Details

Time bar (total: 4.7s)

sample275.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
5.0ms191×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0166
1196
2216
3216

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

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:
10.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
13.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series143.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
44.0ms
(/ (- 1.0 x) (+ 1.0 x))
9.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify40.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0370779
11128734
25001719

prune232.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
58×*-un-lft-identity
41×times-frac
38×add-cube-cbrt
26×associate-*l*
21×difference-of-squares
18×prod-diff
11×add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
10×distribute-lft-out--
9×pow1
7×flip3-- flip--
5×sqrt-div associate-*r* associate-/l*
4×expm1-log1p-u frac-times associate-*r/ associate-/r* associate-/r/ log1p-expm1-u add-log-exp
2×cbrt-undiv sub-neg sqrt-pow1 div-exp pow-prod-down associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×frac-2neg pow1/2 div-sub clear-num sqrt-prod *-commutative
Counts
4 → 150
Calls
4 calls:
12.0ms
(/ (- 1.0 x) (- (* 1.0 1.0) (* x x)))
15.0ms
(sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x)))
0.0ms
(atan (sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))))
35.0ms
(* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))

series157.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ (- 1.0 x) (- (* 1.0 1.0) (* x x)))
68.0ms
(sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x)))
4.0ms
(atan (sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))))
47.0ms
(* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))

simplify100.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
06841774
133921505
250021435

prune377.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
355×add-sqr-sqrt
349×*-un-lft-identity
342×prod-diff
327×add-cube-cbrt
128×difference-of-squares
84×associate-/r/
51×flip3-- flip--
42×div-inv
18×fma-neg
15×associate-*l*
11×distribute-rgt-in distribute-lft-in distribute-lft-out--
8×add-exp-log frac-times add-cbrt-cube
6×pow1 distribute-rgt-out-- add-log-exp
5×associate-*r*
4×expm1-log1p-u associate-*l/ associate-/r* frac-sub log1p-expm1-u sub-div
3×sub-neg associate-/l*
2×associate-*r/
1×cbrt-undiv frac-2neg diff-log div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
4 → 484
Calls
4 calls:
64.0ms
(- (/ 1.0 (- (* 1.0 1.0) (* x x))) (/ x (- (* 1.0 1.0) (* x x))))
5.0ms
(/ x (- (* 1.0 1.0) (* x x)))
0.0ms
(atan (sqrt (* (- (/ 1.0 (- (* 1.0 1.0) (* x x))) (/ x (- (* 1.0 1.0) (* x x)))) (- 1.0 x))))
169.0ms
(* (- (/ 1.0 (- (* 1.0 1.0) (* x x))) (/ x (- (* 1.0 1.0) (* x x)))) (- 1.0 x))

series204.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (/ 1.0 (- (* 1.0 1.0) (* x x))) (/ x (- (* 1.0 1.0) (* x x))))
62.0ms
(/ x (- (* 1.0 1.0) (* x x)))
7.0ms
(atan (sqrt (* (- (/ 1.0 (- (* 1.0 1.0) (* x x))) (/ x (- (* 1.0 1.0) (* x x)))) (- 1.0 x))))
78.0ms
(* (- (/ 1.0 (- (* 1.0 1.0) (* x x))) (/ x (- (* 1.0 1.0) (* x x)))) (- 1.0 x))

simplify149.0ms

Algorithm
egg-herbie
Counts
496 → 496
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0157117332
1500112470

prune828.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-div
18×flip3-- flip--
16×frac-times times-frac
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
10×pow1
8×associate-*r/ associate-*l/ associate-/r/ associate-/l/
6×add-exp-log flip3-+ add-cbrt-cube flip-+
4×expm1-log1p-u sqrt-pow1 associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×pow1/2 pow-prod-down
1×cbrt-undiv sqrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 106
Calls
4 calls:
11.0ms
(sqrt (* (- (* 1.0 1.0) (* x x)) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))
92.0ms
(sqrt (* (- 1.0 x) (- (pow 1.0 3) (pow x 3))))
1.0ms
(atan (/ (sqrt (* (- 1.0 x) (- (pow 1.0 3) (pow x 3)))) (sqrt (* (- (* 1.0 1.0) (* x x)) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))))
32.0ms
(/ (sqrt (* (- 1.0 x) (- (pow 1.0 3) (pow x 3)))) (sqrt (* (- (* 1.0 1.0) (* x x)) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))))

series304.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(sqrt (* (- (* 1.0 1.0) (* x x)) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))
55.0ms
(sqrt (* (- 1.0 x) (- (pow 1.0 3) (pow x 3))))
9.0ms
(atan (/ (sqrt (* (- 1.0 x) (- (pow 1.0 3) (pow x 3)))) (sqrt (* (- (* 1.0 1.0) (* x x)) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))))
158.0ms
(/ (sqrt (* (- 1.0 x) (- (pow 1.0 3) (pow x 3)))) (sqrt (* (- (* 1.0 1.0) (* x x)) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06452295
128592185
250012183

prune513.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01614
11614

end0.0ms

sample720.0ms

Algorithm
intervals
Results
323.0ms8000×body80valid
210.0ms7986×body80nan