Details

Time bar (total: 12.8s)

sample70.0ms

Algorithm
intervals
Results
38.0ms88×body1280valid
9.0ms42×body640valid
8.0ms27×body2560valid
4.0ms28×body320valid
2.0ms52×body80valid
2.0ms19×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.8b
(+ x (sqrt (+ (* x x) 1.0)))
3.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.6b
(sqrt (+ (* x x) 1.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
7×add-cube-cbrt
6×pow1
5×add-exp-log
4×expm1-log1p-u log-prod fma-def flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow hypot-def
Counts
4 → 66
Calls
4 calls:
3.0ms
(+ (* x x) 1.0)
9.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series321.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* x x) 1.0)
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
182.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0357480
11262435
25002412

prune240.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite97.0ms

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:
74.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series139.0ms

Counts
1 → 3
Calls
1 calls:
138.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify95.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07291769
138381380
250031380

prune408.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
13.6b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
17.8b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite831.0ms

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))
259.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
344.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (- 0.0625) (pow x 5))
43.0ms
(/ 0.125 (pow x 3))
185.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
271.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify410.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0500248078

prune6.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.8b
(+ x (hypot x (sqrt 1.0)))
3.9b
(log (+ x (hypot x (sqrt 1.0))))

rewrite6.0ms

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:
0.0ms
(hypot x (sqrt 1.0))
2.0ms
(+ x (hypot x (sqrt 1.0)))
2.0ms
(log (+ x (hypot x (sqrt 1.0))))

series532.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(hypot x (sqrt 1.0))
129.0ms
(+ x (hypot x (sqrt 1.0)))
296.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify86.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (82.0ms)

IterNodesCost
0268349
1886321
23696305
35001303

prune138.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.0b

bsearch85.0ms

Steps
ItersRangePoint
9
8.455209092704733e-09
0.003064448021395057
0.0008724554249750556
10
-4.508778152722845
-1.8057709034692785e-13
-1.0176898016477431

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample1.9s

Algorithm
intervals
Results
966.0ms2339×body1280valid
375.0ms1551×body640valid
228.0ms785×body2560valid
108.0ms774×body320valid
65.0ms2108×body80valid
35.0ms443×body160valid