Details

Time bar (total: 52.6s)

sample54.0ms

Algorithm
intervals
Results
32.0ms296×body80valid

simplify3.8s

Counts
1 → 1
Iterations
IterNodes
done5000
41566
3370
289
131
015

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b
(/ 1.0 (- (* b b) (* a a)))
2.6b
(- (* b b) (* a a))
7.0b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite551.0ms

Algorithm
rewrite-expression-head
Rules
515×times-frac
419×add-sqr-sqrt
403×*-un-lft-identity
395×add-cube-cbrt
339×prod-diff
171×distribute-rgt-in distribute-lft-in
57×div-inv
36×add-exp-log add-cbrt-cube
30×associate-*r*
14×frac-times associate-*l*
13×prod-exp cbrt-unprod
12×difference-of-squares
11×pow1
9×cbrt-undiv div-exp
8×associate-*r/ associate-*l/
7×flip3-- flip--
6×add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u pow-prod-down associate-/r* associate-/r/ frac-sub log1p-expm1-u unswap-sqr
3×sub-neg associate-/l*
2×*-commutative
1×frac-2neg fma-neg diff-log clear-num
Counts
4 → 501
Calls
4 calls:
100.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
25.0ms
(/ 1.0 (- (* b b) (* a a)))
16.0ms
(- (* b b) (* a a))
329.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
85.0ms
(/ 1.0 (- (* b b) (* a a)))
60.0ms
(- (* b b) (* a a))
175.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify4.8s

Counts
513 → 513
Iterations
IterNodes
done5000
12893
0886

prune6.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
0.3b
(/ (/ PI 2.0) (+ a b))
7.0b
(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite790.0ms

Algorithm
rewrite-expression-head
Rules
940×times-frac
738×*-un-lft-identity
713×add-sqr-sqrt
662×add-cube-cbrt
507×prod-diff
171×distribute-rgt-in distribute-lft-in
95×div-inv
59×add-exp-log associate-*l* add-cbrt-cube
33×associate-*r*
27×distribute-lft-out
21×cbrt-undiv div-exp
19×prod-exp cbrt-unprod
14×frac-times
13×fma-neg associate-/l* distribute-lft-out--
11×pow1 difference-of-squares
8×associate-*r/ associate-*l/
6×flip3-- associate-/r/ flip-- add-log-exp unswap-sqr
5×frac-sub
4×expm1-log1p-u pow-prod-down associate-/r* log1p-expm1-u
3×sub-neg
2×flip3-+ *-commutative flip-+
1×frac-2neg diff-log clear-num associate-/l/
Counts
4 → 801
Calls
4 calls:
74.0ms
(- (/ 1.0 a) (/ 1.0 b))
156.0ms
(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
40.0ms
(/ (/ PI 2.0) (+ a b))
377.0ms
(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (/ 1.0 a) (/ 1.0 b))
123.0ms
(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
107.0ms
(/ (/ PI 2.0) (+ a b))
189.0ms
(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify5.9s

Counts
813 → 813
Iterations
IterNodes
done5001
13338
01025

prune9.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ a b))
0.3b
(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b
(* (/ PI 2.0) (/ 1.0 (- b a)))

rewrite941.0ms

Algorithm
rewrite-expression-head
Rules
763×times-frac
622×add-sqr-sqrt
606×*-un-lft-identity
580×add-cube-cbrt
507×prod-diff
171×distribute-rgt-in distribute-lft-in
86×div-inv
59×add-exp-log add-cbrt-cube
33×associate-*r*
27×frac-times
22×prod-exp cbrt-unprod
18×cbrt-undiv div-exp
15×associate-*r/ associate-*l/ associate-/l/
14×associate-*l*
13×fma-neg distribute-lft-out--
11×pow1 difference-of-squares
10×flip3-- flip--
9×frac-sub
6×add-log-exp
4×expm1-log1p-u pow-prod-down associate-/r* associate-/r/ log1p-expm1-u unswap-sqr
3×sub-neg
2×*-commutative distribute-lft-out
1×frac-2neg flip3-+ diff-log clear-num flip-+ associate-/l*
Counts
4 → 708
Calls
4 calls:
62.0ms
(- (/ 1.0 a) (/ 1.0 b))
351.0ms
(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ a b))
306.0ms
(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
90.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))

series522.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (/ 1.0 a) (/ 1.0 b))
196.0ms
(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ a b))
140.0ms
(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
129.0ms
(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify5.4s

Counts
720 → 720
Iterations
IterNodes
done5002
13031
0924

prune7.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* 0.5 (/ PI (* a b))) (+ a b))
0.6b
(/ PI (* a b))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log add-cbrt-cube
10×*-un-lft-identity
8×cbrt-undiv div-exp
7×times-frac
6×add-sqr-sqrt add-cube-cbrt
5×prod-exp associate-/r* cbrt-unprod
4×associate-/l*
2×pow1 expm1-log1p-u frac-2neg clear-num associate-/r/ log1p-expm1-u div-inv distribute-lft-out add-log-exp
1×flip3-+ associate-*r/ flip-+ associate-/l/
Counts
2 → 55
Calls
2 calls:
55.0ms
(/ (* 0.5 (/ PI (* a b))) (+ a b))
16.0ms
(/ PI (* a b))

series173.0ms

Counts
2 → 6
Calls
2 calls:
123.0ms
(/ (* 0.5 (/ PI (* a b))) (+ a b))
50.0ms
(/ PI (* a b))

simplify2.2s

Counts
61 → 61
Iterations
IterNodes
done5015
21230
1297
0111

prune403.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes296.0ms

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
done12
112
09

end0.0ms

sample2.4s

Algorithm
intervals
Results
2.0s9606×body80valid