Details

Time bar (total: 4.6s)

sample274.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
6.0ms244×body80nan

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize10.0ms

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))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
49×add-sqr-sqrt
41×times-frac
26×add-cube-cbrt sqrt-prod
14×sqrt-div
12×distribute-lft-out
10×associate-/l* distribute-lft-out-- difference-of-squares
8×associate-/r*
5×add-exp-log add-cbrt-cube
4×pow1 associate-/r/ associate-/l/
3×add-log-exp
2×rem-sqrt-square flip3-- frac-2neg flip3-+ clear-num flip-- flip-+ div-inv
1×cbrt-undiv sqrt-pow1 pow1/2 div-sub div-exp
Counts
3 → 104
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
9.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms
(/ (- 1.0 x) (+ 1.0 x))

series159.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
98.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
58.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify43.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0372833
11088797
25001775

prune201.0ms

Filtered
113 candidates to 79 candidates (69.9%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1112113
Fresh000
Picked101
Done000
Total1122114

Merged error: 0b

Counts
114 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
1336×sqrt-prod
901×times-frac
820×*-un-lft-identity
595×add-sqr-sqrt
388×add-cube-cbrt
115×distribute-lft-out
101×distribute-lft-out-- difference-of-squares
66×sqrt-div
65×associate-/r*
45×associate-/r/
23×associate-/l*
15×flip3-- flip-- div-inv
8×add-exp-log add-cbrt-cube associate-/l/
5×pow1
4×frac-2neg clear-num add-log-exp
3×rem-sqrt-square flip3-+ flip-+
2×cbrt-undiv div-exp
1×sqrt-undiv sqrt-pow1 pow1/2
Counts
4 → 669
Calls
4 calls:
4.0ms
(atan (/ (sqrt (sqrt (- 1.0 x))) (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))))
15.0ms
(sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))
9.0ms
(/ (+ 1.0 x) (sqrt (- 1.0 x)))
29.0ms
(/ (sqrt (sqrt (- 1.0 x))) (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x)))))

series433.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (/ (sqrt (sqrt (- 1.0 x))) (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))))
238.0ms
(sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))
94.0ms
(/ (+ 1.0 x) (sqrt (- 1.0 x)))
98.0ms
(/ (sqrt (sqrt (- 1.0 x))) (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x)))))

simplify182.0ms

Algorithm
egg-herbie
Counts
681 → 681
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
0104912496
1306112099
2500211393

prune983.0ms

Filtered
681 candidates to 263 candidates (38.6%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New6810681
Fresh011
Picked011
Done000
Total6812683

Merged error: 0b

Counts
683 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
365×*-un-lft-identity
149×add-sqr-sqrt
138×times-frac
128×associate-*l*
88×pow-unpow sum-cubes
76×frac-times
71×sqrt-prod
65×add-cube-cbrt
64×distribute-lft-out
63×associate-/r*
59×sqrt-div
50×distribute-lft-out--
44×unpow-prod-down
43×flip3-+ flip-+
38×associate-*l/
35×associate-/l*
34×difference-of-squares
26×associate-*r*
14×associate-/l/
11×add-exp-log add-cbrt-cube
9×pow1
7×flip3-- frac-2neg clear-num flip--
6×associate-/r/ unswap-sqr
4×distribute-rgt-in associate-+r+ distribute-lft-in associate-*r/ add-log-exp
3×rem-sqrt-square div-inv
2×cbrt-undiv +-commutative sub-neg sqrt-pow1 div-exp pow-prod-down prod-exp *-commutative cbrt-unprod
1×pow1/2 div-sub
Counts
4 → 372
Calls
4 calls:
14.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
70.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
65.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
7.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
137.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
73.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify99.0ms

Algorithm
egg-herbie
Counts
384 → 384
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
016266167
150015970

prune850.0ms

Filtered
384 candidates to 219 candidates (57.0%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New3840384
Fresh000
Picked011
Done011
Total3842386

Merged error: 0b

Counts
386 → 2

regimes16.0ms

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
01411
11411

end0.0ms

sample701.0ms

Algorithm
intervals
Results
312.0ms8000×body80valid
198.0ms7849×body80nan