Details

Time bar (total: 6.2s)

sample67.0ms

Algorithm
intervals
Results
35.0ms80×body1280valid
9.0ms38×body640valid
8.0ms30×body2560valid
5.0ms36×body320valid
2.0ms63×body80valid
1.0ms9×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: 54.0b

localize144.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.8b
(+ x (sqrt (+ (* x x) 1.0)))
1.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.6b
(sqrt (+ (* x x) 1.0))

rewrite22.0ms

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

series304.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* x x) 1.0)
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
171.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0357480
11262435
25002412

prune221.0ms

Pruning

3 alts after pruning (3 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)))

rewrite88.0ms

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:
13.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
55.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series293.0ms

Counts
2 → 6
Calls
2 calls:
156.0ms
(- (+ (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)))

simplify118.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08882291
147681819
250011795

prune463.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

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 (+ (hypot x (sqrt 1.0)) x))

rewrite8.0ms

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

series512.0ms

Counts
3 → 9
Calls
3 calls:
103.0ms
(hypot x (sqrt 1.0))
125.0ms
(+ (hypot x (sqrt 1.0)) x)
283.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify87.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (82.0ms)

IterNodesCost
0268351
1890323
23710307
35001303

prune137.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
0.4b
(/ 1/8 (pow x 3))
11.4b
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
21.1b
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
609×times-frac
290×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
207×unpow-prod-down
90×cube-prod
69×sqr-pow
37×associate-/r*
36×add-exp-log
30×cube-mult unpow3
24×div-exp
15×div-inv associate-/l*
11×add-cbrt-cube
8×pow-to-exp pow-exp
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod
2×frac-2neg clear-num
1×rem-log-exp associate-/r/ log-pow fma-udef
Counts
4 → 455
Calls
4 calls:
15.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
5.0ms
(/ 1/8 (pow x 3))
1.0ms
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
1.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

series377.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
42.0ms
(/ 1/8 (pow x 3))
185.0ms
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
64.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

simplify78.0ms

Algorithm
egg-herbie
Counts
467 → 467
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015924240
150014118

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.3b

bsearch82.0ms

Steps
ItersRangePoint
10
4.9177062248324165e-05
42925490.781275615
0.0006401002984337763
8
-1.0806682141483241
-0.0004106978961831668
-1.013880423339445

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04428
14828
25128
35128

end0.0ms

sample1.9s

Algorithm
intervals
Results
971.0ms2308×body1280valid
383.0ms1569×body640valid
217.0ms782×body2560valid
119.0ms820×body320valid
72.0ms2147×body80valid
30.0ms374×body160valid