Details

Time bar (total: 7.8m)

sample49.0ms

Algorithm
intervals
Results
33.0ms310×body80valid

simplify748.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
747.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize51.0ms

Local error

Found 4 expressions with local error:

9.1b
(/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (- (* b b) (* a a)))
6.9b
(- (* b b) (* a a))
0.3b
(* (/ PI 2) (- (/ 1 a) (/ 1 b)))
0.0b
(- (/ 1 a) (/ 1 b))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
761×times-frac
624×add-sqr-sqrt
603×*-un-lft-identity
571×add-cube-cbrt
508×prod-diff
171×distribute-rgt-in distribute-lft-in
89×div-inv
21×difference-of-squares
19×associate-*r*
18×add-cbrt-cube add-exp-log
14×fma-neg distribute-lft-out--
13×associate-*l*
8×add-log-exp
7×flip3-- flip-- associate-/l/
6×frac-times pow1 associate-*r/
5×cbrt-undiv div-exp frac-sub
4×expm1-log1p-u associate-/r* sub-neg prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
2×diff-log associate-*l/ associate-/r/ unswap-sqr
1×clear-num frac-2neg pow-prod-down *-commutative associate-/l*
Counts
4 → 668
Calls
4 calls:
Slowest
84.0ms
(* (/ PI 2) (- (/ 1 a) (/ 1 b)))
58.0ms
(/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (- (* b b) (* a a)))
16.0ms
(- (* b b) (* a a))
16.0ms
(- (/ 1 a) (/ 1 b))

series297.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(/ (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (- (* b b) (* a a)))
80.0ms
(* (/ PI 2) (- (/ 1 a) (/ 1 b)))
57.0ms
(- (* b b) (* a a))
23.0ms
(- (/ 1 a) (/ 1 b))

simplify4.3m

Counts
1216 → 680
Calls
1216 calls:
Slowest
862.0ms
(* (fma (- (/ 1 (cbrt b))) (/ 1 (* (cbrt b) (cbrt b))) (* (/ 1 (cbrt b)) (/ 1 (* (cbrt b) (cbrt b))))) (/ PI 2))
799.0ms
(/ (* (* (* (/ PI 2) (- (/ 1 a) (/ 1 b))) (* (/ PI 2) (- (/ 1 a) (/ 1 b)))) (* (/ PI 2) (- (/ 1 a) (/ 1 b)))) (* (* (- (* b b) (* a a)) (- (* b b) (* a a))) (- (* b b) (* a a))))
743.0ms
(* (fma (- (/ 1 (cbrt b))) (/ 1 (* (cbrt b) (cbrt b))) (* (/ 1 (cbrt b)) (/ 1 (* (cbrt b) (cbrt b))))) (/ PI 2))
702.0ms
(* (* (- (/ 1 a) (/ 1 b)) (- (/ 1 a) (/ 1 b))) (- (/ 1 a) (/ 1 b)))
680.0ms
(* (fma (- (/ (cbrt 1) (sqrt b))) (/ (* (cbrt 1) (cbrt 1)) (sqrt b)) (* (/ (cbrt 1) (sqrt b)) (/ (* (cbrt 1) (cbrt 1)) (sqrt b)))) (/ PI 2))

prune6.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
272×times-frac
203×add-sqr-sqrt
171×*-un-lft-identity
69×add-cube-cbrt
59×distribute-lft-out--
51×difference-of-squares
36×associate-/l*
26×div-inv
22×add-cbrt-cube add-exp-log
16×associate-/r/
14×associate-*l/
12×associate-/r*
9×cbrt-undiv div-exp
7×flip3-+ flip-+
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×div-sub
2×flip3-- prod-exp cbrt-unprod flip--
1×frac-sub
Counts
4 → 244
Calls
4 calls:
Slowest
51.0ms
(/ (- (/ PI a) (/ PI b)) (* (+ b a) 2))
48.0ms
(/ (/ (- (/ PI a) (/ PI b)) (* (+ b a) 2)) (- b a))
8.0ms
(/ PI b)
7.0ms
(/ PI a)

series300.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(/ (- (/ PI a) (/ PI b)) (* (+ b a) 2))
107.0ms
(/ (/ (- (/ PI a) (/ PI b)) (* (+ b a) 2)) (- b a))
41.0ms
(/ PI b)
24.0ms
(/ PI a)

simplify43.0s

Counts
382 → 256
Calls
382 calls:
Slowest
772.0ms
(/ (- (/ PI a) (/ PI b)) (* (+ (pow b 3) (pow a 3)) 2))
585.0ms
(/ (/ (* (* (- (/ PI a) (/ PI b)) (- (/ PI a) (/ PI b))) (- (/ PI a) (/ PI b))) (* (* (* (+ b a) (+ b a)) (+ b a)) (* (* 2 2) 2))) (* (* (- b a) (- b a)) (- b a)))
491.0ms
(/ (- b a) (/ (- (/ (sqrt PI) (sqrt a)) (sqrt (/ PI b))) 2))
477.0ms
(/ (* (* PI PI) PI) (* (* a a) a))
474.0ms
(/ (* (* PI PI) PI) (* (* b b) b))

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (/ (* (+ b a) 2) (- (/ PI a) (/ PI b))))
0.3b
(/ PI b)
0.3b
(/ PI a)
0.2b
(/ (* (+ b a) 2) (- (/ PI a) (/ PI b)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
195×times-frac
134×add-sqr-sqrt
110×*-un-lft-identity
62×add-cube-cbrt
37×associate-/r*
34×add-exp-log
30×distribute-lft-out--
24×difference-of-squares
22×add-cbrt-cube
20×div-inv
16×div-exp associate-/r/
10×associate-/l*
9×cbrt-undiv
5×pow1 flip3-- frac-sub flip--
4×expm1-log1p-u clear-num frac-2neg prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp
2×associate-*l/ cbrt-unprod associate-/l/
1×flip3-+ flip-+ pow-flip inv-pow
Counts
4 → 214
Calls
4 calls:
Slowest
57.0ms
(/ 1 (/ (* (+ b a) 2) (- (/ PI a) (/ PI b))))
24.0ms
(/ (* (+ b a) 2) (- (/ PI a) (/ PI b)))
7.0ms
(/ PI b)
5.0ms
(/ PI a)

series383.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(/ (* (+ b a) 2) (- (/ PI a) (/ PI b)))
114.0ms
(/ 1 (/ (* (+ b a) 2) (- (/ PI a) (/ PI b))))
33.0ms
(/ PI b)
28.0ms
(/ PI a)

simplify31.8s

Counts
316 → 226
Calls
316 calls:
Slowest
1.4s
(* (* (/ 1 (/ (* (+ b a) 2) (- (/ PI a) (/ PI b)))) (/ 1 (/ (* (+ b a) 2) (- (/ PI a) (/ PI b))))) (/ 1 (/ (* (+ b a) 2) (- (/ PI a) (/ PI b)))))
749.0ms
(* (* (/ (* (+ b a) 2) (- (/ PI a) (/ PI b))) (/ (* (+ b a) 2) (- (/ PI a) (/ PI b)))) (/ (* (+ b a) 2) (- (/ PI a) (/ PI b))))
680.0ms
(/ (* (* (* (+ b a) (+ b a)) (+ b a)) (* (* 2 2) 2)) (* (* (- (/ PI a) (/ PI b)) (- (/ PI a) (/ PI b))) (- (/ PI a) (/ PI b))))
435.0ms
(/ (* (* PI PI) PI) (* (* a a) a))
425.0ms
(/ (* (* PI PI) PI) (* (* b b) b))

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (/ 1 (/ (- (/ PI a) (/ PI b)) (* (+ b a) 2))))
0.3b
(/ PI b)
0.3b
(/ PI a)
0.2b
(/ 1 (/ (- (/ PI a) (/ PI b)) (* (+ b a) 2)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
817×times-frac
431×add-sqr-sqrt
367×*-un-lft-identity
239×add-cube-cbrt
105×add-exp-log
83×associate-/r*
80×distribute-lft-out--
70×div-exp
64×difference-of-squares
56×div-inv
38×associate-/r/
32×associate-*l/
31×add-cbrt-cube
22×rec-exp 1-exp
16×cbrt-undiv flip3-+ flip-+
12×prod-exp associate-/l*
7×pow1
5×pow-flip
4×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×inv-pow
2×cbrt-unprod
1×remove-double-div
Counts
4 → 455
Calls
4 calls:
Slowest
77.0ms
(/ 1 (/ 1 (/ (- (/ PI a) (/ PI b)) (* (+ b a) 2))))
36.0ms
(/ 1 (/ (- (/ PI a) (/ PI b)) (* (+ b a) 2)))
12.0ms
(/ PI a)
7.0ms
(/ PI b)

series391.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(/ 1 (/ (- (/ PI a) (/ PI b)) (* (+ b a) 2)))
116.0ms
(/ 1 (/ 1 (/ (- (/ PI a) (/ PI b)) (* (+ b a) 2))))
34.0ms
(/ PI b)
24.0ms
(/ PI a)

simplify1.9m

Counts
717 → 467
Calls
717 calls:
Slowest
817.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (/ PI a) (/ PI b)) (- (/ PI a) (/ PI b))) (- (/ PI a) (/ PI b))) (* (* (* (+ b a) (+ b a)) (+ b a)) (* (* 2 2) 2))))
725.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (/ (+ (/ (sqrt PI) (sqrt a)) (/ (sqrt PI) (sqrt b))) (+ b a))))
558.0ms
(/ 1 (/ (* (cbrt 1) (cbrt 1)) (/ (+ (sqrt (/ PI a)) (sqrt (/ PI b))) (+ b a))))
546.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt 1) (/ (- (/ PI a) (/ PI b)) (* (- (* b b) (* a a)) 2))))
524.0ms
(/ (sqrt 1) (/ (sqrt 1) (/ (/ (* (cbrt PI) (cbrt PI)) 1) (+ b a))))

prune4.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes103.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch5.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.9s9637×body80valid