Details

Time bar (total: 12.1s)

sample65.0ms

Algorithm
intervals
Results
33.0ms77×body1280valid
12.0ms55×body640valid
6.0ms24×body2560valid
3.0ms25×body320valid
2.0ms61×body80valid
1.0ms14×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.3b

localize7.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
3.4b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.3b
(sqrt (+ (* x x) 1.0))

rewrite23.0ms

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:
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series272.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ x (sqrt (+ (* x x) 1.0)))
169.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
48.0ms
(sqrt (+ (* x x) 1.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0331423
11121385
25002366

prune182.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite91.0ms

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:
72.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series144.0ms

Counts
1 → 3
Calls
1 calls:
144.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify90.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07291769
138381380
250031380

prune390.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
10.2b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.0b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite819.0ms

Algorithm
rewrite-expression-head
Rules
2802×times-frac
2496×add-sqr-sqrt
1944×*-un-lft-identity
1522×prod-diff
1510×add-cube-cbrt
965×associate--r+
652×unpow-prod-down
339×distribute-rgt-neg-in
330×difference-of-squares
297×distribute-lft-neg-in
272×sqr-pow
149×cube-prod
134×distribute-lft-out--
104×div-inv
99×neg-mul-1
49×cube-mult unpow3
40×fma-neg
19×associate-/r*
15×add-exp-log
13×associate-/l*
12×log-prod
9×add-log-exp
8×frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 1793
Calls
4 calls:
6.0ms
(/ (- 0.0625) (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
249.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
333.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (- 0.0625) (pow x 5))
42.0ms
(/ 0.125 (pow x 3))
187.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
64.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify430.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500248078

prune6.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
1.2b
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
3.4b
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
4×pow1 add-exp-log
3×expm1-log1p-u log-prod fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+
1×+-commutative hypot-udef rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
0.0ms
(hypot x (sqrt 1.0))
2.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.0ms
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

series533.0ms

Counts
3 → 9
Calls
3 calls:
101.0ms
(hypot x (sqrt 1.0))
131.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
300.0ms
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

simplify109.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
0288436
11009384
24313367
35001362

prune154.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.5b

bsearch70.0ms

Steps
ItersRangePoint
7
0.00013951198456185504
0.004380743253548005
0.0007874651442734054
9
-3.9934486818618
-6.3299436832828755e-06
-1.013888797647559

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample1.8s

Algorithm
intervals
Results
932.0ms2312×body1280valid
353.0ms1527×body640valid
219.0ms809×body2560valid
111.0ms829×body320valid
72.0ms2130×body80valid
30.0ms393×body160valid