Details

Time bar (total: 24.8s)

sample33.0ms

Algorithm
intervals
Results
19.0ms302×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01521
13121
29021
338521
4186021
done500121

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b
(/ 1.0 (- (* b b) (* a a)))
5.9b
(- (* b b) (* a a))
7.7b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite440.0ms

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:
61.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
17.0ms
(/ 1.0 (- (* b b) (* a a)))
16.0ms
(- (* b b) (* a a))
255.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
49.0ms
(/ 1.0 (- (* b b) (* a a)))
41.0ms
(- (* b b) (* a a))
158.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.2s

Counts
513 → 513
Iterations

Useful iterations: done (2.1s)

IterNodesCost
088627857
1291425859
done500223272

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b
(/ (/ PI 2.0) (+ b a))
7.7b
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite536.0ms

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:
65.0ms
(- (/ 1.0 a) (/ 1.0 b))
94.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
32.0ms
(/ (/ PI 2.0) (+ b a))
252.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (/ 1.0 a) (/ 1.0 b))
84.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
76.0ms
(/ (/ PI 2.0) (+ b a))
181.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.5s

Counts
813 → 813
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0102437421
1336834352
done500130536

prune3.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite330.0ms

Algorithm
rewrite-expression-head
Rules
206×times-frac
167×*-un-lft-identity
122×add-sqr-sqrt
107×add-cube-cbrt
79×associate-*r*
55×add-exp-log add-cbrt-cube
27×distribute-lft-out
18×cbrt-undiv div-exp prod-exp cbrt-unprod
16×associate-/l*
13×div-inv
11×pow1
8×associate-/r/
5×associate-/r*
4×expm1-log1p-u associate-*r/ associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×flip3-+ associate-*l/ flip-+ distribute-lft-out-- difference-of-squares unswap-sqr
2×frac-2neg clear-num *-commutative
1×frac-times flip3-- flip-- associate-/l/
Counts
4 → 248
Calls
4 calls:
162.0ms
(* (* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ (/ PI 2.0) (+ b a))) (/ 1.0 (- b a)))
37.0ms
(/ (/ PI 2.0) (+ b a))
23.0ms
(/ PI (* (+ b a) 2.0))
86.0ms
(* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ (/ PI 2.0) (+ b a)))

series991.0ms

Counts
4 → 12
Calls
4 calls:
323.0ms
(* (* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ (/ PI 2.0) (+ b a))) (/ 1.0 (- b a)))
109.0ms
(/ (/ PI 2.0) (+ b a))
74.0ms
(/ PI (* (+ b a) 2.0))
484.0ms
(* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ (/ PI 2.0) (+ b a)))

simplify809.0ms

Counts
260 → 260
Iterations

Useful iterations: done (796.0ms)

IterNodesCost
03695477
110415253
done50014592

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
55×add-exp-log add-cbrt-cube
43×add-sqr-sqrt
39×*-un-lft-identity
37×times-frac
34×associate-*r*
27×add-cube-cbrt
19×cbrt-undiv div-exp
17×prod-exp cbrt-unprod
13×associate-*l*
8×pow1 associate-/r/
5×associate-/r* div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp unswap-sqr
3×flip3-+ associate-*r/ associate-*l/ flip-+ distribute-lft-out distribute-lft-out-- difference-of-squares
2×frac-2neg pow-prod-down clear-num *-commutative
1×frac-times flip3-- flip-- associate-/l/
Counts
4 → 152
Calls
4 calls:
39.0ms
(/ (* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ PI 2.0)) (+ b a))
99.0ms
(* (/ (* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ PI 2.0)) (+ b a)) (/ 1.0 (- b a)))
26.0ms
(/ PI (* (+ b a) 2.0))
16.0ms
(* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ PI 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
496.0ms
(/ (* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ PI 2.0)) (+ b a))
318.0ms
(* (/ (* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ PI 2.0)) (+ b a)) (/ 1.0 (- b a)))
71.0ms
(/ PI (* (+ b a) 2.0))
248.0ms
(* (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (/ 1.0 b))) (/ PI 2.0))

simplify3.7s

Counts
164 → 164
Iterations

Useful iterations: 2 (883.0ms)

IterNodesCost
02723898
18063813
249643099
done50003099

prune875.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes144.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02348
13348
done3348

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.0s9585×body80valid