Details

Time bar (total: 45.2s)

sample46.0ms

Algorithm
intervals
Results
35.0ms306×body80valid

simplify464.0ms

Calls
1 calls:
Slowest
464.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize52.0ms

Local error

Found 4 expressions with local error:

5.2b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
5.1b
(/ (/ PI (- (* b b) (* a a))) a)
4.5b
(- (* b b) (* a a))
4.5b
(- (* b b) (* a a))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
8×add-log-exp
6×associate-/l*
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×sub-neg fma-neg diff-log prod-diff associate-/r/ div-inv difference-of-squares
1×clear-num frac-2neg fma-udef associate-/l/
Calls
4 calls:
Slowest
17.0ms
(/ (/ PI (- (* b b) (* a a))) a)
5.0ms
(- (* b b) (* a a))
5.0ms
(- (* b b) (* a a))
2.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series358.0ms

Calls
4 calls:
Slowest
155.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
89.0ms
(/ (/ PI (- (* b b) (* a a))) a)
58.0ms
(- (* b b) (* a a))
55.0ms
(- (* b b) (* a a))

simplify1.3s

Calls
26 calls:
Slowest
346.0ms
(/ PI (- (pow (* b b) 3) (pow (* a a) 3)))
291.0ms
(/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a))))
153.0ms
(sqrt (/ PI (- (* b b) (* a a))))
153.0ms
(* (cbrt (/ PI (- (* b b) (* a a)))) (cbrt (/ PI (- (* b b) (* a a)))))
78.0ms
(/ (exp (* b b)) (exp (* a a)))

prune935.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.0b

localize39.0ms

Local error

Found 4 expressions with local error:

10.3b
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
4.5b
(- (* b b) (* a a))
1.0b
(/ 1 (- (* b b) (* a a)))
0.2b
(* (/ PI 2) (/ 1 (- (* b b) (* a a))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
33×prod-diff
28×*-un-lft-identity
26×add-sqr-sqrt
24×add-cube-cbrt
23×div-inv
18×distribute-rgt-in distribute-lft-in
17×frac-times add-exp-log
14×associate-*r*
12×pow1
11×add-cbrt-cube
9×associate-*l/
8×flip3-- associate-*r/ flip--
7×prod-exp
6×add-log-exp
5×associate-*l* un-div-inv frac-sub
4×expm1-log1p-u associate-/r* pow-prod-down associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out--
3×rec-exp sub-neg difference-of-squares
2×*-commutative
1×clear-num frac-2neg fma-neg diff-log pow-flip inv-pow
Calls
4 calls:
Slowest
40.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
12.0ms
(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
10.0ms
(/ 1 (- (* b b) (* a a)))
5.0ms
(- (* b b) (* a a))

series314.0ms

Calls
4 calls:
Slowest
116.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))
88.0ms
(* (/ PI 2) (/ 1 (- (* b b) (* a a))))
65.0ms
(/ 1 (- (* b b) (* a a)))
44.0ms
(- (* b b) (* a a))

simplify31.0s

Calls
124 calls:
Slowest
878.0ms
(* (fma (- (sqrt (/ 1 b))) (sqrt (/ 1 b)) (* (sqrt (/ 1 b)) (sqrt (/ 1 b)))) (* (/ PI 2) (/ 1 (- (* b b) (* a a)))))
815.0ms
(* (* PI 1) (- (pow (/ 1 a) 3) (pow (/ 1 b) 3)))
634.0ms
(* (* 2 (- (* b b) (* a a))) (+ (/ 1 a) (/ 1 b)))
620.0ms
(* (* PI (/ 1 (- (* b b) (* a a)))) (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))
617.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (fma (- (cbrt (/ 1 b))) (* (cbrt (/ 1 b)) (cbrt (/ 1 b))) (* (cbrt (/ 1 b)) (* (cbrt (/ 1 b)) (cbrt (/ 1 b))))))

prune1.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u 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))

series182.0ms

Calls
2 calls:
Slowest
112.0ms
(/ (/ PI (+ b a)) (* 2 (* a b)))
69.0ms
(/ PI (+ b a))

simplify1.8s

Calls
30 calls:
Slowest
387.0ms
(/ (* (* (/ PI (+ b a)) (/ PI (+ b a))) (/ PI (+ b a))) (* (* (* 2 (* a b)) (* 2 (* a b))) (* 2 (* a b))))
294.0ms
(/ (+ (* b b) (- (* a a) (* b a))) (* a b))
263.0ms
(- (log (/ PI (+ b a))) (log (* 2 (* a b))))
224.0ms
(/ (/ PI (- (* b b) (* a a))) 2)
137.0ms
(/ PI (- (* b b) (* a a)))

prune521.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.6b
(/ 1 (* 2 (* a b)))
0.2b
(/ PI (+ b a))
0.1b
(* (/ PI (+ b a)) (/ 1 (* 2 (* a b))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
8×add-exp-log
6×add-sqr-sqrt pow1 *-un-lft-identity associate-*l* add-cube-cbrt
5×add-cbrt-cube
4×associate-/r* associate-*r* associate-/r/ div-inv
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg flip3-+ prod-exp flip-+
1×frac-times pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative cbrt-unprod pow-flip inv-pow
Calls
3 calls:
Slowest
16.0ms
(* (/ PI (+ b a)) (/ 1 (* 2 (* a b))))
3.0ms
(/ 1 (* 2 (* a b)))
1.0ms
(/ PI (+ b a))

series195.0ms

Calls
3 calls:
Slowest
94.0ms
(* (/ PI (+ b a)) (/ 1 (* 2 (* a b))))
66.0ms
(/ PI (+ b a))
35.0ms
(/ 1 (* 2 (* a b)))

simplify2.3s

Calls
33 calls:
Slowest
367.0ms
(+ (log (/ PI (+ b a))) (log (/ 1 (* 2 (* a b)))))
286.0ms
(* PI (/ 1 (* 2 (* a b))))
279.0ms
(+ (log (/ PI (+ b a))) (- (log (* 2 (* a b)))))
272.0ms
(* (/ PI (+ b a)) (/ 1 (* 2 (* a b))))
260.0ms
(* (* (* (/ PI (+ b a)) (/ PI (+ b a))) (/ PI (+ b a))) (* (* (/ 1 (* 2 (* a b))) (/ 1 (* 2 (* a b)))) (/ 1 (* 2 (* a b)))))

prune743.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes165.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.4s9558×body80valid