Details

Time bar (total: 8.8m)

sample74.0ms

Algorithm
intervals
Results
58.0ms301×body80valid

simplify366.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
366.0ms
(* (* (/ 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: 14.9b

localize23.0ms

Local error

Found 4 expressions with local error:

9.1b
(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
4.8b
(- (* b b) (* a a))
0.7b
(/ PI (- (* b b) (* a a)))
0.2b
(/ 2 (- (/ 1 a) (/ 1 b)))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
4182×times-frac
2580×add-sqr-sqrt
2092×*-un-lft-identity
1116×add-cube-cbrt
749×difference-of-squares
427×distribute-lft-out--
331×div-inv
193×associate-/r/
87×associate-/r* flip3-- flip--
24×associate-/l*
20×add-cbrt-cube add-exp-log frac-sub
10×cbrt-undiv div-exp
6×add-log-exp
4×pow1 insert-posit16
3×clear-num frac-2neg
1×sub-neg diff-log associate-/l/
Counts
4 → 1398
Calls
4 calls:
Slowest
73.0ms
(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
31.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))
20.0ms
(/ PI (- (* b b) (* a a)))
15.0ms
(- (* b b) (* a a))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
102.0ms
(/ (/ PI (- (* b b) (* a a))) (/ 2 (- (/ 1 a) (/ 1 b))))
82.0ms
(/ PI (- (* b b) (* a a)))
80.0ms
(/ 2 (- (/ 1 a) (/ 1 b)))
54.0ms
(- (* b b) (* a a))

simplify8.0m

Counts
2582 → 1410
Calls
2582 calls:
Slowest
842.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- (* b b) (* a a))) (cbrt (- (* b b) (* a a))))) (/ 2 (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
810.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) 1) (/ (* (cbrt 2) (cbrt 2)) 1))
807.0ms
(/ (/ (sqrt PI) (sqrt (- (* b b) (* a a)))) (/ 1 (+ (/ 1 (sqrt a)) (/ (sqrt 1) (sqrt b)))))
804.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) 1) (/ (* (cbrt 2) (cbrt 2)) 1))
780.0ms
(/ (/ (* (cbrt PI) (cbrt PI)) 1) (/ (* (cbrt 2) (cbrt 2)) (/ (* (cbrt 1) (cbrt 1)) 1)))

prune10.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
281×add-sqr-sqrt
264×times-frac
231×*-un-lft-identity
87×add-cube-cbrt
80×distribute-lft-out--
69×difference-of-squares
66×associate-*r*
27×div-inv
22×add-cbrt-cube add-exp-log
18×associate-*l* associate-/l*
11×associate-/r*
7×cbrt-undiv div-exp
6×pow1 associate-/r/
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×clear-num frac-2neg flip3-- flip-- distribute-lft-out associate-/l/
1×frac-times flip3-+ div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative frac-sub flip-+
Counts
4 → 261
Calls
4 calls:
Slowest
52.0ms
(* (/ 1/2 (+ b a)) (/ (- (/ PI a) (/ PI b)) (- b a)))
29.0ms
(/ (- (/ PI a) (/ PI b)) (- b a))
8.0ms
(/ PI a)
4.0ms
(/ PI b)

series177.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
83.0ms
(* (/ 1/2 (+ b a)) (/ (- (/ PI a) (/ PI b)) (- b a)))
44.0ms
(/ (- (/ PI a) (/ PI b)) (- b a))
26.0ms
(/ PI b)
23.0ms
(/ PI a)

simplify10.3s

Counts
305 → 273
Calls
305 calls:
Slowest
344.0ms
(* (/ (* (* 1/2 1/2) 1/2) (* (* (+ b a) (+ b a)) (+ b a))) (/ (* (* (- (/ PI a) (/ PI b)) (- (/ PI a) (/ PI b))) (- (/ PI a) (/ PI b))) (* (* (- b a) (- b a)) (- b a))))
261.0ms
(/ (* (* PI PI) PI) (* (* a a) a))
261.0ms
(/ (* (* PI PI) PI) (* (* b b) b))
235.0ms
(* (/ (* (* 1/2 1/2) 1/2) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (/ (- (/ PI a) (/ PI b)) (- b a)) (/ (- (/ PI a) (/ PI b)) (- b a))) (/ (- (/ PI a) (/ PI b)) (- b a))))
224.0ms
(+ (- (log 1/2) (log (+ b a))) (- (log (- (/ PI a) (/ PI b))) (log (- b a))))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
281×add-sqr-sqrt
264×times-frac
231×*-un-lft-identity
87×add-cube-cbrt
80×distribute-lft-out--
69×difference-of-squares
66×associate-*r*
27×div-inv
22×add-cbrt-cube add-exp-log
18×associate-*l* associate-/l*
11×associate-/r*
7×cbrt-undiv div-exp
6×pow1 associate-/r/
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×clear-num frac-2neg flip3-- flip-- distribute-lft-out associate-/l/
1×frac-times flip3-+ div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative frac-sub flip-+
Counts
4 → 261
Calls
4 calls:
Slowest
52.0ms
(* (/ 1/2 (+ b a)) (/ (- (/ PI a) (/ PI b)) (- b a)))
30.0ms
(/ (- (/ PI a) (/ PI b)) (- b a))
7.0ms
(/ PI b)
4.0ms
(/ PI a)

series177.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(* (/ 1/2 (+ b a)) (/ (- (/ PI a) (/ PI b)) (- b a)))
44.0ms
(/ (- (/ PI a) (/ PI b)) (- b a))
27.0ms
(/ PI b)
23.0ms
(/ PI a)

simplify10.5s

Counts
305 → 273
Calls
305 calls:
Slowest
344.0ms
(* (/ (* (* 1/2 1/2) 1/2) (* (* (+ b a) (+ b a)) (+ b a))) (/ (* (* (- (/ PI a) (/ PI b)) (- (/ PI a) (/ PI b))) (- (/ PI a) (/ PI b))) (* (* (- b a) (- b a)) (- b a))))
286.0ms
(/ (- (/ (cbrt PI) a) (/ (cbrt PI) b)) (- b a))
263.0ms
(/ (* (* PI PI) PI) (* (* a a) a))
260.0ms
(/ (* (* PI PI) PI) (* (* b b) b))
235.0ms
(* (/ (* (* 1/2 1/2) 1/2) (* (* (+ b a) (+ b a)) (+ b a))) (* (* (/ (- (/ PI a) (/ PI b)) (- b a)) (/ (- (/ PI a) (/ PI b)) (- b a))) (/ (- (/ PI a) (/ PI b)) (- b a))))

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
151×add-sqr-sqrt
142×times-frac
131×*-un-lft-identity
53×add-cube-cbrt
43×distribute-lft-out--
37×difference-of-squares
19×add-cbrt-cube add-exp-log associate-/l*
16×div-inv
15×associate-/r*
7×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg associate-/r/ insert-posit16 add-log-exp associate-/l/
2×flip3-- prod-exp cbrt-unprod flip-- distribute-lft-out
1×flip3-+ div-sub associate-*r/ frac-sub flip-+
Counts
4 → 181
Calls
4 calls:
Slowest
32.0ms
(/ (- (/ PI a) (/ PI b)) (- b a))
24.0ms
(/ (* 1/2 (/ (- (/ PI a) (/ PI b)) (- b a))) (+ b a))
4.0ms
(/ PI a)
4.0ms
(/ PI b)

series176.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
83.0ms
(/ (* 1/2 (/ (- (/ PI a) (/ PI b)) (- b a))) (+ b a))
44.0ms
(/ (- (/ PI a) (/ PI b)) (- b a))
25.0ms
(/ PI a)
23.0ms
(/ PI b)

simplify6.7s

Counts
223 → 193
Calls
223 calls:
Slowest
391.0ms
(/ (* (* (* 1/2 1/2) 1/2) (/ (* (* (- (/ PI a) (/ PI b)) (- (/ PI a) (/ PI b))) (- (/ PI a) (/ PI b))) (* (* (- b a) (- b a)) (- b a)))) (* (* (+ b a) (+ b a)) (+ b a)))
262.0ms
(/ (* (* (* 1/2 1/2) 1/2) (* (* (/ (- (/ PI a) (/ PI b)) (- b a)) (/ (- (/ PI a) (/ PI b)) (- b a))) (/ (- (/ PI a) (/ PI b)) (- b a)))) (* (* (+ b a) (+ b a)) (+ b a)))
261.0ms
(/ (* (* PI PI) PI) (* (* a a) a))
256.0ms
(/ (* (* PI PI) PI) (* (* b b) b))
254.0ms
(/ (* (* (* 1/2 (/ (- (/ PI a) (/ PI b)) (- b a))) (* 1/2 (/ (- (/ PI a) (/ PI b)) (- b a)))) (* 1/2 (/ (- (/ PI a) (/ PI b)) (- b a)))) (* (* (+ b a) (+ b a)) (+ b a)))

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.1s9511×body80valid