Details

Time bar (total: 11.7s)

sample77.0ms

Algorithm
intervals
Results
42.0ms92×body1280valid
12.0ms43×body640valid
7.0ms22×body2560valid
4.0ms26×body320valid
3.0ms62×body80valid
1.0ms11×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 54.3b

Counts
2 → 1

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.4b
(+ x (sqrt (+ (* x x) 1.0)))
2.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.7b
(sqrt (+ (* x x) 1.0))

rewrite23.0ms

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:
6.0ms
(+ (* x x) 1.0)
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
5.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series318.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* x x) 1.0)
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
171.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
59.0ms
(sqrt (+ (* x x) 1.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0357480
11262435
25002412

prune192.0ms

Filtered
78 candidates to 68 candidates (87.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New73578
Fresh000
Picked101
Done000
Total74579

Merged error: 0.0b

Counts
79 → 5

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)))

rewrite85.0ms

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:
16.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
50.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series278.0ms

Counts
2 → 6
Calls
2 calls:
147.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
132.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify118.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08882291
147681819
250011795

prune380.0ms

Filtered
306 candidates to 121 candidates (39.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3060306
Fresh044
Picked011
Done000
Total3065311

Merged error: 0.0b

Counts
311 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

0.4b
(+ x (hypot x (sqrt 1.0)))
2.5b
(log (+ x (hypot x (sqrt 1.0))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt log-prod add-log-exp
3×pow1 add-exp-log fma-def
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×+-commutative rem-log-exp sum-log log-pow
Counts
2 → 34
Calls
2 calls:
3.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(log (+ x (hypot x (sqrt 1.0))))

series407.0ms

Counts
2 → 6
Calls
2 calls:
122.0ms
(+ x (hypot x (sqrt 1.0)))
284.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify78.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0238284
1786255
23259247
35001245

prune88.0ms

Filtered
40 candidates to 33 candidates (82.5%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New40040
Fresh033
Picked011
Done011
Total40545

Merged error: 0.0b

Counts
45 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.3b
(/ 0.125 (pow x 3))
14.1b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.8b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite490.0ms

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:
7.0ms
(/ (- 0.0625) (pow x 5))
6.0ms
(/ 0.125 (pow x 3))
98.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
161.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (- 0.0625) (pow x 5))
34.0ms
(/ 0.125 (pow x 3))
177.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
52.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify446.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0500248078

prune6.0s

Filtered
1805 candidates to 1216 candidates (67.4%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New180501805
Fresh022
Picked011
Done022
Total180551810

Merged error: 0.0b

Counts
1810 → 5

regimes34.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.5b

bsearch74.0ms

Steps
ItersRangePoint
8
6.042829624826513e-05
0.09081442282169057
0.0009213882467486935
8
-6.238959787773506
-0.00010711273713490883
-0.9988164544060855

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2303×body1280valid
434.0ms1547×body640valid
273.0ms816×body2560valid
134.0ms767×body320valid
89.0ms2152×body80valid
41.0ms415×body160valid

Profiling

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