Details

Time bar (total: 5.5s)

sample74.0ms

Algorithm
intervals
Results
39.0ms83×body1280valid
12.0ms45×body640valid
7.0ms23×body2560valid
4.0ms23×body320valid
3.0ms66×body80valid
1.0ms16×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

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: 52.0b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

1.6b
(+ x (sqrt (+ (* x x) 1.0)))
2.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.0b
(sqrt (+ (* x x) 1.0))

rewrite17.0ms

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))))
4.0ms
(sqrt (+ (* x x) 1.0))

series267.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
164.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms
(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331422
11127385
25002366

prune157.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New56561
Fresh000
Picked101
Done000
Total57562

Merged error: 0.0b

Counts
62 → 5

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite72.0ms

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:
55.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series136.0ms

Counts
1 → 3
Calls
1 calls:
136.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify91.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07291769
138381380
250031380

prune322.0ms

Filtered
275 candidates to 97 candidates (35.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2750275
Fresh044
Picked011
Done000
Total2755280

Merged error: 0.0b

Counts
280 → 5

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
1.6b
(+ x (hypot x (sqrt 1.0)))
2.2b
(log (+ x (hypot x (sqrt 1.0))))

rewrite8.0ms

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

series514.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(hypot x (sqrt 1.0))
126.0ms
(+ x (hypot x (sqrt 1.0)))
285.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify90.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0268349
1886321
23696305
35001303

prune120.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New51253
Fresh213
Picked101
Done011
Total54458

Merged error: 0.0b

Counts
58 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ x (hypot x (sqrt 1.0)))
1.6b
(+ x (hypot x (sqrt 1.0)))
2.3b
(log (sqrt (+ x (hypot x (sqrt 1.0)))))
2.3b
(log (sqrt (+ x (hypot x (sqrt 1.0)))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×log-prod
10×add-sqr-sqrt add-cube-cbrt
8×pow1 sqrt-prod add-log-exp
6×add-exp-log fma-def log-pow
4×expm1-log1p-u log-div flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
2×+-commutative sqrt-pow1 pow1/2 rem-log-exp sum-log
Counts
4 → 78
Calls
4 calls:
3.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(+ x (hypot x (sqrt 1.0)))
4.0ms
(log (sqrt (+ x (hypot x (sqrt 1.0)))))
4.0ms
(log (sqrt (+ x (hypot x (sqrt 1.0)))))

series856.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(+ x (hypot x (sqrt 1.0)))
134.0ms
(+ x (hypot x (sqrt 1.0)))
303.0ms
(log (sqrt (+ x (hypot x (sqrt 1.0)))))
294.0ms
(log (sqrt (+ x (hypot x (sqrt 1.0)))))

simplify105.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0285724
1883658
23992630
35001624

prune252.0ms

Filtered
90 candidates to 76 candidates (84.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New88290
Fresh112
Picked101
Done011
Total90494

Merged error: 0.0b

Counts
94 → 4

regimes31.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch85.0ms

Steps
ItersRangePoint
8
3.410959855244386e-06
0.006602375602419948
0.0012124443990565803
10
-7888799.454350161
-0.0014566459989916651
-1.0280831420371905

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04539
14539

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2384×body1280valid
428.0ms1570×body640valid
260.0ms777×body2560valid
135.0ms810×body320valid
93.0ms2094×body80valid
38.0ms365×body160valid