Details

Time bar (total: 15.1s)

sample100.0ms

Algorithm
intervals
Results
46.0ms72×body1280valid
23.0ms68×body640valid
9.0ms21×body2560valid
6.0ms26×body320valid
3.0ms53×body80valid
2.0ms16×body160valid

simplify5.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.1b

localize7.0ms

Local error

Found 3 expressions with local error:

1.4b
(+ x (sqrt (+ (* x x) 1.0)))
3.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
11.2b
(sqrt (+ (* x x) 1.0))

rewrite23.0ms

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:
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series272.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
167.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms
(sqrt (+ (* x x) 1.0))

simplify32.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0331422
11127385
25002366

prune226.0ms

Filtered
61 candidates to 55 candidates (90.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

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

rewrite243.0ms

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:
145.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
77.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series305.0ms

Counts
2 → 6
Calls
2 calls:
162.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
142.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify126.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
08882291
147681819
250011795

prune444.0ms

Filtered
306 candidates to 121 candidates (39.5%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
16.7b
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
16.7b
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
16.7b
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

rewrite549.0ms

Algorithm
rewrite-expression-head
Rules
52×cbrt-div
30×associate-*r/
26×frac-sub
25×cbrt-prod
23×add-sqr-sqrt
16×frac-times
15×add-cube-cbrt *-un-lft-identity
13×flip3-- flip3-+ flip-- flip-+
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u associate-*l/ add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 117
Calls
4 calls:
392.0ms
(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
50.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
50.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
51.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
530.0ms
(* (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))) (cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))))
463.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
473.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))
449.0ms
(cbrt (- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))))

simplify94.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05724561
126874380
250024225

prune521.0ms

Filtered
129 candidates to 101 candidates (78.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
14.6b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.0b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite858.0ms

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))
5.0ms
(/ 0.125 (pow x 3))
265.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
352.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ (- 0.0625) (pow x 5))
35.0ms
(/ 0.125 (pow x 3))
184.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
63.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify431.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0500248078

prune6.6s

Filtered
1805 candidates to 1216 candidates (67.4%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.7b

bsearch84.0ms

Steps
ItersRangePoint
10
7.712829756242493e-08
8770343.893451896
0.0012127302794364438
9
-1827977.1926269082
-0.00043085380315138777
-1.0384538355180963

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample1.8s

Algorithm
intervals
Results
953.0ms2382×body1280valid
358.0ms1513×body640valid
195.0ms730×body2560valid
103.0ms769×body320valid
67.0ms2212×body80valid
30.0ms394×body160valid