Details

Time bar (total: 5.8s)

sample67.0ms

Algorithm
intervals
Results
33.0ms78×body1280valid
13.0ms52×body640valid
8.0ms27×body2560valid
3.0ms22×body320valid
2.0ms66×body80valid
1.0ms11×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.2b

localize7.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
2.3b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.9b
(sqrt (+ (* x x) 1.0))

rewrite22.0ms

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))

series290.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(+ x (sqrt (+ (* x x) 1.0)))
177.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
49.0ms
(sqrt (+ (* x x) 1.0))

simplify38.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0331422
11127385
25002366

prune195.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite95.0ms

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:
72.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series144.0ms

Counts
1 → 3
Calls
1 calls:
144.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify102.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07291769
138381380
250031380

prune400.0ms

Filtered
275 candidates to 97 candidates (35.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
1.2b
(+ (hypot x (sqrt 1.0)) x)
2.3b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite7.0ms

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))
3.0ms
(+ (hypot x (sqrt 1.0)) x)
3.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series540.0ms

Counts
3 → 9
Calls
3 calls:
109.0ms
(hypot x (sqrt 1.0))
134.0ms
(+ (hypot x (sqrt 1.0)) x)
298.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify89.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0268351
1890323
23710307
35001303

prune143.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
0.3b
(/ 1/8 (pow x 3))
11.4b
(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)))))
20.3b
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

rewrite52.0ms

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:
19.0ms
(/ (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))))

series390.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
42.0ms
(/ 1/8 (pow x 3))
193.0ms
(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)))))
66.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

simplify79.0ms

Algorithm
egg-herbie
Counts
467 → 467
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015924377
150014248

prune1.1s

Filtered
467 candidates to 230 candidates (49.3%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.6b

bsearch91.0ms

Steps
ItersRangePoint
9
7.206039552426127e-07
5.540917366542361
0.0007742239074440529
10
-204248214.92732975
-1.534026600097144e-05
-1.0052763768310868

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04643
15043
25343
35343

end0.0ms

sample1.9s

Algorithm
intervals
Results
963.0ms2360×body1280valid
385.0ms1620×body640valid
209.0ms776×body2560valid
105.0ms781×body320valid
71.0ms2058×body80valid
32.0ms405×body160valid