Details

Time bar (total: 5.1s)

sample31.0ms

Algorithm
intervals
Results
16.0ms100×body1280valid
4.0ms131×body80valid
1.0ms12×body640valid
1.0ms8×body320valid
0.0ms5×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 13.6b

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))
1.7b
(- 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:
7.0ms
(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))))))

series880.0ms

Counts
4 → 12
Calls
4 calls:
277.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
109.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
111.0ms
(/ 1.0 (hypot 1.0 x))
383.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05331129
12036878
25001876

prune280.0ms

Filtered
104 candidates to 84 candidates (80.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.9b

localize12.0ms

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
(/ 1.0 (hypot 1.0 x))
1.2b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite12.0ms

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 (/ 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))

series488.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
106.0ms
(/ 1.0 (hypot 1.0 x))
107.0ms
(/ 1.0 (hypot 1.0 x))
161.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0319561
11141522
25001520

prune343.0ms

Filtered
97 candidates to 85 candidates (87.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

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))
1.2b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.2b
(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

rewrite11.0ms

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:
2.0ms
(/ 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))
1.0ms
(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ 1.0 (hypot 1.0 x))
113.0ms
(/ 1.0 (hypot 1.0 x))
162.0ms
(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))))

simplify163.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (153.0ms)

IterNodesCost
0279665
1931600
24763594
35001592

prune383.0ms

Filtered
98 candidates to 85 candidates (86.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (exp (fma (/ 1 x) (- 0.5 (/ 0.25 (pow x 2))) 0.5)))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(fma (/ 1 x) (- 0.5 (/ 0.25 (pow x 2))) 0.5)
0.6b
(/ 0.25 (pow x 2))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
31×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
11×add-exp-log associate-/r*
8×add-cbrt-cube
6×associate-/l*
5×pow1
4×expm1-log1p-u log-prod div-exp log-pow log1p-expm1-u unpow2 add-log-exp sqr-pow
3×exp-prod
2×cbrt-undiv frac-2neg clear-num fma-udef div-inv
1×pow-to-exp rem-log-exp exp-sum pow-exp
Counts
4 → 108
Calls
4 calls:
1.0ms
(log (exp (fma (/ 1 x) (- 0.5 (/ 0.25 (pow x 2))) 0.5)))
2.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(fma (/ 1 x) (- 0.5 (/ 0.25 (pow x 2))) 0.5)
4.0ms
(/ 0.25 (pow x 2))

series221.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(log (exp (fma (/ 1 x) (- 0.5 (/ 0.25 (pow x 2))) 0.5)))
108.0ms
(/ 1.0 (hypot 1.0 x))
43.0ms
(fma (/ 1 x) (- 0.5 (/ 0.25 (pow x 2))) 0.5)
26.0ms
(/ 0.25 (pow x 2))

simplify43.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0385690
11407615
25002599

prune419.0ms

Filtered
120 candidates to 87 candidates (72.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes107.0ms

Accuracy

99% (0.1b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 15.1b

bsearch157.0ms

Steps
ItersRangePoint
9
7.206039552426127e-07
5.540917366542361
0.0024191707635979032
10
-204248214.92732975
-1.534026600097144e-05
-0.9601416765850218

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05450
15450

end0.0ms

sample816.0ms

Algorithm
intervals
Results
475.0ms2907×body1280valid
117.0ms3990×body80valid
79.0ms606×body640valid
28.0ms319×body320valid
10.0ms178×body160valid