Details

Time bar (total: 15.0s)

sample24.0ms

Algorithm
intervals
Results
13.0ms304×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01521
13121
28721
335921
4146121
done500021

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b
(/ 1.0 (- (* b b) (* a a)))
3.8b
(- (* b b) (* a a))
9.8b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite169.0ms

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:
25.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
3.0ms
(- (* b b) (* a a))
96.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
40.0ms
(/ 1.0 (- (* b b) (* a a)))
33.0ms
(- (* b b) (* a a))
90.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.1s

Counts
513 → 513
Iterations

Useful iterations: done (1.1s)

IterNodesCost
088627857
1244025797
done500125719

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.6b

localize13.0ms

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))
9.8b
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite471.0ms

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:
26.0ms
(- (/ 1.0 a) (/ 1.0 b))
55.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
9.0ms
(/ (/ PI 2.0) (+ b a))
309.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (/ 1.0 a) (/ 1.0 b))
62.0ms
(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
54.0ms
(/ (/ PI 2.0) (+ b a))
97.0ms
(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.2s

Counts
813 → 813
Iterations

Useful iterations: 1 (707.0ms)

IterNodesCost
0102437421
1282134154
done500034154

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
298×times-frac
242×*-un-lft-identity
165×add-sqr-sqrt
154×add-cube-cbrt
79×associate-*l*
55×add-exp-log add-cbrt-cube
41×distribute-lft-out
26×associate-/l*
19×cbrt-undiv div-exp
18×div-inv
17×prod-exp cbrt-unprod
11×pow1
8×associate-/r* associate-/r/
6×fma-udef
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u associate-*r* pow-prod-down associate-*l/ log1p-expm1-u add-log-exp
3×flip3-+ flip-+ distribute-lft-out-- difference-of-squares
2×frac-2neg clear-num *-commutative associate-/l/ unswap-sqr
1×frac-times flip3-- associate-*r/ flip--
Counts
4 → 316
Calls
4 calls:
47.0ms
(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (* (/ (cbrt 1.0) b) (* (cbrt 1.0) (cbrt 1.0)))))))
17.0ms
(* (/ 1.0 (- b a)) (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (* (/ (cbrt 1.0) b) (* (cbrt 1.0) (cbrt 1.0))))))
9.0ms
(/ (/ PI 2.0) (+ b a))
9.0ms
(/ (/ PI 2.0) (+ b a))

series684.0ms

Counts
4 → 12
Calls
4 calls:
266.0ms
(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (* (/ (cbrt 1.0) b) (* (cbrt 1.0) (cbrt 1.0)))))))
305.0ms
(* (/ 1.0 (- b a)) (fma (sqrt 1.0) (/ (sqrt 1.0) a) (- (* (/ (cbrt 1.0) b) (* (cbrt 1.0) (cbrt 1.0))))))
56.0ms
(/ (/ PI 2.0) (+ b a))
57.0ms
(/ (/ PI 2.0) (+ b a))

simplify1.3s

Counts
328 → 328
Iterations

Useful iterations: 2 (595.0ms)

IterNodesCost
03437892
19957682
241245670
done50005670

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (/ 1.0 (* a b))))
0.3b
(/ (/ PI 2.0) (+ b a))
0.3b
(/ (/ PI 2.0) (+ b a))
0.8b
(/ 1.0 (* a b))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
285×times-frac
228×*-un-lft-identity
146×add-sqr-sqrt add-cube-cbrt
73×add-exp-log add-cbrt-cube
58×associate-*l*
41×distribute-lft-out
29×associate-/l*
26×cbrt-undiv div-exp
25×prod-exp cbrt-unprod
18×div-inv
9×pow1 associate-/r*
6×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ associate-*r/ pow-prod-down clear-num flip-+
2×associate-/l/
1×frac-times associate-*r* associate-*l/ *-commutative
Counts
4 → 297
Calls
4 calls:
43.0ms
(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (/ 1.0 (* a b))))
9.0ms
(/ (/ PI 2.0) (+ b a))
9.0ms
(/ (/ PI 2.0) (+ b a))
3.0ms
(/ 1.0 (* a b))

series201.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (/ 1.0 (* a b))))
50.0ms
(/ (/ PI 2.0) (+ b a))
56.0ms
(/ (/ PI 2.0) (+ b a))
22.0ms
(/ 1.0 (* a b))

simplify1.0s

Counts
309 → 309
Iterations

Useful iterations: 2 (408.0ms)

IterNodesCost
03004873
18844643
232394141
done50004141

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes105.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02451
13451
done3451

end0.0ms

sample601.0ms

Algorithm
intervals
Results
435.0ms9589×body80valid