Details

Time bar (total: 6.4s)

sample34.0ms

Algorithm
intervals
Results
19.0ms98×body1280valid
3.0ms118×body80valid
3.0ms21×body640valid
1.0ms11×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: 18.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 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)))))
2.5b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite22.0ms

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

series829.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
105.0ms
(/ 1.0 (hypot 1.0 x))
267.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
353.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05331129
12036878
25002876

prune272.0ms

Filtered
104 candidates to 84 candidates (80.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.1b

localize16.0ms

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
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite10.0ms

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:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(+ 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))

series683.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ 1.0 (hypot 1.0 x))
109.0ms
(/ 1.0 (hypot 1.0 x))
318.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
154.0ms
(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 (40.0ms)

IterNodesCost
0430681
11662625
25001623

prune351.0ms

Filtered
97 candidates to 85 candidates (87.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
2.1b
(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt
9×times-frac
6×add-exp-log add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log-prod log-pow log1p-expm1-u
3×exp-prod fma-def associate-/r* associate-/l*
2×fma-udef
1×cbrt-undiv +-commutative frac-2neg flip3-+ div-exp rem-log-exp exp-sum clear-num sum-log flip-+ div-inv distribute-lft-out
Counts
4 → 74
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(+ 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))
1.0ms
(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

series739.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ 1.0 (hypot 1.0 x))
325.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
150.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
155.0ms
(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

simplify48.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0466707
11743637
25001636

prune332.0ms

Filtered
86 candidates to 76 candidates (88.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

2.0b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
2.0b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
2.9b
(log (sqrt (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))))
2.9b
(log (sqrt (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod
12×log-pow
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow1 sqrt-pow1 sqrt-prod
6×add-exp-log exp-prod
4×expm1-log1p-u add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
2×pow1/2 rem-log-exp exp-sum
Counts
4 → 66
Calls
4 calls:
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))
2.0ms
(log (sqrt (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))))
2.0ms
(log (sqrt (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
153.0ms
(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))
572.0ms
(log (sqrt (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))))
565.0ms
(log (sqrt (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))))

simplify83.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0216900
1621804
22793804
35002792

prune367.0ms

Filtered
78 candidates to 68 candidates (87.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes193.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.4b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04437
14437

end0.0ms

sample796.0ms

Algorithm
intervals
Results
454.0ms2796×body1280valid
120.0ms4124×body80valid
79.0ms610×body640valid
27.0ms309×body320valid
9.0ms161×body160valid