Details

Time bar (total: 5.8s)

sample64.0ms

Algorithm
intervals
Results
33.0ms82×body1280valid
9.0ms42×body640valid
7.0ms25×body2560valid
4.0ms29×body320valid
2.0ms64×body80valid
1.0ms14×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: 53.8b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

1.3b
(+ x (sqrt (+ (* x x) 1.0)))
3.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.0b
(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)))
10.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series400.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
301.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0331422
11127385
25002366

prune163.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New55661
Fresh000
Picked101
Done000
Total56662

Merged error: 0.0b

Counts
62 → 6

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
184×add-sqr-sqrt
140×unpow-prod-down cube-prod
126×*-un-lft-identity
120×add-cube-cbrt
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow1 pow-to-exp pow-exp add-log-exp
5×fma-neg prod-diff
4×distribute-lft-out
3×associate-*r/ associate-*l*
2×expm1-log1p-u diff-log log-pow frac-sub cbrt-unprod log1p-expm1-u
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 300
Calls
2 calls:
13.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
53.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series293.0ms

Counts
2 → 6
Calls
2 calls:
157.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
136.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify122.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
08882291
147681819
250011795

prune381.0ms

Filtered
306 candidates to 121 candidates (39.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New3060306
Fresh055
Picked011
Done000
Total3066312

Merged error: 0.0b

Counts
312 → 6

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
1.3b
(+ x (hypot x (sqrt 1.0)))
3.2b
(log (+ x (hypot x (sqrt 1.0))))

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

series502.0ms

Counts
3 → 9
Calls
3 calls:
98.0ms
(hypot x (sqrt 1.0))
128.0ms
(+ x (hypot x (sqrt 1.0)))
276.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify89.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0268349
1886321
23696305
35001303

prune121.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New51253
Fresh224
Picked011
Done011
Total53659

Merged error: 0.0b

Counts
59 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (pow (log (+ x (hypot x (sqrt 1.0)))) 3))
0.2b
(pow (log (+ x (hypot x (sqrt 1.0)))) 3)
1.3b
(+ x (hypot x (sqrt 1.0)))
3.2b
(log (+ x (hypot x (sqrt 1.0))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×cbrt-prod
12×add-sqr-sqrt add-cube-cbrt
10×pow1
8×unpow-prod-down cube-prod
6×add-exp-log add-log-exp
5×log-pow add-cbrt-cube
4×expm1-log1p-u log-prod log1p-expm1-u
3×pow-unpow fma-def
2×cube-mult log-div flip3-+ unpow3 flip-+ distribute-lft-out sqr-pow
1×+-commutative pow-to-exp pow-pow pow1/3 rem-log-exp pow-exp sum-log rem-cbrt-cube rem-cube-cbrt
Counts
4 → 86
Calls
4 calls:
2.0ms
(cbrt (pow (log (+ x (hypot x (sqrt 1.0)))) 3))
2.0ms
(pow (log (+ x (hypot x (sqrt 1.0)))) 3)
4.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(log (+ x (hypot x (sqrt 1.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
287.0ms
(cbrt (pow (log (+ x (hypot x (sqrt 1.0)))) 3))
493.0ms
(pow (log (+ x (hypot x (sqrt 1.0)))) 3)
123.0ms
(+ x (hypot x (sqrt 1.0)))
283.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify73.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0672918
13210864
25002853

prune213.0ms

Filtered
98 candidates to 63 candidates (64.3%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New97198
Fresh123
Picked011
Done022
Total986104

Merged error: 0.0b

Counts
104 → 6

regimes38.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch72.0ms

Steps
ItersRangePoint
8
2.0999504916654036e-06
0.011261476250181132
0.0007621891009820894
9
-3.7752751361666412
-2.6386627092684764e-08
-1.007464588653423

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample1.9s

Algorithm
intervals
Results
952.0ms2342×body1280valid
363.0ms1545×body640valid
219.0ms805×body2560valid
112.0ms838×body320valid
69.0ms2079×body80valid
30.0ms391×body160valid