Details

Time bar (total: 5.5s)

sample67.0ms

Algorithm
intervals
Results
31.0ms68×body1280valid
12.0ms46×body640valid
10.0ms35×body2560valid
3.0ms23×body320valid
2.0ms72×body80valid
1.0ms12×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
2.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.6b
(sqrt (+ (* x x) 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u fma-def flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow hypot-def
Counts
3 → 52
Calls
3 calls:
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series258.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ x (sqrt (+ (* x x) 1.0)))
159.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms
(sqrt (+ (* x x) 1.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0331422
11127385
25002366

prune164.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv expm1-log1p-u associate-*r/ pow-prod-down *-commutative log1p-expm1-u div-inv add-log-exp
Counts
1 → 272
Calls
1 calls:
71.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series131.0ms

Counts
1 → 3
Calls
1 calls:
131.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify89.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07291769
138381380
250031380

prune357.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.5b
(+ (hypot x (sqrt 1.0)) x)
2.5b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 add-exp-log log-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef rem-log-exp sum-log log-pow
Counts
3 → 44
Calls
3 calls:
0.0ms
(hypot x (sqrt 1.0))
2.0ms
(+ (hypot x (sqrt 1.0)) x)
2.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series489.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(hypot x (sqrt 1.0))
128.0ms
(+ (hypot x (sqrt 1.0)) x)
267.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify87.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (82.0ms)

IterNodesCost
0268351
1890323
23710307
35001303

prune133.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
0.1b
(/ 1/8 (pow x 3))
15.1b
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
20.4b
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
609×times-frac
290×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
207×unpow-prod-down
90×cube-prod
69×sqr-pow
37×associate-/r*
36×add-exp-log
30×cube-mult unpow3
24×div-exp
15×div-inv associate-/l*
11×add-cbrt-cube
8×pow-to-exp pow-exp
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod
2×frac-2neg clear-num
1×rem-log-exp associate-/r/ log-pow fma-udef
Counts
4 → 455
Calls
4 calls:
18.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
4.0ms
(/ 1/8 (pow x 3))
1.0ms
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
0.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

series363.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
39.0ms
(/ 1/8 (pow x 3))
178.0ms
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
62.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

simplify84.0ms

Algorithm
egg-herbie
Counts
467 → 467
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015924240
150014118

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.2b

bsearch90.0ms

Steps
ItersRangePoint
10
4.127477794865454e-14
0.2287861600326909
0.0009302221890111671
10
-578421416.8415484
-0.03925098124715615
-1.0286748310635179

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04428
14828
25128
35128

end0.0ms

sample1.9s

Algorithm
intervals
Results
931.0ms2301×body1280valid
377.0ms1608×body640valid
230.0ms837×body2560valid
102.0ms750×body320valid
65.0ms2109×body80valid
30.0ms395×body160valid