Details

Time bar (total: 6.4s)

sample73.0ms

Algorithm
intervals
Results
34.0ms72×body1280valid
14.0ms51×body640valid
7.0ms23×body2560valid
5.0ms27×body320valid
4.0ms72×body80valid
1.0ms11×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: 52.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.8b
(+ x (sqrt (+ (* x x) 1.0)))
2.7b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.7b
(sqrt (+ (* x x) 1.0))

rewrite24.0ms

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

series275.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ x (sqrt (+ (* x x) 1.0)))
173.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms
(sqrt (+ (* x x) 1.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331422
11127385
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))))
0.2b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite252.0ms

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:
152.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
79.0ms
(* 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 (97.0ms)

IterNodesCost
08882291
147681819
250011795

prune457.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.8b
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.7b
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
3×pow1 add-exp-log log-prod fma-def
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative rem-log-exp sum-log log-pow
Counts
2 → 32
Calls
2 calls:
2.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.0ms
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

series428.0ms

Counts
2 → 6
Calls
2 calls:
137.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
291.0ms
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

simplify100.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0255366
1909318
23872309
35001304

prune109.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
0.3b
(/ 1/8 (pow x 3))
11.7b
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
18.0b
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
609×times-frac
290×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
207×unpow-prod-down
90×cube-prod
69×sqr-pow
37×associate-/r*
36×add-exp-log
30×cube-mult unpow3
24×div-exp
15×div-inv associate-/l*
11×add-cbrt-cube
8×pow-to-exp pow-exp
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod
2×frac-2neg clear-num
1×rem-log-exp associate-/r/ log-pow fma-udef
Counts
4 → 455
Calls
4 calls:
16.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
5.0ms
(/ 1/8 (pow x 3))
1.0ms
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
0.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
35.0ms
(/ 1/8 (pow x 3))
197.0ms
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
58.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

simplify90.0ms

Algorithm
egg-herbie
Counts
467 → 467
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015924240
150014118

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.2b

bsearch103.0ms

Steps
ItersRangePoint
10
4.8244160186105205e-08
257763.20554958374
0.0010473279622313881
10
-772.3369502403921
-4.163765984402517e-10
-1.024334867874778

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05030
15430
25730
35730

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2336×body1280valid
442.0ms1588×body640valid
255.0ms838×body2560valid
141.0ms760×body320valid
112.0ms2077×body80valid
44.0ms401×body160valid