- (* b b) (* a a))
0.6b
(/ PI (- (* b b) (* a a)))
0.1b
(/ 2 (- (/ 1 a) (/ 1 b)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
43×associate-/r/
42×times-frac
25×*-un-lft-identity
23×add-sqr-sqrt
22×div-inv
21×add-cube-cbrt
19×associate-/r*
18×flip3-- flip--
8×frac-sub
6×add-cbrt-cube add-exp-log associate-/l* add-log-exp
4×pow1 insert-posit16 distribute-lft-out--
3×clear-num frac-2neg difference-of-squares
1×cbrt-undiv sub-neg diff-log div-exp associate-/l/
Calls
4 calls:
Slowest
13.0ms
(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
4.0ms
(- (* b b) (* a a))
2.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))
2.0ms
(/ PI (- (* b b) (* a a)))

series198.0ms

Calls
4 calls:
Slowest
84.0ms
(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
58.0ms
(/ PI (- (* b b) (* a a)))
33.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))
24.0ms
(- (* b b) (* a a))

simplify19.9s

Calls
130 calls:
Slowest
697.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
674.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
491.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) (/ 2 (- (pow (/ 1 a) 3) (pow (/ 1 b) 3))))
453.0ms
(/ (/ 1 (- (* b b) (* a a))) (+ (* (/ 1 a) (/ 1 a)) (+ (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))
410.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (/ 2 (- (pow (/ 1 a) 3) (pow (/ 1 b) 3))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.2b

localize16.0ms

Local error

Found 4 expressions with local error:

9.3b
(/ (/ (/ PI (+ b a)) (- b a)) (/ 2 (- (/ 1 a) (/ 1 b))))
0.3b
(/ PI (+ b a))
0.2b
(/ (/ PI (+ b a)) (- b a))
0.1b
(/ 2 (- (/ 1 a) (/ 1 b)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
330×times-frac
155×associate-/r/
126×*-un-lft-identity
124×add-sqr-sqrt
122×add-cube-cbrt
69×div-inv
35×flip3-- flip--
30×associate-/l*
29×flip3-+ flip-+
26×frac-sub
21×associate-/r*
11×add-cbrt-cube add-exp-log
4×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 distribute-lft-out-- add-log-exp
2×associate-/l/
1×difference-of-squares
Calls
4 calls:
Slowest
9.0ms
(/ (/ (/ PI (+ b a)) (- b a)) (/ 2 (- (/ 1 a) (/ 1 b))))
4.0ms
(/ (/ PI (+ b a)) (- b a))
2.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))
1.0ms
(/ PI (+ b a))

series207.0ms

Calls
4 calls:
Slowest
81.0ms
(/ (/ (/ PI (+ b a)) (- b a)) (/ 2 (- (/ 1 a) (/ 1 b))))
65.0ms
(/ (/ PI (+ b a)) (- b a))
39.0ms
(/ PI (+ b a))
22.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))

simplify1.1m

Calls
447 calls:
Slowest
818.0ms
(/ (/ (* (cbrt (/ PI (+ b a))) (cbrt (/ PI (+ b a)))) (* (cbrt (- b a)) (cbrt (- b a)))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
634.0ms
(/ (/ (* (cbrt (/ PI (+ b a))) (cbrt (/ PI (+ b a)))) (* (cbrt (- b a)) (cbrt (- b a)))) (/ 2 (- (pow (/ 1 a) 3) (pow (/ 1 b) 3))))
561.0ms
(/ (sqrt (/ (/ PI (+ b a)) (- b a))) (/ 2 (- (pow (/ 1 a) 3) (pow (/ 1 b) 3))))
560.0ms
(/ (/ (/ PI (+ (pow b 3) (pow a 3))) (* (cbrt (- b a)) (cbrt (- b a)))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
473.0ms
(/ (/ (sqrt (/ PI (+ b a))) 1) (/ 2 (- (pow (/ 1 a) 3) (pow (/ 1 b) 3))))

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ PI (+ b a))
0.2b
(/ (/ PI (+ b a)) (* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a)))
0.1b
(/ 2 (- (/ 1 a) (/ 1 b)))
0.0b
(* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
17×associate-/r/
14×*-un-lft-identity
12×add-sqr-sqrt associate-/r*
11×add-cbrt-cube add-exp-log
10×add-cube-cbrt div-inv
7×associate-*l*
6×pow1 times-frac flip3-- flip-- associate-/l*
4×frac-times associate-*r/ insert-posit16 distribute-lft-out-- add-log-exp
3×clear-num frac-2neg flip3-+ associate-*r* flip-+
2×distribute-rgt-in cbrt-undiv sub-neg distribute-lft-in div-exp associate-*l/ prod-exp frac-sub cbrt-unprod
1×pow-prod-down *-commutative difference-of-squares associate-/l/
Calls
4 calls:
Slowest
7.0ms
(/ (/ PI (+ b a)) (* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a)))
5.0ms
(* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a))
2.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))
1.0ms
(/ PI (+ b a))

series139.0ms

Calls
4 calls:
Slowest
67.0ms
(/ (/ PI (+ b a)) (* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a)))
33.0ms
(/ PI (+ b a))
20.0ms
(* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a))
19.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))

simplify4.5s

Calls
76 calls:
Slowest
336.0ms
(/ (* (* (/ PI (+ b a)) (/ PI (+ b a))) (/ PI (+ b a))) (* (* (* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a)) (* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a))) (* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a))))
303.0ms
(/ (* (* (/ PI (+ b a)) (/ PI (+ b a))) (/ PI (+ b a))) (* (* (* (/ 2 (- (/ 1 a) (/ 1 b))) (/ 2 (- (/ 1 a) (/ 1 b)))) (/ 2 (- (/ 1 a) (/ 1 b)))) (* (* (- b a) (- b a)) (- b a))))
292.0ms
(- (log (/ PI (+ b a))) (+ (log (/ 2 (- (/ 1 a) (/ 1 b)))) (log (- b a))))
215.0ms
(- (log (/ PI (+ b a))) (log (* (/ 2 (- (/ 1 a) (/ 1 b))) (- b a))))
210.0ms
(* (- (/ 1 a) (/ 1 b)) (+ b a))

prune748.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ PI (+ b a))
0.2b
(/ (/ PI (+ b a)) (/ 2 (- (/ 1 a) (/ 1 b))))
0.1b
(/ (/ (/ PI (+ b a)) (/ 2 (- (/ 1 a) (/ 1 b)))) (- b a))
0.1b
(/ 2 (- (/ 1 a) (/ 1 b)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
351×times-frac
177×associate-/r/
129×*-un-lft-identity
127×add-sqr-sqrt
125×add-cube-cbrt
79×div-inv
53×associate-/l*
37×flip3-+ flip-+
33×flip3-- flip--
32×frac-sub
21×associate-/r*
11×add-cbrt-cube add-exp-log
4×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 distribute-lft-out-- add-log-exp
2×associate-/l/
1×difference-of-squares
Calls
4 calls:
Slowest
8.0ms
(/ (/ (/ PI (+ b a)) (/ 2 (- (/ 1 a) (/ 1 b)))) (- b a))
4.0ms
(/ (/ PI (+ b a)) (/ 2 (- (/ 1 a) (/ 1 b))))
2.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))
1.0ms
(/ PI (+ b a))

series179.0ms

Calls
4 calls:
Slowest
65.0ms
(/ (/ (/ PI (+ b a)) (/ 2 (- (/ 1 a) (/ 1 b)))) (- b a))
56.0ms
(/ (/ PI (+ b a)) (/ 2 (- (/ 1 a) (/ 1 b))))
39.0ms
(/ PI (+ b a))
19.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))

simplify54.3s

Calls
464 calls:
Slowest
519.0ms
(/ (/ 1 (/ 2 (- (pow (/ 1 a) 3) (pow (/ 1 b) 3)))) (* (cbrt (- b a)) (cbrt (- b a))))
432.0ms
(/ (/ (/ PI (- (* b b) (* a a))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))) 1)
432.0ms
(/ (/ (/ PI (- (* b b) (* a a))) 2) (* (cbrt (- b a)) (cbrt (- b a))))
409.0ms
(/ (/ (/ PI (+ (pow b 3) (pow a 3))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))) (sqrt (- b a)))
403.0ms
(/ (/ (* (cbrt (/ PI (+ b a))) (cbrt (/ PI (+ b a)))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))) (* (cbrt (- b a)) (cbrt (- b a))))

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes80.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.5s9553×body80valid