Details

Time bar (total: 1.8m)

sample65.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
26.0ms230×body80nan

simplify208.0ms

Calls
1 calls:
Slowest
208.0ms
(* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (sqrt 2) (/ 4 (- 1 (* v v))))
0.0b
(/ 4 (- 1 (* v v)))
0.0b
(* (/ (sqrt 2) (/ 4 (- 1 (* v v)))) (sqrt (fma (* v v) -3 1)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
474×times-frac
294×add-sqr-sqrt
262×*-un-lft-identity
219×add-cube-cbrt
141×sqrt-prod
131×associate-*l*
86×difference-of-squares
30×associate-/r/
26×associate-/r*
19×add-cbrt-cube add-exp-log
16×div-inv
14×flip3-- flip--
10×unswap-sqr
9×associate-/l*
7×cbrt-undiv div-exp
6×associate-*r*
5×pow1
3×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×pow-prod-down associate-*l/ *-commutative
Calls
3 calls:
Slowest
57.0ms
(* (/ (sqrt 2) (/ 4 (- 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
10.0ms
(/ (sqrt 2) (/ 4 (- 1 (* v v))))
8.0ms
(/ 4 (- 1 (* v v)))

series563.0ms

Calls
3 calls:
Slowest
323.0ms
(* (/ (sqrt 2) (/ 4 (- 1 (* v v)))) (sqrt (fma (* v v) -3 1)))
187.0ms
(/ (sqrt 2) (/ 4 (- 1 (* v v))))
52.0ms
(/ 4 (- 1 (* v v)))

simplify59.3s

Calls
497 calls:
Slowest
572.0ms
(/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (/ (* (* 4 4) 4) (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v)))))
542.0ms
(/ 1 (/ 4 (- (pow 1 3) (pow (* v v) 3))))
480.0ms
(/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* (/ 4 (- 1 (* v v))) (/ 4 (- 1 (* v v)))) (/ 4 (- 1 (* v v)))))
463.0ms
(/ (sqrt 1) (/ 4 (- (* 1 1) (* (* v v) (* v v)))))
461.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (* (cbrt 4) (cbrt 4)) (+ (sqrt 1) v)))

prune4.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (* (sqrt 2) (sqrt (fma (* v v) -3 1))) (/ 4 (- 1 (* v v))))
0.0b
(/ 4 (- 1 (* v v)))
0.0b
(* (sqrt 2) (sqrt (fma (* v v) -3 1)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
53×add-sqr-sqrt
45×*-un-lft-identity
35×add-cube-cbrt
26×associate-/r*
20×difference-of-squares
19×add-cbrt-cube add-exp-log
10×sqrt-prod
7×pow1 cbrt-undiv div-exp associate-/r/
6×associate-*r* associate-*l*
4×div-inv associate-/l* unswap-sqr
3×expm1-log1p-u flip3-- pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u flip-- add-log-exp
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×sqrt-unprod *-commutative
Calls
3 calls:
Slowest
17.0ms
(/ (* (sqrt 2) (sqrt (fma (* v v) -3 1))) (/ 4 (- 1 (* v v))))
13.0ms
(* (sqrt 2) (sqrt (fma (* v v) -3 1)))
7.0ms
(/ 4 (- 1 (* v v)))

series516.0ms

Calls
3 calls:
Slowest
325.0ms
(/ (* (sqrt 2) (sqrt (fma (* v v) -3 1))) (/ 4 (- 1 (* v v))))
154.0ms
(* (sqrt 2) (sqrt (fma (* v v) -3 1)))
36.0ms
(/ 4 (- 1 (* v v)))

simplify13.0s

Calls
149 calls:
Slowest
485.0ms
(/ (sqrt (fma (* v v) -3 1)) (/ (sqrt 4) (- (sqrt 1) v)))
384.0ms
(/ (sqrt 2) (/ 4 (- (* 1 1) (* (* v v) (* v v)))))
382.0ms
(- (+ (* 1/4 (sqrt 2)) (* 3/32 (* (sqrt 2) (pow v 4)))) (* 5/8 (* (sqrt 2) (pow v 2))))
356.0ms
(/ (* (* (* (sqrt 2) (sqrt (fma (* v v) -3 1))) (* (sqrt 2) (sqrt (fma (* v v) -3 1)))) (* (sqrt 2) (sqrt (fma (* v v) -3 1)))) (* (* (/ 4 (- 1 (* v v))) (/ 4 (- 1 (* v v)))) (/ 4 (- 1 (* v v)))))
337.0ms
(/ (* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* (sqrt (fma (* v v) -3 1)) (sqrt (fma (* v v) -3 1))) (sqrt (fma (* v v) -3 1)))) (* (* (/ 4 (- 1 (* v v))) (/ 4 (- 1 (* v v)))) (/ 4 (- 1 (* v v)))))

prune1.6s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

2.5b
(log (- 1 (* v v)))
0.0b
(/ (* (sqrt 2) (sqrt (fma (* v v) -3 1))) (exp (- (log 4) (log (- 1 (* v v))))))
0.0b
(* (sqrt 2) (sqrt (fma (* v v) -3 1)))
0.0b
(exp (- (log 4) (log (- 1 (* v v)))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
69×exp-sum
50×add-sqr-sqrt
48×prod-diff
44×*-un-lft-identity
39×add-cube-cbrt
37×pow1
29×log-pow
26×associate-/r* times-frac
14×log-prod
11×add-cbrt-cube
10×add-exp-log sqrt-prod
9×associate--l+
8×log-div exp-prod
6×associate-*r* associate-*l* associate--r-
5×add-log-exp
4×expm1-log1p-u sub-neg flip3-- insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- unswap-sqr
3×pow-prod-down difference-of-squares
2×cbrt-undiv log1p-def sqrt-pow1 pow1/2 exp-diff div-exp prod-exp cbrt-unprod rem-exp-log
1×clear-num frac-2neg sqrt-unprod diff-log rem-log-exp associate-/r/ *-commutative div-inv associate-/l*
Calls
4 calls:
Slowest
51.0ms
(/ (* (sqrt 2) (sqrt (fma (* v v) -3 1))) (exp (- (log 4) (log (- 1 (* v v))))))
27.0ms
(exp (- (log 4) (log (- 1 (* v v)))))
16.0ms
(* (sqrt 2) (sqrt (fma (* v v) -3 1)))
4.0ms
(log (- 1 (* v v)))

series891.0ms

Calls
4 calls:
Slowest
413.0ms
(/ (* (sqrt 2) (sqrt (fma (* v v) -3 1))) (exp (- (log 4) (log (- 1 (* v v))))))
188.0ms
(exp (- (log 4) (log (- 1 (* v v)))))
157.0ms
(* (sqrt 2) (sqrt (fma (* v v) -3 1)))
132.0ms
(log (- 1 (* v v)))

simplify23.5s

Calls
165 calls:
Slowest
581.0ms
(/ (sqrt (fma (* v v) -3 1)) (exp (fma (- (cbrt (log (- 1 (* v v))))) (* (cbrt (log (- 1 (* v v)))) (cbrt (log (- 1 (* v v))))) (* (cbrt (log (- 1 (* v v)))) (* (cbrt (log (- 1 (* v v)))) (cbrt (log (- 1 (* v v)))))))))
536.0ms
(/ (sqrt (fma (* v v) -3 1)) (exp (fma (- (cbrt (log (- 1 (* v v))))) (* (cbrt (log (- 1 (* v v)))) (cbrt (log (- 1 (* v v))))) (* (cbrt (log (- 1 (* v v)))) (* (cbrt (log (- 1 (* v v)))) (cbrt (log (- 1 (* v v)))))))))
535.0ms
(/ (sqrt (fma (* v v) -3 1)) (exp (fma (- (cbrt (log (- 1 (* v v))))) (* (cbrt (log (- 1 (* v v)))) (cbrt (log (- 1 (* v v))))) (* (cbrt (log (- 1 (* v v)))) (* (cbrt (log (- 1 (* v v)))) (cbrt (log (- 1 (* v v)))))))))
494.0ms
(/ (sqrt (fma (* v v) -3 1)) (exp (fma (- (cbrt (log (- 1 (* v v))))) (* (cbrt (log (- 1 (* v v)))) (cbrt (log (- 1 (* v v))))) (* (cbrt (log (- 1 (* v v)))) (* (cbrt (log (- 1 (* v v)))) (cbrt (log (- 1 (* v v)))))))))
483.0ms
(/ (sqrt 2) (exp (fma (sqrt (log 4)) (sqrt (log 4)) (- (* (cbrt (log (- 1 (* v v)))) (* (cbrt (log (- 1 (* v v)))) (cbrt (log (- 1 (* v v))))))))))

prune2.5s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.3s8163×body80nan
1.2s8000×body80valid