Details

Time bar (total: 5.8s)

sample32.0ms

Algorithm
intervals
Results
15.0ms86×body1280valid
4.0ms127×body80valid
3.0ms22×body640valid
1.0ms14×body320valid
0.0ms7×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1266
2336
3356
4416
5446
6446

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
12×prod-diff
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-neg associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg hypot-udef flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 85
Calls
4 calls:
0.0ms
(hypot 1.0 x)
2.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series756.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(hypot 1.0 x)
99.0ms
(/ 1.0 (hypot 1.0 x))
257.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
346.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify62.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05331074
12023830
25002827

prune246.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
2.2b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×+-commutative flip3-+ sum-log flip-+ fma-udef distribute-lft-out
Counts
4 → 85
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series654.0ms

Counts
4 → 12
Calls
4 calls:
311.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
99.0ms
(/ 1.0 (hypot 1.0 x))
98.0ms
(/ 1.0 (hypot 1.0 x))
146.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0430681
11662625
25001623

prune349.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.2b
(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
2.2b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
5×pow1
4×expm1-log1p-u exp-prod log1p-expm1-u add-log-exp
3×log-prod exp-sum
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×log-pow fma-udef rem-exp-log
Counts
4 → 85
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series522.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ 1.0 (hypot 1.0 x))
103.0ms
(/ 1.0 (hypot 1.0 x))
159.0ms
(exp (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
156.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify160.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 3 (152.0ms)

IterNodesCost
0273648
1913592
24559571
35001565

prune378.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.2b
(pow E (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
2.2b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
9×add-exp-log
8×add-cbrt-cube
6×pow1 associate-/r* associate-/l*
4×expm1-log1p-u pow-unpow log1p-expm1-u add-log-exp
3×unpow-prod-up unpow-prod-down log-prod
2×cbrt-undiv frac-2neg div-exp pow-exp clear-num div-inv
1×pow-to-exp e-exp-1 pow-pow log-pow fma-udef sqr-pow
Counts
4 → 92
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(pow E (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series792.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ 1.0 (hypot 1.0 x))
109.0ms
(/ 1.0 (hypot 1.0 x))
423.0ms
(pow E (log (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
156.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0359776
11368725
25002716

prune387.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes214.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.1b

bsearch168.0ms

Steps
ItersRangePoint
9
8.455209092704733e-09
0.003064448021395057
8.33977184994014e-05
10
-4.508778152722845
-1.8057709034692785e-13
-0.0025755882761485938

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05151
15151

end0.0ms

sample871.0ms

Algorithm
intervals
Results
504.0ms2853×body1280valid
124.0ms4041×body80valid
91.0ms619×body640valid
32.0ms337×body320valid
9.0ms150×body160valid