Details

Time bar (total: 6.3s)

sample67.0ms

Algorithm
intervals
Results
34.0ms76×body1280valid
13.0ms56×body640valid
7.0ms26×body2560valid
3.0ms21×body320valid
2.0ms68×body80valid
1.0ms9×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 53.8b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ x (sqrt (+ (* x x) 1.0)))
1.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.0b
(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))))
5.0ms
(sqrt (+ (* x x) 1.0))

series267.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
167.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0331422
11127385
25002366

prune182.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New57461
Fresh000
Picked101
Done000
Total58462

Merged error: 0.0b

Counts
62 → 4

localize11.0ms

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)))

rewrite271.0ms

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:
195.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
55.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series285.0ms

Counts
2 → 6
Calls
2 calls:
151.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
133.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify127.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
08882291
147681819
250011795

prune483.0ms

Filtered
306 candidates to 121 candidates (39.5%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New3060306
Fresh033
Picked011
Done000
Total3064310

Merged error: 0.0b

Counts
310 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.6b
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
1.8b
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

rewrite7.0ms

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

series585.0ms

Counts
3 → 9
Calls
3 calls:
105.0ms
(hypot x (sqrt 1.0))
140.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
340.0ms
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

simplify128.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
0288436
11009384
24313367
35001362

prune192.0ms

Filtered
51 candidates to 48 candidates (94.1%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New49251
Fresh202
Picked011
Done011
Total51455

Merged error: 0.0b

Counts
55 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1/8 (pow x 3))
0.4b
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
13.9b
(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)))))
20.9b
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

rewrite56.0ms

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:
5.0ms
(/ 1/8 (pow x 3))
16.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
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)))))
1.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

series368.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ 1/8 (pow x 3))
85.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
181.0ms
(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)))))
62.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

simplify85.0ms

Algorithm
egg-herbie
Counts
467 → 467
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015924240
150014118

prune1.1s

Filtered
467 candidates to 230 candidates (49.3%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New4670467
Fresh011
Picked011
Done022
Total4674471

Merged error: 0.0b

Counts
471 → 4

regimes37.0ms

Accuracy

99.8% (0.1b remaining)

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

bsearch84.0ms

Steps
ItersRangePoint
8
3.88064682879673e-06
0.018000635171863108
0.0008398495868326429
10
-1421.6155834850151
-1.485944467815708e-07
-1.0153027309600835

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05030
15430
25730
35730

end0.0ms

sample1.9s

Algorithm
intervals
Results
956.0ms2342×body1280valid
358.0ms1525×body640valid
232.0ms839×body2560valid
98.0ms731×body320valid
64.0ms2144×body80valid
32.0ms419×body160valid