Details

Time bar (total: 21.0s)

sample102.0ms

Algorithm
intervals
Results
68.0ms745×body80nan
20.0ms256×body80valid

simplify23.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
23.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
63×*-un-lft-identity
50×times-frac
39×add-sqr-sqrt
29×add-cube-cbrt
26×sqrt-prod
16×distribute-lft-out
15×log-prod
13×div-inv
8×associate-/l* difference-of-squares
6×distribute-rgt-out add-exp-log
5×add-cbrt-cube add-log-exp
4×pow1
3×log-div associate-/r* insert-posit16
2×flip3-+ sqrt-div frac-add distribute-rgt1-in flip-+ associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp rem-log-exp log-pow flip--
Counts
3 → 103
Calls
3 calls:
Slowest
24.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
12.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
9.0ms
(/ (sqrt (- 1 (* x x))) x)

series524.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
288.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
138.0ms
(/ (sqrt (- 1 (* x x))) x)
97.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify6.0s

Counts
113 → 112
Calls
113 calls:
Slowest
412.0ms
(+ (* 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))))))
399.0ms
(log (- (* (/ 1 x) (/ 1 x)) (* (/ (sqrt (- 1 (* x x))) x) (/ (sqrt (- 1 (* x x))) x))))
355.0ms
(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
350.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (+ (* 3/32 (pow x 4)) (log x))))
327.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))

prune1.1s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
20×add-sqr-sqrt
18×*-un-lft-identity
13×associate-*r*
11×times-frac add-cube-cbrt
8×pow1 add-cbrt-cube prod-exp
6×log-div
5×flip3-+ rem-log-exp associate-*l* flip-+ add-log-exp
4×frac-times div-exp associate-*l/ distribute-lft-out
3×insert-posit16 unswap-sqr
2×rec-exp 1-exp pow-prod-down associate-*r/ log-pow un-div-inv sqrt-prod cbrt-unprod
1×cbrt-undiv +-commutative log-prod sum-log *-commutative div-inv
Counts
3 → 79
Calls
3 calls:
Slowest
85.0ms
(* (+ (sqrt (- 1 (* x x))) 1) (/ 1 x))
30.0ms
(log (* (+ (sqrt (- 1 (* x x))) 1) (/ 1 x)))
16.0ms
(+ (sqrt (- 1 (* x x))) 1)

series438.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
258.0ms
(log (* (+ (sqrt (- 1 (* x x))) 1) (/ 1 x)))
118.0ms
(* (+ (sqrt (- 1 (* x x))) 1) (/ 1 x))
61.0ms
(+ (sqrt (- 1 (* x x))) 1)

simplify6.9s

Counts
60 → 88
Calls
60 calls:
Slowest
775.0ms
(* (* (* (+ (sqrt (- 1 (* x x))) 1) (+ (sqrt (- 1 (* x x))) 1)) (+ (sqrt (- 1 (* x x))) 1)) (/ (* (* 1 1) 1) (* (* x x) x)))
458.0ms
(* (* (* (+ (sqrt (- 1 (* x x))) 1) (+ (sqrt (- 1 (* x x))) 1)) (+ (sqrt (- 1 (* x x))) 1)) (* (* (/ 1 x) (/ 1 x)) (/ 1 x)))
424.0ms
(+ (* 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))))))
372.0ms
(- (log 2) (+ (* 1/4 (pow x 2)) (+ (* 3/32 (pow x 4)) (log x))))
333.0ms
(log (* (- (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x)))) (* 1 1)) (/ 1 x)))

prune706.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample5.0s

Algorithm
intervals
Results
3.5s24001×body80nan
1.1s8000×body80valid