Details

Time bar (total: 12.2s)

sample65.0ms

Algorithm
intervals
Results
32.0ms78×body1280valid
12.0ms52×body640valid
6.0ms24×body2560valid
4.0ms26×body320valid
2.0ms64×body80valid
1.0ms12×body160valid

simplify6.0ms

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: 53.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ x (sqrt (+ (* x x) 1.0)))
2.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.9b
(sqrt (+ (* x x) 1.0))

rewrite45.0ms

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:
17.0ms
(+ x (sqrt (+ (* x x) 1.0)))
17.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms
(sqrt (+ (* x x) 1.0))

series238.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(+ x (sqrt (+ (* x x) 1.0)))
151.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
40.0ms
(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0331422
11127385
25002366

prune186.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite110.0ms

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:
87.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series124.0ms

Counts
1 → 3
Calls
1 calls:
124.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify94.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07291769
138381380
250031380

prune381.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.3b
(+ (hypot x (sqrt 1.0)) x)
2.8b
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×add-exp-log
5×pow1 *-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt fma-def rem-log-exp
2×expm1-log1p-u log-div flip3-+ associate-*r/ prod-exp log-pow add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative log-prod 1-exp pow-prod-down sum-log distribute-lft-out
Counts
2 → 34
Calls
2 calls:
5.0ms
(+ (hypot x (sqrt 1.0)) x)
10.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

series375.0ms

Counts
2 → 6
Calls
2 calls:
118.0ms
(+ (hypot x (sqrt 1.0)) x)
256.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

simplify125.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (121.0ms)

IterNodesCost
0258271
11000244
24895235
35001234

prune153.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 0.0625) (pow x 5))
0.6b
(/ 0.125 (pow x 3))
10.0b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
18.4b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite935.0ms

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:
11.0ms
(/ (- 0.0625) (pow x 5))
8.0ms
(/ 0.125 (pow x 3))
300.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
397.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (- 0.0625) (pow x 5))
32.0ms
(/ 0.125 (pow x 3))
177.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
48.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify420.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500248078

prune6.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes23.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.0b

bsearch85.0ms

Steps
ItersRangePoint
10
8.950540206577903e-05
66689094922.78456
0.0010409337121578906
10
-1500.694570789724
-6.177030851099824e-09
-0.9991699645395472

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14625
24625

end0.0ms

sample2.0s

Algorithm
intervals
Results
973.0ms2373×body1280valid
395.0ms1600×body640valid
223.0ms802×body2560valid
101.0ms728×body320valid
68.0ms2109×body80valid
32.0ms388×body160valid