Details

Time bar (total: 15.2s)

sample33.0ms

Algorithm
intervals
Results
17.0ms80×body1280valid
4.0ms137×body80valid
3.0ms19×body640valid
1.0ms12×body320valid
0.0ms8×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: 16.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
2.7b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×add-sqr-sqrt
21×add-cube-cbrt
12×prod-diff
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-def fma-neg associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 92
Calls
4 calls:
8.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
2.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series859.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
107.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
112.0ms
(/ 1.0 (hypot 1.0 x))
370.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify57.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05331129
12036878
25001876

prune282.0ms

Filtered
104 candidates to 84 candidates (80.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.7b

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

rewrite13.0ms

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))))))
5.0ms
(/ 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))

series701.0ms

Counts
4 → 12
Calls
4 calls:
328.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
105.0ms
(/ 1.0 (hypot 1.0 x))
113.0ms
(/ 1.0 (hypot 1.0 x))
154.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0430681
11662625
25001623

prune369.0ms

Filtered
97 candidates to 85 candidates (87.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.5b
(expm1 (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.0b
(log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.2b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
5×expm1-log1p-u
4×pow1 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
1×cbrt-undiv log1p-udef expm1-log1p frac-2neg log1p-expm1 div-exp clear-num fma-udef div-inv expm1-udef
Counts
4 → 61
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(expm1 (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0ms
(log1p (+ 1.0 (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))

series2.2s

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ 1.0 (hypot 1.0 x))
1.1s
(expm1 (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
797.0ms
(log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
161.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify74.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0607838
12735760
25001757

prune550.0ms

Filtered
73 candidates to 65 candidates (89.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (log1p (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.5b
(expm1 (expm1 (log1p (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))
1.0b
(log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.2b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×expm1-log1p-u log1p-expm1-u
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
2×expm1-log1p expm1-udef
1×log1p-udef log1p-expm1 fma-udef
Counts
4 → 43
Calls
4 calls:
0.0ms
(expm1 (log1p (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.0ms
(expm1 (expm1 (log1p (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))
0.0ms
(log1p (+ 1.0 (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))

series8.1s

Counts
4 → 12
Calls
4 calls:
2.6s
(expm1 (log1p (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
4.6s
(expm1 (expm1 (log1p (log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))
784.0ms
(log1p (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
153.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify43.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010842116
150011971

prune373.0ms

Filtered
55 candidates to 49 candidates (89.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes245.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.9b

bsearch128.0ms

Steps
ItersRangePoint
10
9.558161037350472e-13
0.8818080259852756
0.0010999112910662773
5
-0.0026665893748653055
-0.00123344211380614
-0.0023638476354078493

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05553
15553

end0.0ms

sample1.0s

Algorithm
intervals
Results
683.0ms2847×body1280valid
122.0ms4058×body80valid
83.0ms608×body640valid
30.0ms320×body320valid
10.0ms167×body160valid