Details

Time bar (total: 2.4m)

sample96.0ms

Algorithm
intervals
Results
75.0ms301×body80valid

simplify2.2s

Counts
1 → 1
Iterations
IterNodes
55056
41336
3350
292
130
015

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (/ PI 2) a) (/ (/ PI 2) b))
0.2b
(/ (/ PI 2) a)
0.3b
(/ (/ PI 2) b)
8.3b
(/ (- (/ (/ PI 2) a) (/ (/ PI 2) b)) (* (+ a b) (- b a)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
363×times-frac
240×add-sqr-sqrt
216×*-un-lft-identity
132×add-cube-cbrt
53×associate-/l*
45×distribute-lft-out--
27×difference-of-squares
23×div-inv
19×add-cbrt-cube add-exp-log
8×cbrt-undiv div-exp associate-/r/
7×associate-/r*
6×add-log-exp
5×flip3-- flip-- associate-/l/
4×frac-times pow1 insert-posit16
3×clear-num frac-2neg flip3-+ flip-+
2×associate-*l/ associate-*r/ frac-sub
1×sub-neg diff-log div-sub prod-exp cbrt-unprod
Counts
4 → 262
Calls
4 calls:
40.0ms
(- (/ (/ PI 2) a) (/ (/ PI 2) b))
7.0ms
(/ (/ PI 2) a)
7.0ms
(/ (/ PI 2) b)
73.0ms
(/ (- (/ (/ PI 2) a) (/ (/ PI 2) b)) (* (+ a b) (- b a)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (/ (/ PI 2) a) (/ (/ PI 2) b))
48.0ms
(/ (/ PI 2) a)
63.0ms
(/ (/ PI 2) b)
147.0ms
(/ (- (/ (/ PI 2) a) (/ (/ PI 2) b)) (* (+ a b) (- b a)))

simplify1.0s

Counts
274 → 274
Iterations
IterNodes
23143
11073
0438

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
3274×times-frac
2256×*-un-lft-identity
2108×add-sqr-sqrt
834×add-cube-cbrt
550×distribute-lft-out--
376×difference-of-squares
190×distribute-lft-out
167×associate-/l*
134×div-inv
21×add-cbrt-cube add-exp-log
16×associate-/r/
15×associate-/r*
10×cbrt-undiv div-exp
7×flip3-+ flip-+
6×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
3×div-sub
2×flip3-- flip--
1×frac-sub
Counts
4 → 1008
Calls
4 calls:
109.0ms
(/ (/ (- (/ (/ PI 2) a) (/ (/ PI 2) b)) (+ a b)) (- b a))
14.0ms
(/ (/ PI 2) a)
111.0ms
(/ (- (/ (/ PI 2) a) (/ (/ PI 2) b)) (+ a b))
15.0ms
(/ (/ PI 2) b)

series415.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (/ (- (/ (/ PI 2) a) (/ (/ PI 2) b)) (+ a b)) (- b a))
42.0ms
(/ (/ PI 2) a)
172.0ms
(/ (- (/ (/ PI 2) a) (/ (/ PI 2) b)) (+ a b))
42.0ms
(/ (/ PI 2) b)

simplify1.8s

Counts
1020 → 1020
Iterations
IterNodes
13015
01253

prune12.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1/2 a) (/ 1/2 b))
0.1b
(/ (/ (/ PI 1) (/ (+ a b) (- (/ 1/2 a) (/ 1/2 b)))) (- b a))
0.2b
(/ (+ a b) (- (/ 1/2 a) (/ 1/2 b)))
0.8b
(/ (/ PI 1) (/ (+ a b) (- (/ 1/2 a) (/ 1/2 b))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
20283×times-frac
12431×*-un-lft-identity
11693×add-sqr-sqrt
5763×add-cube-cbrt
2591×distribute-lft-out--
2217×difference-of-squares
1235×div-inv
1117×distribute-lft-out
737×associate-/l*
288×associate-/r/
95×flip3-- flip--
94×frac-sub
72×associate-/r*
48×add-exp-log
36×add-cbrt-cube
34×div-exp
22×cbrt-undiv
6×add-log-exp
4×pow1 1-exp insert-posit16 associate-/l/
3×clear-num frac-2neg
1×sub-neg flip3-+ diff-log flip-+
Counts
4 → 5262
Calls
4 calls:
24.0ms
(- (/ 1/2 a) (/ 1/2 b))
477.0ms
(/ (/ (/ PI 1) (/ (+ a b) (- (/ 1/2 a) (/ 1/2 b)))) (- b a))
31.0ms
(/ (+ a b) (- (/ 1/2 a) (/ 1/2 b)))
43.0ms
(/ (/ PI 1) (/ (+ a b) (- (/ 1/2 a) (/ 1/2 b))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (/ 1/2 a) (/ 1/2 b))
131.0ms
(/ (/ (/ PI 1) (/ (+ a b) (- (/ 1/2 a) (/ 1/2 b)))) (- b a))
137.0ms
(/ (+ a b) (- (/ 1/2 a) (/ 1/2 b)))
155.0ms
(/ (/ PI 1) (/ (+ a b) (- (/ 1/2 a) (/ 1/2 b))))

simplify41.8s

Counts
5274 → 5274
Iterations
IterNodes
113747
05535

prune1.1m

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ PI (/ (+ b a) (- (* 1/2 b) (* a 1/2))))
0.0b
(/ (+ b a) (- (* 1/2 b) (* a 1/2)))
0.1b
(/ (/ (/ PI (/ (+ b a) (- (* 1/2 b) (* a 1/2)))) (* a b)) (- b a))
0.8b
(/ (/ PI (/ (+ b a) (- (* 1/2 b) (* a 1/2)))) (* a b))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
1562×times-frac
782×*-un-lft-identity
606×add-sqr-sqrt
478×add-cube-cbrt
129×associate-/l*
88×distribute-lft-out
69×associate-/r/
64×distribute-lft-out-- difference-of-squares
61×add-cbrt-cube add-exp-log
46×div-inv
35×cbrt-undiv div-exp
30×flip3-- flip--
27×associate-/r*
6×prod-exp cbrt-unprod
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp associate-/l/
1×flip3-+ flip-+
Counts
4 → 681
Calls
4 calls:
27.0ms
(/ PI (/ (+ b a) (- (* 1/2 b) (* a 1/2))))
33.0ms
(/ (+ b a) (- (* 1/2 b) (* a 1/2)))
60.0ms
(/ (/ (/ PI (/ (+ b a) (- (* 1/2 b) (* a 1/2)))) (* a b)) (- b a))
53.0ms
(/ (/ PI (/ (+ b a) (- (* 1/2 b) (* a 1/2)))) (* a b))

series583.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ PI (/ (+ b a) (- (* 1/2 b) (* a 1/2))))
114.0ms
(/ (+ b a) (- (* 1/2 b) (* a 1/2)))
185.0ms
(/ (/ (/ PI (/ (+ b a) (- (* 1/2 b) (* a 1/2)))) (* a b)) (- b a))
168.0ms
(/ (/ PI (/ (+ b a) (- (* 1/2 b) (* a 1/2)))) (* a b))

simplify957.0ms

Counts
693 → 693
Iterations
IterNodes
12322
0894

prune7.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes96.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
218
118
014

end0.0ms

sample2.6s

Algorithm
intervals
Results
2.3s9593×body80valid