Details

Time bar (total: 27.9s)

sample91.0ms

Algorithm
intervals
Results
74.0ms311×body80valid

simplify393.0ms

Calls
1 calls:
Slowest
393.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize43.0ms

Local error

Found 4 expressions with local error:

9.1b
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
4.4b
(- (* b b) (* a a))
0.3b
(/ 1 (- (* b b) (* a a)))
0.1b
(* (/ PI 2) (/ 1 (- (* b b) (* a a))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
17×frac-times add-exp-log
14×associate-*r*
12×pow1 *-un-lft-identity
11×add-cbrt-cube
10×add-sqr-sqrt
9×associate-*l/
8×flip3-- associate-*r/ add-cube-cbrt flip--
7×prod-exp div-inv
6×add-log-exp
5×associate-*l* un-div-inv frac-sub
4×associate-/r* pow-prod-down associate-/r/ cbrt-unprod insert-posit16 distribute-lft-out--
3×rec-exp sub-neg difference-of-squares
2×distribute-rgt-in distribute-lft-in *-commutative
1×clear-num frac-2neg diff-log pow-flip inv-pow
Calls
4 calls:
Slowest
27.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
5.0ms
(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
3.0ms
(- (* b b) (* a a))
2.0ms
(/ 1 (- (* b b) (* a a)))

series270.0ms

Calls
4 calls:
Slowest
106.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
62.0ms
(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
59.0ms
(/ 1 (- (* b b) (* a a)))
43.0ms
(- (* b b) (* a a))

simplify13.8s

Calls
90 calls:
Slowest
826.0ms
(* (* (* (* (/ PI 2) (/ PI 2)) (/ PI 2)) (* (* (/ 1 (- (* b b) (* a a))) (/ 1 (- (* b b) (* a a)))) (/ 1 (- (* b b) (* a a))))) (* (* (- (/ 1 a) (/ 1 b)) (- (/ 1 a) (/ 1 b))) (- (/ 1 a) (/ 1 b))))
542.0ms
(* (* PI (/ 1 (- (* b b) (* a a)))) (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))
486.0ms
(* (* 2 (- (* b b) (* a a))) (+ (/ 1 a) (/ 1 b)))
419.0ms
(* (* (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (* (/ PI 2) (/ 1 (- (* b b) (* a a))))) (* (/ PI 2) (/ 1 (- (* b b) (* a a))))) (* (* (- (/ 1 a) (/ 1 b)) (- (/ 1 a) (/ 1 b))) (- (/ 1 a) (/ 1 b))))
407.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ PI (+ b a))
0.2b
(/ (/ PI (+ b a)) (* 2 (* a b)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
6×times-frac associate-/r/ associate-/l*
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×associate-/r* add-cbrt-cube add-exp-log div-inv
3×flip3-+ flip-+
2×pow1 clear-num frac-2neg insert-posit16 add-log-exp
1×cbrt-undiv div-exp associate-/l/
Calls
2 calls:
Slowest
5.0ms
(/ (/ PI (+ b a)) (* 2 (* a b)))
1.0ms
(/ PI (+ b a))

series137.0ms

Calls
2 calls:
Slowest
84.0ms
(/ (/ PI (+ b a)) (* 2 (* a b)))
54.0ms
(/ PI (+ b a))

simplify1.9s

Calls
30 calls:
Slowest
407.0ms
(/ (* (* (/ PI (+ b a)) (/ PI (+ b a))) (/ PI (+ b a))) (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))))
347.0ms
(- (log (/ PI (+ b a))) (log (* 2 (* a b))))
315.0ms
(/ (+ (* b b) (- (* a a) (* b a))) (* a b))
218.0ms
(/ (/ PI (- (* b b) (* a a))) 2)
95.0ms
(/ PI (- (* b b) (* a a)))

prune471.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.4b
(* PI (/ 1 (+ b a)))
0.2b
(/ (* PI (/ 1 (+ b a))) (* 2 (* a b)))
0.0b
(/ 1 (+ b a))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
6×associate-*r* add-exp-log
5×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-cube-cbrt
4×pow1 associate-/r* associate-/r/
3×insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg flip3-+ associate-*r/ un-div-inv flip-+ associate-/l/
1×cbrt-undiv rec-exp times-frac div-exp *-commutative pow-flip associate-/l* inv-pow
Calls
3 calls:
Slowest
9.0ms
(/ (* PI (/ 1 (+ b a))) (* 2 (* a b)))
3.0ms
(* PI (/ 1 (+ b a)))
2.0ms
(/ 1 (+ b a))

series202.0ms

Calls
3 calls:
Slowest
79.0ms
(/ (* PI (/ 1 (+ b a))) (* 2 (* a b)))
72.0ms
(* PI (/ 1 (+ b a)))
51.0ms
(/ 1 (+ b a))

simplify1.6s

Calls
29 calls:
Slowest
881.0ms
(/ (* (* (* PI (/ 1 (+ b a))) (* PI (/ 1 (+ b a)))) (* PI (/ 1 (+ b a)))) (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))))
345.0ms
(- (log (* PI (/ 1 (+ b a)))) (log (* 2 (* a b))))
94.0ms
(+ (* b b) (- (* a a) (* b a)))
68.0ms
(+ (* b b) (- (* a a) (* b a)))
65.0ms
(/ (/ 1 (+ b a)) (* a b))

prune536.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ b a))
0.5b
(cbrt (+ b a))
0.5b
(cbrt (+ b a))
0.5b
(* (cbrt (+ b a)) (cbrt (+ b a)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1 flip3-+ flip-+
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
13.0ms
(* (cbrt (+ b a)) (cbrt (+ b a)))
2.0ms
(cbrt (+ b a))
1.0ms
(cbrt (+ b a))
1.0ms
(cbrt (+ b a))

series871.0ms

Calls
4 calls:
Slowest
252.0ms
(* (cbrt (+ b a)) (cbrt (+ b a)))
228.0ms
(cbrt (+ b a))
196.0ms
(cbrt (+ b a))
194.0ms
(cbrt (+ b a))

simplify2.6s

Calls
59 calls:
Slowest
279.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow a 2)) 1/3) b)) (pow a 1/3)) (* 1/9 (* (pow (/ 1 (pow a 5)) 1/3) (pow b 2))))
278.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow a 2)) 1/3) b)) (pow a 1/3)) (* 1/9 (* (pow (/ 1 (pow a 5)) 1/3) (pow b 2))))
268.0ms
(- (+ (* 2/3 (* (pow (/ 1 a) 1/3) b)) (pow a 2/3)) (* 1/9 (* (pow (/ 1 (pow a 4)) 1/3) (pow b 2))))
243.0ms
(- (+ (* 1/3 (* (pow (/ 1 (pow a 2)) 1/3) b)) (pow a 1/3)) (* 1/9 (* (pow (/ 1 (pow a 5)) 1/3) (pow b 2))))
150.0ms
(* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a))))

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes148.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.3s9564×body80valid