Details

Time bar (total: 10.4s)

sample24.0ms

Algorithm
intervals
Results
14.0ms312×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01521
13021
28621
335221
4141621
done500021

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b
(/ 1.0 (- (* b b) (* a a)))
4.0b
(- (* b b) (* a a))
11.3b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite107.0ms

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))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
3.0ms
(- (* b b) (* a a))
70.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms
(/ 1.0 (- (* b b) (* a a)))
34.0ms
(- (* b b) (* a a))
86.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.1s

Counts
165 → 165
Iterations

Useful iterations: 2 (359.0ms)

IterNodesCost
02583239
18023164
235302682
done50002682

prune397.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.3b
(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
11.3b
(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
110×add-exp-log add-cbrt-cube
103×add-sqr-sqrt
90×times-frac
88×*-un-lft-identity
78×associate-*r*
51×prod-exp cbrt-unprod
48×add-cube-cbrt
47×frac-times
33×associate-*l/
30×cbrt-undiv div-exp
29×sqrt-prod
20×pow1
19×associate-*r/
16×distribute-lft-out--
15×associate-*l*
14×difference-of-squares
10×flip3-- pow-prod-down flip--
9×frac-sub
7×div-inv
6×distribute-lft-out add-log-exp unswap-sqr
4×associate-/r/
3×sub-neg *-commutative
2×distribute-rgt-in distribute-lft-in
1×flip3-+ diff-log flip-+
Counts
4 → 246
Calls
4 calls:
17.0ms
(- (/ 1.0 a) (/ 1.0 b))
46.0ms
(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
27.0ms
(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
184.0ms
(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series663.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (/ 1.0 a) (/ 1.0 b))
200.0ms
(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
146.0ms
(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
286.0ms
(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify543.0ms

Counts
258 → 258
Iterations

Useful iterations: done (530.0ms)

IterNodesCost
03926141
113445725
done50005173

prune540.0ms

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

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
98×times-frac
88×*-un-lft-identity
80×add-sqr-sqrt
47×add-exp-log add-cbrt-cube
34×add-cube-cbrt
21×distribute-lft-out--
19×difference-of-squares
16×cbrt-undiv div-exp associate-/r/
15×prod-exp cbrt-unprod
14×associate-*l/
12×associate-*l* div-inv
11×associate-/l*
9×pow1 associate-/r*
8×associate-/l/ distribute-lft-out
7×flip3-+ flip-+
6×frac-times flip3-- flip-- add-log-exp
5×frac-sub
3×pow-prod-down
2×frac-2neg associate-*r/ clear-num
1×sub-neg diff-log associate-*r* *-commutative
Counts
4 → 182
Calls
4 calls:
17.0ms
(- (/ 1.0 a) (/ 1.0 b))
43.0ms
(/ (/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a)) (- b a))
40.0ms
(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a))
74.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0))

series493.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(- (/ 1.0 a) (/ 1.0 b))
95.0ms
(/ (/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a)) (- b a))
102.0ms
(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a))
67.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0))

simplify1.2s

Counts
194 → 194
Iterations

Useful iterations: 2 (477.0ms)

IterNodesCost
03014727
18674565
238904009
done50014009

prune439.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(* (/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a)) (/ 1 (- b a)))
0.2b
(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a))
0.3b
(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
112×add-exp-log
72×add-cbrt-cube
59×add-sqr-sqrt
51×*-un-lft-identity
50×prod-exp
45×times-frac
36×div-exp
30×cbrt-unprod
22×add-cube-cbrt associate-*r* associate-*l*
21×cbrt-undiv
15×associate-*l/
13×distribute-lft-out--
11×pow1 difference-of-squares
7×frac-times div-inv associate-/l/
6×flip3-- associate-/r/ flip-- add-log-exp
5×rec-exp 1-exp frac-sub
4×pow-prod-down associate-/r*
3×associate-*r/ distribute-lft-out unswap-sqr
2×flip3-+ *-commutative flip-+
1×sub-neg frac-2neg diff-log clear-num un-div-inv associate-/l*
Counts
4 → 171
Calls
4 calls:
17.0ms
(- (/ 1.0 a) (/ 1.0 b))
116.0ms
(* (/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a)) (/ 1 (- b a)))
41.0ms
(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a))
72.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0))

series288.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (/ 1.0 a) (/ 1.0 b))
92.0ms
(* (/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a)) (/ 1 (- b a)))
103.0ms
(/ (* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0)) (+ b a))
62.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (* (/ PI 2.0) 1.0))

simplify1.4s

Counts
183 → 183
Iterations

Useful iterations: 2 (544.0ms)

IterNodesCost
02964289
19243999
237103171
done50003171

prune352.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.3b 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
01723
12323
done2323

end0.0ms

sample579.0ms

Algorithm
intervals
Results
423.0ms9585×body80valid