Details

Time bar (total: 32.4s)

sample156.0ms

Algorithm
intervals
Results
95.0ms732×body80nan
36.0ms256×body80valid

simplify65.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
65.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (- 1 (* x x)))
0.0b
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
0.0b
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
35×times-frac
28×add-sqr-sqrt
20×add-cube-cbrt
16×distribute-lft-out
15×log-prod
13×fma-def div-inv
11×sqrt-prod
6×distribute-rgt-out
5×pow1 add-log-exp
4×add-exp-log
3×expm1-log1p-u log-div add-cbrt-cube insert-posit16 log1p-expm1-u
2×flip3-+ sqrt-div frac-add distribute-rgt1-in flip-+ difference-of-squares
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-- pow1/2 rem-log-exp log-pow flip--
Counts
3 → 90
Calls
3 calls:
Slowest
42.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
27.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
13.0ms
(sqrt (- 1 (* x x)))

series487.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
293.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
114.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
81.0ms
(sqrt (- 1 (* x x)))

simplify4.9s

Counts
72 → 99
Calls
72 calls:
Slowest
432.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
421.0ms
(+ (* 1/3 (/ 1 (* (pow x 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ 1 (* (pow x 3) (sqrt -1)))) (+ (log (sqrt -1)) (/ 1 (* x (sqrt -1))))))
420.0ms
(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
372.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))
302.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (+ (* 3/32 (pow x 4)) (log x))))

prune877.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (sqrt (- 1 (* x x)))) (sqrt (sqrt (- 1 (* x x)))))
0.0b
(sqrt (- 1 (* x x)))
0.0b
(sqrt (- 1 (* x x)))
0.0b
(sqrt (sqrt (- 1 (* x x))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
61×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
27×*-un-lft-identity
20×pow1/2 add-cube-cbrt
17×swap-sqr
14×difference-of-squares
11×associate-*r* associate-*l*
9×flip3-- pow-prod-up flip-- unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
2×associate-*l/ associate-*r/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 158
Calls
4 calls:
Slowest
52.0ms
(* (sqrt (sqrt (- 1 (* x x)))) (sqrt (sqrt (- 1 (* x x)))))
16.0ms
(sqrt (sqrt (- 1 (* x x))))
12.0ms
(sqrt (- 1 (* x x)))
12.0ms
(sqrt (- 1 (* x x)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
149.0ms
(sqrt (sqrt (- 1 (* x x))))
83.0ms
(sqrt (- 1 (* x x)))
61.0ms
(sqrt (- 1 (* x x)))
56.0ms
(* (sqrt (sqrt (- 1 (* x x)))) (sqrt (sqrt (- 1 (* x x)))))

simplify11.5s

Counts
171 → 170
Calls
171 calls:
Slowest
444.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
436.0ms
(* (- 1 (* x x)) (- 1 (* x x)))
419.0ms
(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
399.0ms
(* (sqrt (sqrt (- (pow 1 3) (pow (* x x) 3)))) (sqrt (sqrt (- 1 (* x x)))))
398.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))

prune1.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1 x))
0.6b
(cbrt (/ 1 x))
0.6b
(cbrt (/ 1 x))
0.6b
(* (cbrt (/ 1 x)) (cbrt (/ 1 x)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
119×cbrt-prod
97×add-sqr-sqrt
79×times-frac
67×*-un-lft-identity
57×add-cube-cbrt
18×swap-sqr
16×associate-*r* associate-*l* unswap-sqr
11×pow1
9×pow1/3 div-inv
7×cbrt-div
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 165
Calls
4 calls:
Slowest
13.0ms
(* (cbrt (/ 1 x)) (cbrt (/ 1 x)))
2.0ms
(cbrt (/ 1 x))
2.0ms
(cbrt (/ 1 x))
2.0ms
(cbrt (/ 1 x))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
296.0ms
(* (cbrt (/ 1 x)) (cbrt (/ 1 x)))
290.0ms
(cbrt (/ 1 x))
272.0ms
(cbrt (/ 1 x))
263.0ms
(cbrt (/ 1 x))

simplify3.5s

Counts
170 → 177
Calls
170 calls:
Slowest
541.0ms
(* (pow (/ 1 (pow x 2)) 1/3) (pow (cbrt -1) 2))
157.0ms
(* (pow (/ -1 x) 1/3) (cbrt -1))
123.0ms
(* (* (cbrt (cbrt (/ 1 x))) (cbrt (cbrt (/ 1 x)))) (* (cbrt (cbrt (/ 1 x))) (cbrt (cbrt (/ 1 x)))))
121.0ms
(* (pow (/ -1 x) 1/3) (cbrt -1))
107.0ms
(* (pow (/ -1 x) 1/3) (cbrt -1))

prune2.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
3.1s23745×body80nan
1.1s8000×body80valid