Details

Time bar (total: 11.2s)

sample24.0ms

Algorithm
intervals
Results
13.0ms298×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01521
13021
28621
335221
4141621
done500121

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b
(/ 1.0 (- (* b b) (* a a)))
5.2b
(- (* b b) (* a a))
7.7b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
47×times-frac
39×*-un-lft-identity
36×add-exp-log add-cbrt-cube
31×add-cube-cbrt
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×div-inv distribute-lft-out--
4×pow-prod-down associate-/r* associate-/r/ frac-sub unswap-sqr
3×sub-neg associate-/l*
2×distribute-rgt-in distribute-lft-in *-commutative
1×frac-2neg diff-log clear-num
Counts
4 → 153
Calls
4 calls:
22.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
7.0ms
(/ 1.0 (- (* b b) (* a a)))
3.0ms
(- (* b b) (* a a))
71.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms
(/ 1.0 (- (* b b) (* a a)))
30.0ms
(- (* b b) (* a a))
87.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.5s

Counts
165 → 165
Iterations

Useful iterations: 2 (637.0ms)

IterNodesCost
02583239
18023164
235472682
done50002682

prune404.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- b a))
0.2b
(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
0.2b
(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
7.7b
(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
194×add-exp-log
112×add-cbrt-cube
95×prod-exp
84×add-sqr-sqrt
71×*-un-lft-identity
68×times-frac
59×div-exp
51×cbrt-unprod
47×frac-times
41×add-cube-cbrt
34×associate-*r*
32×associate-*l*
31×cbrt-undiv
29×associate-*r/
23×associate-*l/
20×pow1
12×distribute-lft-out--
11×difference-of-squares
10×rec-exp flip3-- 1-exp pow-prod-down flip--
8×frac-sub
6×associate-/r/ div-inv unswap-sqr
5×associate-/r*
4×add-log-exp
3×*-commutative distribute-lft-out associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-2neg flip3-+ clear-num flip-+
Counts
4 → 254
Calls
4 calls:
5.0ms
(/ 1.0 (- b a))
34.0ms
(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
34.0ms
(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
159.0ms
(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1.0 (- b a))
65.0ms
(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
48.0ms
(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
99.0ms
(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify724.0ms

Counts
266 → 266
Iterations

Useful iterations: done (716.0ms)

IterNodesCost
03885822
113195174
done50004236

prune735.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
61×add-exp-log *-un-lft-identity add-cbrt-cube
54×times-frac
35×add-cube-cbrt
34×associate-*l*
29×frac-times associate-*r/
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
15×associate-/l/
13×associate-*r*
12×flip3-- flip-- distribute-lft-out--
11×pow1 difference-of-squares
10×distribute-rgt-in distribute-lft-in frac-sub
9×associate-/r*
7×associate-*l/
6×sub-neg associate-/r/ div-inv
4×pow-prod-down associate-/l* add-log-exp
2×frac-2neg clear-num *-commutative distribute-lft-out unswap-sqr
1×flip3-+ flip-+
Counts
4 → 205
Calls
4 calls:
6.0ms
(/ 1.0 (- b a))
71.0ms
(/ (* (/ PI 2.0) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (+ b a))
67.0ms
(* (/ PI 2.0) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
73.0ms
(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series254.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 1.0 (- b a))
90.0ms
(/ (* (/ PI 2.0) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (+ b a))
72.0ms
(* (/ PI 2.0) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
50.0ms
(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.6s

Counts
217 → 217
Iterations

Useful iterations: 2 (803.0ms)

IterNodesCost
03184278
19494171
241983483
done50003483

prune495.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log add-cbrt-cube
44×*-un-lft-identity times-frac
32×add-sqr-sqrt
24×associate-*r/
21×prod-exp cbrt-unprod
20×add-cube-cbrt
19×cbrt-undiv div-exp
14×associate-/r/
9×pow1 flip3-- flip-- div-inv
8×distribute-rgt-in distribute-lft-in distribute-lft-out associate-/l*
6×add-log-exp
5×sub-neg associate-/r* distribute-lft-out--
4×associate-/l/ difference-of-squares
3×associate-*l* pow-prod-down frac-sub
2×frac-2neg clear-num
1×flip3-+ diff-log associate-*r* *-commutative flip-+
Counts
4 → 147
Calls
4 calls:
18.0ms
(- (/ 1.0 a) (/ 1.0 b))
56.0ms
(/ (/ (* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a))) (+ b a))
56.0ms
(/ (* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a)))
50.0ms
(* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

series261.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (/ 1.0 a) (/ 1.0 b))
93.0ms
(/ (/ (* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a))) (+ b a))
71.0ms
(/ (* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a)))
61.0ms
(* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

simplify1.4s

Counts
159 → 159
Iterations

Useful iterations: 2 (512.0ms)

IterNodesCost
02603829
17243708
234913042
done50013042

prune300.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01419
11719
done1719

end0.0ms

sample586.0ms

Algorithm
intervals
Results
427.0ms9537×body80valid