Details

Time bar (total: 5.8s)

sample46.0ms

Algorithm
intervals
Results
14.0ms479×body80nan
10.0ms205×body160nan
7.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

prune2.0ms

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: 30.6b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.0b
(- (* x x) 1.0)
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
28.4b
(sqrt (- (* x x) 1.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1
5×add-exp-log
4×expm1-log1p-u log-prod sqrt-prod add-cbrt-cube log1p-expm1-u
3×fma-def prod-diff
2×log-div flip3-- flip3-+ sqrt-div flip-- flip-+ distribute-lft-out difference-of-squares
1×+-commutative sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log rem-log-exp sum-log log-pow
Counts
4 → 71
Calls
4 calls:
7.0ms
(+ x (sqrt (- (* x x) 1.0)))
5.0ms
(- (* x x) 1.0)
7.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms
(sqrt (- (* x x) 1.0))

series357.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ x (sqrt (- (* x x) 1.0)))
45.0ms
(- (* x x) 1.0)
192.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
56.0ms
(sqrt (- (* x x) 1.0))

simplify51.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0384532
11355471
25001457

prune198.0ms

Filtered
83 candidates to 67 candidates (80.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New81283
Fresh000
Picked011
Done000
Total81384

Merged error: 0.0b

Counts
84 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.0b
(sqrt (- x (sqrt 1.0)))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
22×sqrt-prod
17×*-un-lft-identity
14×sqrt-div
11×add-cube-cbrt
10×pow1
9×associate-*r*
7×add-exp-log associate-*l*
6×add-cbrt-cube add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u frac-times flip3-- flip-- log1p-expm1-u difference-of-squares unswap-sqr
3×log-prod fma-def sqrt-pow1 pow1/2 pow-prod-down
2×log-div associate-*r/ associate-*l/ distribute-lft-out--
1×+-commutative rem-sqrt-square sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 96
Calls
4 calls:
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
9.0ms
(sqrt (- x (sqrt 1.0)))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
14.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series703.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
67.0ms
(sqrt (- x (sqrt 1.0)))
292.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
196.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify52.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05271182
118441066
250011049

prune384.0ms

Filtered
108 candidates to 86 candidates (79.6%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1071108
Fresh101
Picked011
Done011
Total1083111

Merged error: 0.0b

Counts
111 → 3

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
0.2b
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
0.3b
(/ (pow (sqrt 1.0) 4) (pow x 4))
0.6b
(/ (* 1/4 1.0) (pow x 2))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
114×*-un-lft-identity
98×add-sqr-sqrt
87×unpow-prod-down times-frac
82×add-cube-cbrt
48×prod-diff
33×log-pow
31×pow1
29×add-exp-log
24×sqrt-prod distribute-lft-out--
21×sqr-pow
20×associate--l+
16×log-prod
15×div-exp associate-/r*
13×associate--r+
11×add-cbrt-cube associate-/l*
8×pow-to-exp pow-exp difference-of-squares
6×pow-flip fma-neg inv-pow add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log prod-exp div-inv
2×sub-neg frac-2neg clear-num unpow2
1×associate--l- log-div flip3-- flip-- cbrt-unprod fma-udef associate--r-
Counts
4 → 252
Calls
4 calls:
1.0ms
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
14.0ms
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
11.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
6.0ms
(/ (* 1/4 1.0) (pow x 2))

series483.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
156.0ms
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
111.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
25.0ms
(/ (* 1/4 1.0) (pow x 2))

simplify115.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
08293752
133942759
250022659

prune709.0ms

Filtered
264 candidates to 140 candidates (53.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New2631264
Fresh000
Picked101
Done112
Total2652267

Merged error: 0b

Counts
267 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (sqrt 1.0) 4) (pow x 4))
0.5b
(cbrt x)
0.5b
(cbrt x)
0.6b
(/ (* 1/4 1.0) (pow x 2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
87×unpow-prod-down
78×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
29×add-exp-log
24×sqrt-prod
21×sqr-pow
15×div-exp associate-/r*
11×add-cbrt-cube associate-/l*
8×pow-to-exp pow-exp
6×cbrt-prod
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv prod-exp
2×frac-2neg pow1/3 clear-num div-inv unpow2
1×cbrt-unprod
Counts
4 → 172
Calls
4 calls:
12.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
6.0ms
(/ (* 1/4 1.0) (pow x 2))

series493.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
193.0ms
(cbrt x)
172.0ms
(cbrt x)
24.0ms
(/ (* 1/4 1.0) (pow x 2))

simplify59.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04681237
120591041
25001927

prune673.0ms

Filtered
184 candidates to 110 candidates (59.8%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1840184
Fresh000
Picked011
Done011
Total1842186

Merged error: 0b

Counts
186 → 2

regimes14.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample1.3s

Algorithm
intervals
Results
361.0ms16296×body80nan
344.0ms7530×body160nan
226.0ms8000×body80valid