Details

Time bar (total: 2.7s)

sample288.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
6.0ms234×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
20×times-frac
13×add-cube-cbrt
6×distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log associate-/r* add-cbrt-cube
2×pow1 associate-/r/ associate-/l/ add-log-exp
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ div-inv
Counts
2 → 53
Calls
2 calls:
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
13.0ms
(/ (- 1.0 x) (+ 1.0 x))

series54.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
50.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify92.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0233384
1688359
23022356
35002356

prune124.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
44×add-sqr-sqrt
35×times-frac
32×sqrt-prod
26×add-cube-cbrt
8×distribute-lft-out distribute-lft-out-- difference-of-squares
7×associate-/r*
6×pow1 add-exp-log sqrt-div add-cbrt-cube
5×associate-/l*
4×add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp clear-num flip-- div-inv
Counts
4 → 103
Calls
4 calls:
0.0ms
(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
4.0ms
(sqrt (+ 1.0 x))
4.0ms
(sqrt (+ 1.0 x))
13.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series153.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
32.0ms
(sqrt (+ 1.0 x))
29.0ms
(sqrt (+ 1.0 x))
89.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify124.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0338890
1966822
24225777
35001777

prune251.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
109×sqrt-prod
108×*-un-lft-identity
96×add-sqr-sqrt
91×times-frac
60×add-cube-cbrt
26×difference-of-squares
17×distribute-lft-out--
15×associate-/r*
12×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
7×distribute-lft-out
6×pow1
4×flip3-- associate-/r/ flip-- associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp clear-num flip-+ div-inv
1×sqrt-undiv div-sub
Counts
4 → 185
Calls
4 calls:
4.0ms
(sqrt (- 1.0 x))
4.0ms
(sqrt (+ 1.0 x))
14.0ms
(/ (sqrt (- (* 1.0 1.0) (* x x))) (sqrt (- 1.0 x)))
11.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(sqrt (- 1.0 x))
29.0ms
(sqrt (+ 1.0 x))
60.0ms
(/ (sqrt (- (* 1.0 1.0) (* x x))) (sqrt (- 1.0 x)))
89.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify69.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05201991
118831879
250011807

prune510.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01915
11915

end0.0ms

sample694.0ms

Algorithm
intervals
Results
309.0ms8000×body80valid
197.0ms8035×body80nan