Details

Time bar (total: 5.9s)

sample31.0ms

Algorithm
intervals
Results
15.0ms91×body1280valid
4.0ms132×body80valid
2.0ms18×body640valid
1.0ms9×body320valid
0.0ms6×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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize8.0ms

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)))))
2.2b
(- 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))))))

series791.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(hypot 1.0 x)
103.0ms
(/ 1.0 (hypot 1.0 x))
264.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
362.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05331074
12023830
25002827

prune251.0ms

Filtered
97 candidates to 79 candidates (81.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.7b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
7×pow1
6×associate-/r* associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 sqrt-div associate-*r/ div-exp clear-num div-inv
1×flip3-+ pow1/2 pow-prod-down sqrt-prod flip-+ fma-udef
Counts
4 → 83
Calls
4 calls:
2.0ms
(/ 1.0 (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)))))
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:
108.0ms
(/ 1.0 (hypot 1.0 x))
113.0ms
(/ 1.0 (hypot 1.0 x))
277.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
155.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0416641
11548607
25001600

prune345.0ms

Filtered
95 candidates to 83 candidates (87.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.5b
(* (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.7b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.7b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×pow1
19×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1
9×pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp unswap-sqr
3×pow-sqr
2×sqrt-div associate-*r/ fma-udef
1×pow2 flip3-+ pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod flip-+
Counts
4 → 86
Calls
4 calls:
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms
(* (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (sqrt (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))

series938.0ms

Counts
4 → 12
Calls
4 calls:
464.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
158.0ms
(* (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
160.0ms
(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))

simplify52.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0383977
11627857
25002826

prune318.0ms

Filtered
98 candidates to 67 candidates (68.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (cbrt (pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
0.5b
(cbrt (pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3))
1.7b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.7b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
34×sqrt-prod
32×cbrt-prod
18×associate-*l*
14×add-cube-cbrt *-un-lft-identity
12×unswap-sqr
8×pow1 unpow-prod-down cube-prod
6×add-exp-log associate-*r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-prod-down
2×cube-mult sqrt-pow1 pow1/2 unpow3 fma-udef
1×pow1/3 sqrt-unprod prod-exp *-commutative rem-cbrt-cube cbrt-unprod
Counts
4 → 95
Calls
4 calls:
17.0ms
(* (sqrt (cbrt (pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
1.0ms
(cbrt (pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3))
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))

series604.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* (sqrt (cbrt (pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3))) (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))
153.0ms
(cbrt (pow (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) 3))
148.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
150.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify165.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02591454
19161211
249171169
350011169

prune361.0ms

Filtered
107 candidates to 75 candidates (70.1%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

regimes325.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.2b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05048
15048

end0.0ms

sample831.0ms

Algorithm
intervals
Results
481.0ms2898×body1280valid
118.0ms4007×body80valid
80.0ms602×body640valid
29.0ms325×body320valid
10.0ms168×body160valid