Details

Time bar (total: 5.7s)

sample98.0ms

Algorithm
intervals
Results
41.0ms60×body1280valid
23.0ms56×body640valid
10.0ms22×body2560valid
6.0ms28×body320valid
4.0ms75×body80valid
2.0ms15×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune3.0ms

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: 49.7b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
2.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
12.3b
(sqrt (+ (* x x) 1.0))

rewrite21.0ms

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:
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
8.0ms
(sqrt (+ (* x x) 1.0))

series269.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(+ x (sqrt (+ (* x x) 1.0)))
168.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify32.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0331422
11127385
25002366

prune175.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New58361
Fresh000
Picked101
Done000
Total59362

Merged error: 0b

Counts
62 → 3

localize15.0ms

Local error

Found 1 expressions with local error:

0.3b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite76.0ms

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:
53.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series135.0ms

Counts
1 → 3
Calls
1 calls:
135.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify96.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07291769
138381380
250031380

prune367.0ms

Filtered
275 candidates to 97 candidates (35.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2750275
Fresh022
Picked011
Done000
Total2753278

Merged error: 0b

Counts
278 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b
(+ (hypot x (sqrt 1.0)) x)
2.8b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt log-prod add-log-exp
3×pow1 add-exp-log fma-def
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×+-commutative rem-log-exp sum-log log-pow
Counts
2 → 34
Calls
2 calls:
3.0ms
(+ (hypot x (sqrt 1.0)) x)
3.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series542.0ms

Counts
2 → 6
Calls
2 calls:
129.0ms
(+ (hypot x (sqrt 1.0)) x)
413.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify90.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0238286
1790257
23276249
35001245

prune114.0ms

Filtered
40 candidates to 33 candidates (82.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New39140
Fresh101
Picked011
Done011
Total40343

Merged error: 0b

Counts
43 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
0.5b
(/ 1/8 (pow x 3))
12.6b
(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)))))
17.8b
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

rewrite60.0ms

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))
5.0ms
(/ 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)))))
1.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
40.0ms
(/ 1/8 (pow x 3))
183.0ms
(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)))))
82.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

simplify86.0ms

Algorithm
egg-herbie
Counts
467 → 467
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015924240
150014118

prune1.1s

Filtered
467 candidates to 230 candidates (49.3%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New4670467
Fresh000
Picked011
Done022
Total4673470

Merged error: 0b

Counts
470 → 3

regimes27.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.5b

bsearch90.0ms

Steps
ItersRangePoint
8
2.0262054515877825e-05
0.3235305135594418
0.0010048358779444152
10
-85019.06990604498
-4.503960361653909e-11
-1.0167321160990819

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04428
14828
25128
35128

end0.0ms

sample1.9s

Algorithm
intervals
Results
983.0ms2346×body1280valid
372.0ms1551×body640valid
227.0ms802×body2560valid
108.0ms770×body320valid
65.0ms2096×body80valid
35.0ms435×body160valid