Details

Time bar (total: 20.5s)

sample84.0ms

Algorithm
intervals
Results
66.0ms314×body80valid

simplify2.0s

Counts
1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
952×times-frac
786×*-un-lft-identity
776×add-sqr-sqrt
258×add-cube-cbrt
228×distribute-lft-out--
197×difference-of-squares
84×associate-/l*
71×div-inv
67×distribute-lft-out
15×associate-/r* add-cbrt-cube add-exp-log
14×associate-/r/
7×flip3-- flip--
6×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp associate-/l/
3×div-sub
1×flip3-+ frac-sub flip-+
Counts
4 → 505
Calls
4 calls:
Slowest
58.0ms
(/ (- (/ PI a) (/ PI b)) (- b a))
47.0ms
(/ (/ (- (/ PI a) (/ PI b)) (- b a)) (+ a b))
7.0ms
(/ PI a)
6.0ms
(/ PI b)

series581.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
459.0ms
(/ (/ (- (/ PI a) (/ PI b)) (- b a)) (+ a b))
56.0ms
(/ (- (/ PI a) (/ PI b)) (- b a))
40.0ms
(/ PI b)
27.0ms
(/ PI a)

simplify936.0ms

Counts
517 → 517

prune5.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.7b
(/ PI (* a b))
0.1b
(/ (/ PI (* a b)) (+ a b))
0.0b
(* (/ (/ PI (* a b)) (+ a b)) 1/2)

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
70×*-un-lft-identity
45×add-sqr-sqrt
40×add-cube-cbrt
34×associate-*l*
31×add-cbrt-cube add-exp-log
15×distribute-lft-out
12×cbrt-undiv div-exp div-inv
10×associate-/l*
7×prod-exp cbrt-unprod
5×pow1 associate-/r*
4×associate-/r/
3×associate-*r* insert-posit16 add-log-exp
2×clear-num frac-2neg flip3-+ flip-+ unswap-sqr
1×pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
3 → 139
Calls
3 calls:
Slowest
33.0ms
(/ (/ PI (* a b)) (+ a b))
32.0ms
(* (/ (/ PI (* a b)) (+ a b)) 1/2)
6.0ms
(/ PI (* a b))

series169.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
82.0ms
(* (/ (/ PI (* a b)) (+ a b)) 1/2)
59.0ms
(/ (/ PI (* a b)) (+ a b))
27.0ms
(/ PI (* a b))

simplify654.0ms

Counts
148 → 148

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ PI (* a b))
0.3b
(* (/ (/ PI (* a b)) (+ a b)) (sqrt 1/2))
0.2b
(* (* (/ (/ PI (* a b)) (+ a b)) (sqrt 1/2)) (sqrt 1/2))
0.1b
(/ (/ PI (* a b)) (+ a b))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
74×*-un-lft-identity
54×add-sqr-sqrt
52×add-cbrt-cube add-exp-log
44×add-cube-cbrt
35×associate-*l*
17×cbrt-undiv div-exp prod-exp cbrt-unprod
15×distribute-lft-out
12×associate-*r* div-inv
11×pow1
10×associate-/l*
8×sqrt-prod
5×associate-/r*
4×pow-prod-down associate-/r/ insert-posit16 add-log-exp unswap-sqr
3×associate-*l/
2×clear-num frac-2neg flip3-+ *-commutative flip-+
1×associate-/l/
Counts
4 → 173
Calls
4 calls:
Slowest
88.0ms
(* (* (/ (/ PI (* a b)) (+ a b)) (sqrt 1/2)) (sqrt 1/2))
48.0ms
(* (/ (/ PI (* a b)) (+ a b)) (sqrt 1/2))
22.0ms
(/ (/ PI (* a b)) (+ a b))
12.0ms
(/ PI (* a b))

series676.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
334.0ms
(* (* (/ (/ PI (* a b)) (+ a b)) (sqrt 1/2)) (sqrt 1/2))
233.0ms
(* (/ (/ PI (* a b)) (+ a b)) (sqrt 1/2))
81.0ms
(/ (/ PI (* a b)) (+ a b))
27.0ms
(/ PI (* a b))

simplify904.0ms

Counts
185 → 185

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
157×times-frac
101×add-sqr-sqrt
96×*-un-lft-identity
92×add-cube-cbrt
43×associate-*l*
34×add-cbrt-cube add-exp-log
17×associate-/l*
14×cbrt-undiv div-exp
11×div-inv
10×associate-/r*
6×pow1 prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* unswap-sqr
2×associate-*l/ associate-/r/ distribute-lft-out associate-/l/
1×flip3-+ pow-prod-down *-commutative flip-+
Counts
4 → 196
Calls
4 calls:
Slowest
31.0ms
(/ (* (/ (/ PI a) b) 1/2) (+ a b))
14.0ms
(* (/ (/ PI a) b) 1/2)
10.0ms
(/ (/ PI a) b)
4.0ms
(/ PI a)

series230.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
104.0ms
(/ (* (/ (/ PI a) b) 1/2) (+ a b))
53.0ms
(* (/ (/ PI a) b) 1/2)
44.0ms
(/ (/ PI a) b)
28.0ms
(/ PI a)

simplify810.0ms

Counts
208 → 208

prune1.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes102.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
2.2s9570×body80valid