Details

Time bar (total: 8.3s)

sample169.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
11.0ms238×body80nan

simplify7.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 91
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
35.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
103.0ms
(/ (- 1.0 x) (+ 1.0 x))

series265.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
175.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
83.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify99.0ms

Counts
100 → 100

prune325.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
0.0b
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
0.0b
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
0.0b
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

rewrite353.0ms

Algorithm
rewrite-expression-head
Rules
184×*-un-lft-identity
91×times-frac
79×add-sqr-sqrt
55×distribute-lft-out
51×associate-*l*
44×unpow-prod-down cube-prod
36×add-cube-cbrt
19×distribute-lft-out-- difference-of-squares
11×add-exp-log sum-cubes add-cbrt-cube
9×pow1 associate-/r*
6×flip3-+ flip-+
5×sqrt-div associate-/l*
4×frac-times associate-*r/ associate-/r/ add-log-exp
3×associate-*r*
2×cbrt-undiv sqrt-pow1 div-exp pow-prod-down associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×distribute-rgt-in flip3-- frac-2neg distribute-lft-in pow1/2 div-sub clear-num sqrt-prod *-commutative flip--
Counts
4 → 175
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
59.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
54.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
228.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series415.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
219.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
74.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
112.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify102.0ms

Counts
187 → 187

prune755.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ (pow 1.0 3) (pow x 3)))
0.0b
(atan (sqrt (* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
0.0b
(sqrt (* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
0.0b
(* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
184×*-un-lft-identity
77×times-frac
56×distribute-lft-out
48×unpow-prod-down cube-prod
36×add-sqr-sqrt
34×associate-*l*
24×distribute-lft-out--
22×add-cube-cbrt
16×frac-times
14×sqrt-div
13×flip3-+ flip-+
9×pow1 associate-/r*
8×add-exp-log associate-*l/ add-cbrt-cube
6×flip3-- associate-/r/ sum-cubes frac-sub flip-- sub-div
4×associate-*r/ add-log-exp difference-of-squares
3×distribute-rgt-out-- associate-*r* div-inv associate-/l*
2×sqrt-pow1 pow-prod-down
1×cbrt-undiv distribute-rgt-in frac-2neg distribute-lft-in pow1/2 div-exp prod-exp clear-num sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
4 → 150
Calls
4 calls:
47.0ms
(/ x (+ (pow 1.0 3) (pow x 3)))
1.0ms
(atan (sqrt (* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
383.0ms
(sqrt (* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
1.5s
(* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(/ x (+ (pow 1.0 3) (pow x 3)))
21.0ms
(atan (sqrt (* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
204.0ms
(sqrt (* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
122.0ms
(* (- (/ 1.0 (+ (pow 1.0 3) (pow x 3))) (/ x (+ (pow 1.0 3) (pow x 3)))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify101.0ms

Counts
162 → 162

prune836.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

simplify113.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.1s8000×body80valid
481.0ms8071×body80nan