Details

Time bar (total: 5.5s)

sample69.0ms

Algorithm
intervals
Results
39.0ms84×body1280valid
8.0ms29×body2560valid
7.0ms34×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

localize6.0ms

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))

rewrite24.0ms

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)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series264.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ x (sqrt (+ (* x x) 1.0)))
166.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms
(sqrt (+ (* x x) 1.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0331422
11127385
25002366

prune185.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

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)))

rewrite239.0ms

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:
143.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
74.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series292.0ms

Counts
2 → 6
Calls
2 calls:
157.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
134.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify124.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08882291
147681819
250011795

prune462.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.8b
(+ (hypot x (sqrt 1.0)) x)
1.8b
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
7×add-exp-log
6×pow1 *-un-lft-identity
5×add-log-exp
4×add-sqr-sqrt add-cube-cbrt
3×expm1-log1p-u fma-def rem-log-exp add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ associate-*r/ prod-exp log-pow flip-+
1×+-commutative log-prod hypot-udef 1-exp pow-prod-down sum-log distribute-lft-out
Counts
3 → 44
Calls
3 calls:
0.0ms
(hypot x (sqrt 1.0))
3.0ms
(+ (hypot x (sqrt 1.0)) x)
4.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

series510.0ms

Counts
3 → 9
Calls
3 calls:
97.0ms
(hypot x (sqrt 1.0))
132.0ms
(+ (hypot x (sqrt 1.0)) x)
280.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

simplify32.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0288336
11100310
25002294

prune144.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-div
34×associate-*r/
30×flip3-+ flip-+
28×frac-times
26×log-div
20×add-exp-log
14×pow1 associate-*l/
13×*-un-lft-identity
12×prod-exp
10×add-log-exp
9×fma-def
7×add-sqr-sqrt add-cube-cbrt rem-log-exp
6×pow-prod-down
4×expm1-log1p-u log-pow add-cbrt-cube log1p-expm1-u
3×+-commutative 1-exp sum-log distribute-lft-out
1×log-prod
Counts
4 → 98
Calls
4 calls:
3.0ms
(+ (hypot x (sqrt 1.0)) x)
2.0ms
(+ (hypot x (sqrt 1.0)) x)
3.0ms
(+ (hypot x (sqrt 1.0)) x)
103.0ms
(log (* 1 (* (* (cbrt (+ (hypot x (sqrt 1.0)) x)) (cbrt (+ (hypot x (sqrt 1.0)) x))) (cbrt (+ (hypot x (sqrt 1.0)) x)))))

series677.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(+ (hypot x (sqrt 1.0)) x)
134.0ms
(+ (hypot x (sqrt 1.0)) x)
128.0ms
(+ (hypot x (sqrt 1.0)) x)
288.0ms
(log (* 1 (* (* (cbrt (+ (hypot x (sqrt 1.0)) x)) (cbrt (+ (hypot x (sqrt 1.0)) x))) (cbrt (+ (hypot x (sqrt 1.0)) x)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
05161702
114451578
250011378

prune310.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.7% (0.1b remaining)

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

bsearch64.0ms

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
04425
14625
24625

end0.0ms

sample1.8s

Algorithm
intervals
Results
943.0ms2341×body1280valid
343.0ms1504×body640valid
235.0ms862×body2560valid
105.0ms810×body320valid
62.0ms2112×body80valid
28.0ms371×body160valid