Details

Time bar (total: 5.5s)

sample282.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
9.0ms264×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

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite60.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 97
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
33.0ms
(/ (- 1.0 x) (+ 1.0 x))
20.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series125.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
28.0ms
(/ (- 1.0 x) (+ 1.0 x))
93.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0370779
11128734
25001719

prune322.0ms

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

rewrite314.0ms

Algorithm
rewrite-expression-head
Rules
609×*-un-lft-identity
500×times-frac
348×add-sqr-sqrt
324×prod-diff
323×add-cube-cbrt
127×distribute-lft-out
86×associate-/r/
43×flip3-+ flip-+ div-inv
18×fma-neg
17×sqrt-prod
14×distribute-lft-out--
8×add-exp-log associate-/r* add-cbrt-cube difference-of-squares
6×distribute-rgt-out-- associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u
2×cbrt-undiv flip3-- frac-2neg div-exp clear-num frac-sub flip-- sub-div
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 475
Calls
4 calls:
147.0ms
(sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0))))
11.0ms
(/ x (+ x 1.0))
11.0ms
(/ 1.0 (+ x 1.0))
102.0ms
(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0))))
33.0ms
(/ x (+ x 1.0))
22.0ms
(/ 1.0 (+ x 1.0))
57.0ms
(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

simplify157.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
0113011360
134488189
250018146

prune1.6s

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

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
117×*-un-lft-identity
88×times-frac
72×add-sqr-sqrt
59×add-cube-cbrt
26×distribute-lft-out
24×swap-sqr
20×add-exp-log add-cbrt-cube
18×associate-*r* associate-*l*
16×sqrt-div
12×pow1 associate-/r/
11×associate-*r/ associate-*l/
9×frac-times frac-sub
8×associate-/r*
6×cbrt-undiv flip3-+ div-exp flip-+ div-inv associate-/l*
5×sub-div
4×expm1-log1p-u prod-exp sqrt-prod cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×frac-2neg clear-num
1×pow2 rem-sqrt-square flip3-- sqrt-pow1 pow-plus pow1/2 pow-prod-down pow-sqr *-commutative pow-prod-up flip-- difference-of-squares
Counts
4 → 192
Calls
4 calls:
11.0ms
(/ 1.0 (+ x 1.0))
11.0ms
(/ 1.0 (+ x 1.0))
40.0ms
(sqrt (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
55.0ms
(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))

series189.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1.0 (+ x 1.0))
22.0ms
(/ 1.0 (+ x 1.0))
107.0ms
(sqrt (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
34.0ms
(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))

simplify101.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
08041642
138001520
250021486

prune1.1s

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
01821
11821

end0.0ms

sample809.0ms

Algorithm
intervals
Results
358.0ms8000×body80valid
253.0ms7993×body80nan