Details

Time bar (total: 22.5s)

sample67.0ms

Algorithm
intervals
Results
49.0ms322×body80valid

simplify842.0ms

Counts
1 → 1
Iterations
IterNodes
done2002
41476
3358
294
132
015

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.5b

localize50.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ PI (+ a b)) (* 2 (- b a)))
0.3b
(/ PI (+ a b))
8.5b
(* (/ (/ PI (+ a b)) (* 2 (- b a))) (- (/ 1 a) (/ 1 b)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
82×*-un-lft-identity
66×add-sqr-sqrt
40×add-cube-cbrt
35×add-cbrt-cube add-exp-log
24×associate-*l*
21×associate-/l*
19×associate-*r*
13×cbrt-undiv div-exp distribute-lft-out
12×associate-/r/
10×div-inv
9×prod-exp cbrt-unprod difference-of-squares
7×associate-*r/ distribute-lft-out--
5×pow1 associate-/r*
4×flip3-+ flip3-- flip-+ flip--
3×frac-times insert-posit16 add-log-exp
2×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in frac-sub
1×pow-prod-down associate-*l/ *-commutative unswap-sqr associate-/l/
Counts
3 → 168
Calls
3 calls:
20.0ms
(/ (/ PI (+ a b)) (* 2 (- b a)))
13.0ms
(/ PI (+ a b))
90.0ms
(* (/ (/ PI (+ a b)) (* 2 (- b a))) (- (/ 1 a) (/ 1 b)))

series297.0ms

Counts
3 → 9
Calls
3 calls:
89.0ms
(/ (/ PI (+ a b)) (* 2 (- b a)))
56.0ms
(/ PI (+ a b))
151.0ms
(* (/ (/ PI (+ a b)) (* 2 (- b a))) (- (/ 1 a) (/ 1 b)))

simplify682.0ms

Counts
177 → 177
Iterations
IterNodes
done2002
1852
0268

prune774.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
52×add-sqr-sqrt
44×times-frac
31×add-cbrt-cube add-exp-log
23×add-cube-cbrt
19×associate-*r*
18×associate-*l*
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod difference-of-squares
8×associate-*r/
7×div-inv distribute-lft-out distribute-lft-out-- associate-/l/
6×frac-times associate-/r/
5×pow1 associate-/r* flip3-- flip--
4×frac-sub associate-/l*
3×insert-posit16 add-log-exp
2×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in flip3-+ associate-*l/ flip-+ unswap-sqr
1×pow-prod-down *-commutative
Counts
3 → 133
Calls
3 calls:
28.0ms
(/ (* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b))) (* 2 (- b a)))
46.0ms
(* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b)))
7.0ms
(/ PI (+ a b))

series321.0ms

Counts
3 → 9
Calls
3 calls:
127.0ms
(/ (* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b))) (* 2 (- b a)))
123.0ms
(* (/ PI (+ a b)) (- (/ 1 a) (/ 1 b)))
70.0ms
(/ PI (+ a b))

simplify660.0ms

Counts
142 → 142
Iterations
IterNodes
done2002
1756
0227

prune614.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
1562×times-frac
816×*-un-lft-identity
814×add-sqr-sqrt
310×add-cube-cbrt
189×difference-of-squares
147×distribute-lft-out--
133×div-inv
117×associate-/r/
85×distribute-lft-out
49×associate-/r*
31×add-cbrt-cube add-exp-log
28×flip3-+ flip-+
22×associate-/l*
21×flip3-- flip--
20×frac-sub
16×cbrt-undiv div-exp
3×pow1 clear-num frac-2neg prod-exp cbrt-unprod insert-posit16 add-log-exp associate-/l/
2×associate-*r/
Counts
3 → 630
Calls
3 calls:
38.0ms
(/ (/ PI (+ a b)) (/ (* 2 (- b a)) (- (/ 1 a) (/ 1 b))))
28.0ms
(/ (* 2 (- b a)) (- (/ 1 a) (/ 1 b)))
11.0ms
(/ PI (+ a b))

series296.0ms

Counts
3 → 9
Calls
3 calls:
141.0ms
(/ (/ PI (+ a b)) (/ (* 2 (- b a)) (- (/ 1 a) (/ 1 b))))
65.0ms
(/ (* 2 (- b a)) (- (/ 1 a) (/ 1 b)))
90.0ms
(/ PI (+ a b))

simplify951.0ms

Counts
639 → 639
Iterations
IterNodes
done2001
0890

prune2.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
5807×times-frac
2805×*-un-lft-identity
2735×add-sqr-sqrt
1391×add-cube-cbrt
504×difference-of-squares
394×div-inv
392×distribute-lft-out--
259×distribute-lft-out
194×associate-/r/
100×add-exp-log
66×div-exp
64×associate-/r*
61×associate-/l*
56×flip3-- flip--
55×frac-sub
52×add-cbrt-cube
30×cbrt-undiv
8×rec-exp 1-exp prod-exp
5×pow1 associate-/l/
4×clear-num frac-2neg cbrt-unprod insert-posit16 add-log-exp
2×associate-*r/
1×flip3-+ flip-+ pow-flip inv-pow
Counts
4 → 1682
Calls
4 calls:
38.0ms
(/ (/ 1 (/ (+ a b) PI)) (/ (* 2 (- b a)) (- (/ 1 a) (/ 1 b))))
57.0ms
(/ (* 2 (- b a)) (- (/ 1 a) (/ 1 b)))
27.0ms
(/ (+ a b) PI)
20.0ms
(/ 1 (/ (+ a b) PI))

series281.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ (/ 1 (/ (+ a b) PI)) (/ (* 2 (- b a)) (- (/ 1 a) (/ 1 b))))
40.0ms
(/ (* 2 (- b a)) (- (/ 1 a) (/ 1 b)))
61.0ms
(/ (+ a b) PI)
62.0ms
(/ 1 (/ (+ a b) PI))

simplify1.8s

Counts
1694 → 1694
Iterations
IterNodes
done2141
02141

prune8.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes99.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done18
118
014

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.2s9663×body80valid