Details

Time bar (total: 8.3s)

sample86.0ms

Algorithm
intervals
Results
44.0ms78×body1280valid
17.0ms55×body640valid
6.0ms15×body2560valid
6.0ms27×body320valid
4.0ms64×body80valid
2.0ms17×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.2b

localize7.0ms

Local error

Found 3 expressions with local error:

1.3b
(+ x (sqrt (+ (* x x) 1.0)))
3.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.5b
(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:
9.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series273.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
167.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0331422
11127385
25002366

prune180.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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)))

rewrite242.0ms

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:
144.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
76.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series296.0ms

Counts
2 → 6
Calls
2 calls:
158.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
137.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify126.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
08882291
147681819
250011795

prune463.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
0.1b
(* (- 1/36) (pow (/ x (sqrt 1.0)) 6))
15.6b
(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
36.2b
(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity times-frac
26×associate-*r*
25×unpow-prod-down
14×add-exp-log
10×associate-*l* sqrt-prod
8×add-cbrt-cube
6×add-log-exp
5×unswap-sqr
4×pow1 expm1-log1p-u prod-exp log1p-expm1-u
3×distribute-lft-neg-in distribute-rgt-neg-in associate-/r* associate-/l*
2×associate-+r+ flip3-+ div-exp pow-exp flip-+ div-inv associate-/l/ sqr-pow
1×cbrt-undiv +-commutative distribute-lft-neg-out distribute-rgt-in pow-to-exp neg-mul-1 fma-def frac-2neg distribute-lft-in clear-num sum-log *-commutative cbrt-unprod fma-udef
Counts
4 → 114
Calls
4 calls:
0.0ms
(fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
28.0ms
(* (- 1/36) (pow (/ x (sqrt 1.0)) 6))
14.0ms
(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
43.0ms
(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
144.0ms
(fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
176.0ms
(* (- 1/36) (pow (/ x (sqrt 1.0)) 6))
286.0ms
(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
478.0ms
(/ (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))) (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

simplify86.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05762289
125012078
250012052

prune443.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

1.8b
(exp (log (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))))
14.1b
(/ (exp (log (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))) (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
14.6b
(log (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))
15.6b
(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×log-prod times-frac
15×exp-sum
6×pow1 add-exp-log log-div add-cbrt-cube associate-/l* add-log-exp
4×expm1-log1p-u exp-prod flip3-+ exp-diff flip-+ log1p-expm1-u
3×associate-/r*
2×associate-+r+ log-pow associate-/l/
1×cbrt-undiv +-commutative distribute-rgt-in fma-def frac-2neg distribute-lft-in div-exp rem-log-exp clear-num sum-log div-inv rem-exp-log
Counts
4 → 94
Calls
4 calls:
9.0ms
(exp (log (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))))
25.0ms
(/ (exp (log (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))) (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
8.0ms
(log (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))
15.0ms
(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
297.0ms
(exp (log (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))))
486.0ms
(/ (exp (log (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))) (fma (pow (/ x (sqrt 1.0)) 3) 1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
530.0ms
(log (+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))))
297.0ms
(+ (* (- 1/36) (pow (/ x (sqrt 1.0)) 6)) (* (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04543512
118363183
250023014

prune413.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.1b

bsearch84.0ms

Steps
ItersRangePoint
10
2.1112891761060846e-05
363928.4733812492
0.0008366604278243518
7
-14.579906112121636
-0.10438916540540782
-0.9974553788798113

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.2s2304×body1280valid
511.0ms1573×body640valid
335.0ms835×body2560valid
156.0ms781×body320valid
119.0ms2104×body80valid
50.0ms403×body160valid