Details

Time bar (total: 5.9s)

sample69.0ms

Algorithm
intervals
Results
34.0ms76×body1280valid
14.0ms50×body640valid
7.0ms24×body2560valid
3.0ms21×body320valid
2.0ms77×body80valid
1.0ms8×body160valid

simplify4.0ms

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: 49.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ x (sqrt (+ (* x x) 1.0)))
1.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.3b
(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))

series275.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(+ x (sqrt (+ (* x x) 1.0)))
176.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331423
11121385
25002366

prune183.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

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)))

rewrite91.0ms

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))))
56.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series305.0ms

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))))
145.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify118.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08882291
147681819
250011795

prune453.0ms

Pruning

4 alts after pruning (3 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)
1.6b
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

rewrite9.0ms

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:
3.0ms
(+ (hypot x (sqrt 1.0)) x)
5.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

series416.0ms

Counts
2 → 6
Calls
2 calls:
129.0ms
(+ (hypot x (sqrt 1.0)) x)
287.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

simplify126.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (122.0ms)

IterNodesCost
0258271
11000244
24895235
35001234

prune108.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (* 1.0 1.0) 1/8) (pow x 3))
0.1b
(/ (pow (sqrt 1.0) 6) (pow x 5))
12.6b
(log (* 1 (- (/ (* (* 1.0 1.0) 1/8) (pow x 3)) (- (* 1/16 (/ (pow (sqrt 1.0) 6) (pow x 5))) (* (- 1/2) (/ 1.0 x))))))
21.2b
(- (/ (* (* 1.0 1.0) 1/8) (pow x 3)) (- (* 1/16 (/ (pow (sqrt 1.0) 6) (pow x 5))) (* (- 1/2) (/ 1.0 x))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
130×times-frac
99×unpow-prod-down
90×add-sqr-sqrt *-un-lft-identity
88×add-cube-cbrt
49×prod-diff
44×add-exp-log
25×sqr-pow
24×sqrt-prod
19×associate-/r*
18×cube-prod div-exp
16×fma-neg
15×add-cbrt-cube
11×prod-exp associate-/l*
9×pow-to-exp associate-*r/ pow-exp add-log-exp
8×frac-sub
7×pow1
6×cube-mult unpow3 div-inv
5×log-div
4×cbrt-undiv expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log rem-log-exp cbrt-unprod associate--r+
2×sub-neg frac-2neg clear-num log-pow
1×log-prod 1-exp pow-prod-down distribute-lft-out-- associate--r- difference-of-squares
Counts
4 → 266
Calls
4 calls:
9.0ms
(/ (* (* 1.0 1.0) 1/8) (pow x 3))
8.0ms
(/ (pow (sqrt 1.0) 6) (pow x 5))
27.0ms
(log (* 1 (- (/ (* (* 1.0 1.0) 1/8) (pow x 3)) (- (* 1/16 (/ (pow (sqrt 1.0) 6) (pow x 5))) (* (- 1/2) (/ 1.0 x))))))
30.0ms
(- (/ (* (* 1.0 1.0) 1/8) (pow x 3)) (- (* 1/16 (/ (pow (sqrt 1.0) 6) (pow x 5))) (* (- 1/2) (/ 1.0 x))))

series606.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (* (* 1.0 1.0) 1/8) (pow x 3))
142.0ms
(/ (pow (sqrt 1.0) 6) (pow x 5))
297.0ms
(log (* 1 (- (/ (* (* 1.0 1.0) 1/8) (pow x 3)) (- (* 1/16 (/ (pow (sqrt 1.0) 6) (pow x 5))) (* (- 1/2) (/ 1.0 x))))))
124.0ms
(- (/ (* (* 1.0 1.0) 1/8) (pow x 3)) (- (* 1/16 (/ (pow (sqrt 1.0) 6) (pow x 5))) (* (- 1/2) (/ 1.0 x))))

simplify72.0ms

Algorithm
egg-herbie
Counts
278 → 278
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010915447
150023668

prune819.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes31.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch100.0ms

Steps
ItersRangePoint
10
1.4316099847845607e-10
21.660028671588154
0.000930940902558544
9
-8.718619127186496
-1.4100946153605287e-08
-1.0389449137501827

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05532
16332
26632
36632

end0.0ms

sample1.9s

Algorithm
intervals
Results
962.0ms2355×body1280valid
373.0ms1555×body640valid
233.0ms819×body2560valid
108.0ms784×body320valid
65.0ms2073×body80valid
33.0ms414×body160valid