Details

Time bar (total: 5.6s)

sample31.0ms

Algorithm
intervals
Results
15.0ms93×body1280valid
4.0ms132×body80valid
2.0ms20×body640valid
1.0ms9×body320valid
0.0ms2×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: 15.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
1.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
12×prod-diff
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r* sqrt-prod associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 60
Calls
2 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series439.0ms

Counts
2 → 6
Calls
2 calls:
103.0ms
(/ 1.0 (hypot 1.0 x))
336.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify48.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0422844
11629601
25001599

prune158.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.5b

localize12.0ms

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))
0.8b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite17.0ms

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:
6.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
4.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series647.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
97.0ms
(/ 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))

simplify49.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0430681
11662625
25001623

prune341.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.8b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
0.8b
(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

rewrite14.0ms

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 log-prod log-pow log1p-expm1-u add-log-exp
3×exp-prod
2×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
1×rem-log-exp exp-sum
Counts
4 → 86
Calls
4 calls:
4.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
3.0ms
(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

series515.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ 1.0 (hypot 1.0 x))
103.0ms
(/ 1.0 (hypot 1.0 x))
148.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
156.0ms
(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

simplify164.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (156.0ms)

IterNodesCost
0279665
1931600
24763594
35001592

prune360.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.8b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
0.8b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
0.8b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×add-cube-cbrt *-un-lft-identity
11×pow1
6×add-exp-log pow1/3 swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
3×fma-udef
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 72
Calls
4 calls:
14.0ms
(* (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (cbrt (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))
0.0ms
(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))

series1.2s

Counts
4 → 12
Calls
4 calls:
782.0ms
(* (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (cbrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
155.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
154.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
148.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
03831202
115491077
25002970

prune316.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes169.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 15.1b

bsearch147.0ms

Steps
ItersRangePoint
11
1.661404138935296e-22
2.5556453819330236
0.0025906881160018247
9
-0.04331797882383785
-2.2082264187638084e-10
-8.830421450453418e-05

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04849
14849

end0.0ms

sample811.0ms

Algorithm
intervals
Results
452.0ms2858×body1280valid
111.0ms4057×body80valid
76.0ms626×body640valid
27.0ms318×body320valid
8.0ms141×body160valid