Details

Time bar (total: 5.3s)

sample65.0ms

Algorithm
intervals
Results
31.0ms78×body1280valid
14.0ms58×body640valid
5.0ms17×body2560valid
4.0ms27×body320valid
2.0ms68×body80valid
1.0ms8×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune5.0ms

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: 52.2b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
12.7b
(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))

series286.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(+ x (sqrt (+ (* x x) 1.0)))
178.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms
(sqrt (+ (* x x) 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0331422
11127385
25002366

prune168.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New57461
Fresh000
Picked101
Done000
Total58462

Merged error: 0.0b

Counts
62 → 4

localize11.0ms

Local error

Found 1 expressions with local error:

0.2b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite74.0ms

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:
56.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series144.0ms

Counts
1 → 3
Calls
1 calls:
143.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify96.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07291769
138381380
250031380

prune330.0ms

Filtered
275 candidates to 97 candidates (35.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2750275
Fresh033
Picked011
Done000
Total2754279

Merged error: 0.0b

Counts
279 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.7b
(+ 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))))

series523.0ms

Counts
3 → 9
Calls
3 calls:
98.0ms
(hypot x (sqrt 1.0))
134.0ms
(+ x (hypot x (sqrt 1.0)))
290.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify93.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
0268349
1886321
23696305
35001303

prune126.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New52153
Fresh112
Picked011
Done011
Total53457

Merged error: 0.0b

Counts
57 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ x (hypot x (sqrt 1.0)))
0.7b
(+ x (hypot x (sqrt 1.0)))
0.7b
(+ x (hypot x (sqrt 1.0)))
2.2b
(log (* (* (cbrt (+ x (hypot x (sqrt 1.0)))) (cbrt (+ x (hypot x (sqrt 1.0))))) (cbrt (+ x (hypot x (sqrt 1.0))))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×log-div
24×pow1
15×log-pow
14×associate-*l/
13×*-un-lft-identity
10×add-exp-log add-log-exp
9×fma-def pow1/3 pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt
6×pow-plus
5×pow-prod-down
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×+-commutative rem-log-exp prod-exp sum-log pow-sqr distribute-lft-out
2×pow2
1×log-prod pow3
Counts
4 → 105
Calls
4 calls:
3.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(+ x (hypot x (sqrt 1.0)))
16.0ms
(log (* (* (cbrt (+ x (hypot x (sqrt 1.0)))) (cbrt (+ x (hypot x (sqrt 1.0))))) (cbrt (+ x (hypot x (sqrt 1.0))))))

series859.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(+ x (hypot x (sqrt 1.0)))
123.0ms
(+ x (hypot x (sqrt 1.0)))
314.0ms
(+ x (hypot x (sqrt 1.0)))
295.0ms
(log (* (* (cbrt (+ x (hypot x (sqrt 1.0)))) (cbrt (+ x (hypot x (sqrt 1.0))))) (cbrt (+ x (hypot x (sqrt 1.0))))))

simplify97.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
04121734
19961610
235791407
350021292

prune275.0ms

Filtered
117 candidates to 84 candidates (71.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1161117
Fresh011
Picked101
Done022
Total1174121

Merged error: 0.0b

Counts
121 → 4

regimes31.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch81.0ms

Steps
ItersRangePoint
9
2.1846438371975785e-05
719.5386143167987
0.0010880883006274397
10
-43540924890.08803
-0.0051836583041924315
-1.0218652365231677

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample1.9s

Algorithm
intervals
Results
935.0ms2300×body1280valid
396.0ms1686×body640valid
211.0ms796×body2560valid
103.0ms745×body320valid
63.0ms2070×body80valid
36.0ms403×body160valid