Details

Time bar (total: 5.5s)

sample61.0ms

Algorithm
intervals
Results
26.0ms61×body1280valid
12.0ms49×body640valid
9.0ms32×body2560valid
3.0ms22×body320valid
2.0ms73×body80valid
1.0ms19×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize7.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
4.0b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.1b
(sqrt (+ (* x x) 1.0))

rewrite18.0ms

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))

series281.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
173.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
48.0ms
(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331422
11127385
25002366

prune194.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

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)))

rewrite94.0ms

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:
14.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
55.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series295.0ms

Counts
2 → 6
Calls
2 calls:
160.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
135.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify127.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
08882291
147681819
250011795

prune467.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
1.0b
(+ (hypot x (sqrt 1.0)) x)
4.0b
(log (+ (hypot x (sqrt 1.0)) x))

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

series702.0ms

Counts
3 → 9
Calls
3 calls:
96.0ms
(hypot x (sqrt 1.0))
130.0ms
(+ (hypot x (sqrt 1.0)) x)
476.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify90.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0268351
1890323
23710307
35001303

prune143.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (hypot x (sqrt 1.0)))
0.0b
(sqrt (hypot x (sqrt 1.0)))
4.0b
(log (fma (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))) x))
15.7b
(fma (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))) x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-prod
5×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×log-prod
2×rem-sqrt-square sqrt-pow1 pow1/2
1×rem-log-exp log-pow fma-udef
Counts
4 → 54
Calls
4 calls:
2.0ms
(sqrt (hypot x (sqrt 1.0)))
1.0ms
(sqrt (hypot x (sqrt 1.0)))
1.0ms
(log (fma (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))) x))
1.0ms
(fma (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))) x)

series677.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(sqrt (hypot x (sqrt 1.0)))
111.0ms
(sqrt (hypot x (sqrt 1.0)))
263.0ms
(log (fma (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))) x))
187.0ms
(fma (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))) x)

simplify85.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0219545
1646477
22875438
35003434

prune174.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes40.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.1b

bsearch85.0ms

Steps
ItersRangePoint
10
9.558161037350472e-13
0.8818080259852756
0.0011756572267579168
9
-1052513.600169936
-0.041603525395973645
-1.0296783040954165

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04434
14434

end0.0ms

sample1.9s

Algorithm
intervals
Results
958.0ms2307×body1280valid
362.0ms1538×body640valid
218.0ms801×body2560valid
111.0ms797×body320valid
65.0ms2130×body80valid
33.0ms427×body160valid