Details

Time bar (total: 15.4s)

sample298.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
8.0ms265×body80nan

simplify11.0ms

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

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

rewrite31.0ms

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)))
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
15.0ms
(/ (- 1.0 x) (+ 1.0 x))

series153.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
55.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify40.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0370779
11128734
25001719

prune244.0ms

Filtered
106 candidates to 76 candidates (71.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
670×sqrt-prod
586×*-un-lft-identity
528×times-frac
514×add-sqr-sqrt
228×add-cube-cbrt
138×swap-sqr
82×distribute-lft-out
74×distribute-lft-out--
62×associate-*r* associate-*l*
52×difference-of-squares
25×unswap-sqr
20×add-exp-log add-cbrt-cube
16×sqrt-div associate-/l*
14×associate-/r*
12×associate-/r/
11×pow1
6×cbrt-undiv sqrt-undiv flip3-+ div-exp flip-+ div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u associate-/l/ add-log-exp
2×flip3-- frac-2neg clear-num flip--
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ pow-prod-down associate-*l/ rem-square-sqrt pow-sqr *-commutative pow-prod-up
Counts
4 → 504
Calls
4 calls:
110.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
15.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
13.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
0.0ms
(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))

series221.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
88.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
95.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
2.0ms
(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))

simplify145.0ms

Algorithm
egg-herbie
Counts
516 → 516
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
09517951
148696800
250016798

prune827.0ms

Filtered
516 candidates to 201 candidates (39.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
3407×sqrt-prod
2861×times-frac
2081×*-un-lft-identity
1970×add-sqr-sqrt
1125×add-cube-cbrt
626×associate-*l*
310×distribute-lft-out
168×distribute-lft-out-- difference-of-squares
112×unswap-sqr
86×associate-*r*
70×associate-/l*
60×sqrt-div
50×associate-/r/
32×add-exp-log add-cbrt-cube
25×flip3-+ flip-+ div-inv
20×associate-/r*
13×cbrt-undiv div-exp
6×pow1 sqrt-undiv prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l/
2×frac-2neg clear-num
1×frac-times flip3-- sqrt-unprod associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 1689
Calls
4 calls:
20.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))
0.0ms
(atan (sqrt (* (/ (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))))))
776.0ms
(* (/ (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))))
45.0ms
(/ (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series573.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))
3.0ms
(atan (sqrt (* (/ (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))))))
35.0ms
(* (/ (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))))
287.0ms
(/ (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify294.0ms

Algorithm
egg-herbie
Counts
1701 → 1701
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0268233240
1500131178

prune2.9s

Filtered
1701 candidates to 554 candidates (32.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
3707×sqrt-prod
2394×times-frac
2021×add-sqr-sqrt
1343×*-un-lft-identity
873×add-cube-cbrt
813×associate-*l*
243×difference-of-squares
196×associate-*r*
189×unswap-sqr
139×distribute-lft-out--
96×distribute-lft-out
94×add-exp-log add-cbrt-cube
56×sqrt-div
36×cbrt-undiv div-exp associate-/r/
32×prod-exp cbrt-unprod
23×associate-/r*
18×div-inv
16×associate-/l*
15×flip3-- flip--
11×pow1
9×sqrt-undiv
6×frac-times associate-*l/
5×flip3-+ flip-+
4×expm1-log1p-u associate-*r/ pow-prod-down log1p-expm1-u associate-/l/ add-log-exp
3×sqrt-unprod
2×frac-2neg clear-num *-commutative
Counts
4 → 1534
Calls
4 calls:
14.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))
17.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (sqrt (+ 1.0 x)))))
350.0ms
(* (* (/ (/ (sqrt (- 1.0 x)) (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (sqrt (sqrt (+ 1.0 x))))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (sqrt (+ 1.0 x)))))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))))
1.2s
(* (/ (/ (sqrt (- 1.0 x)) (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (sqrt (sqrt (+ 1.0 x))))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (sqrt (+ 1.0 x))))))

series881.0ms

Counts
4 → 12
Calls
4 calls:
257.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x))))
256.0ms
(/ (sqrt (- 1.0 x)) (sqrt (sqrt (sqrt (+ 1.0 x)))))
130.0ms
(* (* (/ (/ (sqrt (- 1.0 x)) (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (sqrt (sqrt (+ 1.0 x))))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (sqrt (+ 1.0 x)))))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (+ 1.0 x)))))
238.0ms
(* (/ (/ (sqrt (- 1.0 x)) (sqrt (- (* 1.0 1.0) (* x x)))) (sqrt (sqrt (sqrt (+ 1.0 x))))) (/ (sqrt (- 1.0 x)) (sqrt (sqrt (sqrt (+ 1.0 x))))))

simplify321.0ms

Algorithm
egg-herbie
Counts
1546 → 1546
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0322237912
1500237071

prune4.7s

Filtered
1546 candidates to 685 candidates (44.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03554
13554

end0.0ms

sample690.0ms

Algorithm
intervals
Results
308.0ms8000×body80valid
194.0ms7740×body80nan