Details

Time bar (total: 22.3s)

sample119.0ms

Algorithm
intervals
Results
78.0ms745×body80nan
24.0ms256×body80valid

simplify28.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
28.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
59×times-frac
46×add-sqr-sqrt
36×add-cube-cbrt
26×sqrt-prod
16×distribute-lft-out
15×log-prod
14×div-inv
13×fma-def
8×associate-/l* difference-of-squares
6×distribute-rgt-out add-exp-log
5×add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u log-div associate-/r* insert-posit16 log1p-expm1-u
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 → 122
Calls
3 calls:
Slowest
42.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
19.0ms
(/ (sqrt (- 1 (* x x))) x)
15.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))

series487.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
228.0ms
(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
143.0ms
(/ (sqrt (- 1 (* x x))) x)
116.0ms
(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify6.4s

Counts
124 → 131
Calls
124 calls:
Slowest
425.0ms
(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
404.0ms
(sqrt (- (pow 1 3) (pow (* x x) 3)))
392.0ms
(+ (* 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))))))
367.0ms
(- (/ 1 x) (+ (* 1/2 x) (* 1/8 (pow x 3))))
341.0ms
(+ (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))) (+ (sqrt -1) (* 1/8 (/ 1 (* (pow x 4) (sqrt -1))))))

prune1.2s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
21×add-sqr-sqrt
19×*-un-lft-identity
13×associate-*l*
12×add-cube-cbrt
11×times-frac
8×pow1 add-cbrt-cube prod-exp
5×log-div flip3-+ rem-log-exp associate-*r* flip-+ add-log-exp
4×frac-times div-exp associate-*r/ distribute-lft-out
3×expm1-log1p-u fma-def insert-posit16 log1p-expm1-u unswap-sqr
2×rec-exp 1-exp pow-prod-down associate-*l/ log-pow sqrt-prod cbrt-unprod
1×distribute-rgt-in cbrt-undiv +-commutative log-prod sum-log distribute-lft-in *-commutative div-inv
Counts
3 → 88
Calls
3 calls:
Slowest
54.0ms
(* (/ 1 x) (+ 1 (sqrt (- 1 (* x x)))))
29.0ms
(log (* (/ 1 x) (+ 1 (sqrt (- 1 (* x x))))))
16.0ms
(+ 1 (sqrt (- 1 (* x x))))

series360.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
205.0ms
(log (* (/ 1 x) (+ 1 (sqrt (- 1 (* x x))))))
93.0ms
(* (/ 1 x) (+ 1 (sqrt (- 1 (* x x)))))
61.0ms
(+ 1 (sqrt (- 1 (* x x))))

simplify7.9s

Counts
64 → 97
Calls
64 calls:
Slowest
1.1s
(* (* (* (/ 1 x) (/ 1 x)) (/ 1 x)) (* (* (+ 1 (sqrt (- 1 (* x x)))) (+ 1 (sqrt (- 1 (* x x))))) (+ 1 (sqrt (- 1 (* x x))))))
733.0ms
(log (* (/ 1 x) (- (* 1 1) (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x)))))))
650.0ms
(+ (* 1 1) (- (* (sqrt (- 1 (* x x))) (sqrt (- 1 (* x x)))) (* 1 (sqrt (- 1 (* x x))))))
398.0ms
(+ (* 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))))))
388.0ms
(log (* (/ 1 x) (+ (pow 1 3) (pow (sqrt (- 1 (* x x))) 3))))

prune851.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.7s

Algorithm
intervals
Results
3.1s24001×body80nan
1.1s8000×body80valid