Details

Time bar (total: 5.6s)

sample71.0ms

Algorithm
intervals
Results
40.0ms84×body1280valid
8.0ms29×body2560valid
8.0ms34×body640valid
4.0ms32×body320valid
2.0ms69×body80valid
1.0ms8×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: 51.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.8b
(+ x (sqrt (+ (* x x) 1.0)))
1.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.9b
(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))))
4.0ms
(sqrt (+ (* x x) 1.0))

series281.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
175.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
48.0ms
(sqrt (+ (* x x) 1.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331422
11127385
25002366

prune194.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

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))))
0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite91.0ms

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:
15.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
57.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series302.0ms

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))))
142.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify122.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
08882291
147681819
250011795

prune466.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.8b
(+ 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)))))

series514.0ms

Counts
3 → 9
Calls
3 calls:
101.0ms
(hypot x (sqrt 1.0))
129.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
284.0ms
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

simplify106.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0288436
11009384
24313367
35001362

prune152.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
0.8b
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
0.8b
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
1.3b
(log (* (* (cbrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0))))) (cbrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))) (cbrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×log-div
24×pow1
15×log-pow
14×associate-*l/
10×add-exp-log add-log-exp
9×fma-def pow1/3 pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×+-commutative rem-log-exp prod-exp sum-log pow-sqr
2×pow2
1×log-prod pow3
Counts
4 → 102
Calls
4 calls:
3.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
3.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
3.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
14.0ms
(log (* (* (cbrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0))))) (cbrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))) (cbrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))))

series703.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
130.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
137.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
300.0ms
(log (* (* (cbrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0))))) (cbrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))) (cbrt (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))))

simplify117.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
04292389
111192199
241831907
350011772

prune329.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

99.7% (0.1b remaining)

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

bsearch78.0ms

Steps
ItersRangePoint
7
0.0008659720100092236
0.04032056371688071
0.0011131417783554753
9
-3875183.9477288676
-0.008763241487176904
-0.9973237802495053

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05030
15430
25730
35730

end0.0ms

sample1.9s

Algorithm
intervals
Results
966.0ms2341×body1280valid
360.0ms1504×body640valid
231.0ms862×body2560valid
108.0ms810×body320valid
64.0ms2112×body80valid
28.0ms371×body160valid