Details

Time bar (total: 57.0s)

sample109.0ms

Algorithm
intervals
Results
49.0ms233×body80nan
19.0ms256×body80valid

simplify39.0ms

Calls
1 calls:
Slowest
36.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune7.0ms

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) (+ 1 x))
0.0b
(atan (sqrt (/ (- 1 x) (+ 1 x))))
0.0b
(sqrt (/ (- 1 x) (+ 1 x)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
86×*-un-lft-identity
61×add-sqr-sqrt
49×times-frac
30×sqrt-prod
28×add-cube-cbrt
20×difference-of-squares
15×sqrt-div
14×distribute-lft-out
12×associate-/l*
10×distribute-lft-out--
8×associate-/r*
5×add-cbrt-cube add-exp-log
4×pow1 associate-/r/ associate-/l/
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg flip3-+ flip3-- flip-+ div-inv flip--
1×cbrt-undiv sqrt-pow1 pow1/2 div-sub div-exp
Calls
3 calls:
Slowest
20.0ms
(/ (- 1 x) (+ 1 x))
14.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series87.0ms

Calls
3 calls:
Slowest
46.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
31.0ms
(/ (- 1 x) (+ 1 x))
10.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify4.1s

Calls
120 calls:
Slowest
333.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
318.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
237.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
208.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
146.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (/ (+ 1 x) (- 1 x))))
0.0b
(/ (+ 1 x) (- 1 x))
0.0b
(atan (/ 1 (sqrt (/ (+ 1 x) (- 1 x)))))
0.0b
(sqrt (/ (+ 1 x) (- 1 x)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
272×*-un-lft-identity
244×times-frac
197×add-sqr-sqrt
150×sqrt-prod
113×add-cube-cbrt
54×difference-of-squares
51×associate-/r*
39×distribute-lft-out
30×sqrt-div
27×associate-/r/ distribute-lft-out--
15×associate-/l*
10×add-exp-log
8×add-cbrt-cube
7×pow1 div-inv
6×flip3-- flip-- associate-/l/
4×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ div-exp flip-+ pow-flip
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2
1×rec-exp 1-exp inv-pow
Calls
4 calls:
Slowest
42.0ms
(/ 1 (sqrt (/ (+ 1 x) (- 1 x))))
41.0ms
(/ (+ 1 x) (- 1 x))
28.0ms
(sqrt (/ (+ 1 x) (- 1 x)))
5.0ms
(atan (/ 1 (sqrt (/ (+ 1 x) (- 1 x)))))

series147.0ms

Calls
4 calls:
Slowest
57.0ms
(/ 1 (sqrt (/ (+ 1 x) (- 1 x))))
57.0ms
(sqrt (/ (+ 1 x) (- 1 x)))
29.0ms
(/ (+ 1 x) (- 1 x))
4.0ms
(atan (/ 1 (sqrt (/ (+ 1 x) (- 1 x)))))

simplify11.9s

Calls
376 calls:
Slowest
550.0ms
(/ (* (* (+ 1 x) (+ 1 x)) (+ 1 x)) (* (* (- 1 x) (- 1 x)) (- 1 x)))
392.0ms
(/ (cbrt (+ 1 x)) (- 1 x))
392.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (/ (+ 1 x) (- (pow 1 3) (pow x 3)))))
332.0ms
(/ 1 (sqrt (/ (+ 1 x) (- (pow 1 3) (pow x 3)))))
332.0ms
(/ (sqrt 1) (sqrt (/ (+ 1 x) (- (pow 1 3) (pow x 3)))))

prune2.9s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

7.5b
(log (- 1 x))
0.0b
(/ 1 (sqrt (exp (- (log1p x) (log (- 1 x))))))
0.0b
(atan (/ 1 (sqrt (exp (- (log1p x) (log (- 1 x)))))))
0.0b
(sqrt (exp (- (log1p x) (log (- 1 x)))))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
95×sqrt-prod
91×*-un-lft-identity
90×add-sqr-sqrt
80×exp-sum
76×add-cube-cbrt
66×times-frac
60×prod-diff
25×pow1
22×associate-/r*
18×log-prod log-pow
14×sqrt-pow1 exp-diff sqrt-div
12×log-div exp-prod associate--r+
10×associate--r-
9×add-exp-log pow-flip
8×difference-of-squares
7×associate-/r/ distribute-lft-out--
6×sub-neg flip3-- add-cbrt-cube flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×log1p-def pow1/2 div-exp
1×cbrt-undiv rem-sqrt-square rec-exp clear-num frac-2neg 1-exp rem-log-exp div-inv inv-pow
Calls
4 calls:
Slowest
44.0ms
(/ 1 (sqrt (exp (- (log1p x) (log (- 1 x))))))
33.0ms
(sqrt (exp (- (log1p x) (log (- 1 x)))))
9.0ms
(log (- 1 x))
3.0ms
(atan (/ 1 (sqrt (exp (- (log1p x) (log (- 1 x)))))))

series379.0ms

Calls
4 calls:
Slowest
210.0ms
(/ 1 (sqrt (exp (- (log1p x) (log (- 1 x))))))
136.0ms
(sqrt (exp (- (log1p x) (log (- 1 x)))))
31.0ms
(log (- 1 x))
3.0ms
(atan (/ 1 (sqrt (exp (- (log1p x) (log (- 1 x)))))))

simplify31.4s

Calls
232 calls:
Slowest
592.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (exp (fma (* (cbrt (log1p x)) (cbrt (log1p x))) (cbrt (log1p x)) (- (* (cbrt (log (- 1 x))) (* (cbrt (log (- 1 x))) (cbrt (log (- 1 x))))))))))
581.0ms
(/ (sqrt 1) (sqrt (exp (fma (* (cbrt (log1p x)) (cbrt (log1p x))) (cbrt (log1p x)) (- (* (cbrt (log (- 1 x))) (* (cbrt (log (- 1 x))) (cbrt (log (- 1 x))))))))))
579.0ms
(/ 1 (sqrt (exp (fma (* (cbrt (log1p x)) (cbrt (log1p x))) (cbrt (log1p x)) (- (* (cbrt (log (- 1 x))) (* (cbrt (log (- 1 x))) (cbrt (log (- 1 x))))))))))
561.0ms
(sqrt (exp (fma (* (cbrt (log1p x)) (cbrt (log1p x))) (cbrt (log1p x)) (- (* (cbrt (log (- 1 x))) (* (cbrt (log (- 1 x))) (cbrt (log (- 1 x)))))))))
494.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (exp (fma (sqrt (log1p x)) (sqrt (log1p x)) (- (* (cbrt (log (- 1 x))) (* (cbrt (log (- 1 x))) (cbrt (log (- 1 x))))))))))

prune2.3s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.0s

Algorithm
intervals
Results
990.0ms8000×body80valid
818.0ms8247×body80nan