Details

Time bar (total: 30.9s)

sample50.0ms

Algorithm
intervals
Results
22.0ms82×body1280valid
8.0ms139×body80valid
4.0ms19×body640valid
2.0ms13×body320valid
0.0ms3×body160valid

simplify42.0ms

Counts
1 → 1
Iterations
IterNodes
done42
642
540
434
332
226
119
09

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize44.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×prod-diff
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt
3×fma-neg sqrt-prod add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 31
Calls
1 calls:
12.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series521.0ms

Counts
1 → 3
Calls
1 calls:
520.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.5s

Counts
34 → 34
Iterations
IterNodes
done5000
21238
1301
0121

prune212.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.8b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
13×add-sqr-sqrt add-cube-cbrt
12×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log distribute-lft-out
4×associate-/r*
3×expm1-log1p-u pow1 fma-def log1p-expm1-u associate-/l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate--r+ associate-/l/
1×distribute-rgt-in cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg distribute-lft-in fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
3 → 73
Calls
3 calls:
26.0ms
(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
5.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series2.1s

Counts
3 → 9
Calls
3 calls:
1.5s
(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
491.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
174.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify2.3s

Counts
82 → 82
Iterations
IterNodes
done5000
1928
0298

prune521.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* 1.0 1.0) (- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.5b
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.8b
(- (/ (* 1.0 1.0) (fma (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* (* 1.0 1.0) 1.0))) (/ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (fma (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* (* 1.0 1.0) 1.0))))
1.6b
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite426.0ms

Algorithm
rewrite-expression-head
Rules
88×associate-*r/
60×sqrt-div
53×pow1
51×prod-diff
46×times-frac
44×add-sqr-sqrt
40×*-un-lft-identity
38×add-cube-cbrt
31×flip3-+ flip-+
28×sqrt-pow1
20×pow-prod-down
17×frac-sub div-inv
13×add-log-exp
12×frac-times
10×pow1/2 pow-prod-up
8×fma-neg associate-*l/
6×add-cbrt-cube add-exp-log pow-sqr
5×sub-div
4×expm1-log1p-u swap-sqr associate-*r* associate-*l* sqrt-prod log1p-expm1-u
3×associate-+r+ sub-neg diff-log
2×sum-log flip3-- distribute-rgt-out-- flip-- difference-of-squares
1×pow2 +-commutative associate-+r- rem-square-sqrt fma-def pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 191
Calls
4 calls:
205.0ms
(+ (* 1.0 1.0) (- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
92.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
19.0ms
(- (/ (* 1.0 1.0) (fma (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* (* 1.0 1.0) 1.0))) (/ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (fma (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* (* 1.0 1.0) 1.0))))
93.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series9.8s

Counts
4 → 12
Calls
4 calls:
923.0ms
(+ (* 1.0 1.0) (- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
253.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.7s
(- (/ (* 1.0 1.0) (fma (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* (* 1.0 1.0) 1.0))) (/ (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (fma (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)) (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) (* (* 1.0 1.0) 1.0))))
965.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify4.7s

Counts
203 → 203
Iterations
IterNodes
done5000
11835
0577

prune1.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma 0.1875 (/ (* x x) (/ (pow (sqrt 1.0) 5) (* x x))) (/ 0.5 (sqrt 1.0)))
0.7b
(/ (pow (sqrt 1.0) 5) (* x x))
0.7b
(- 0.5 (fma 0.1875 (/ (* x x) (/ (pow (sqrt 1.0) 5) (* x x))) (/ 0.5 (sqrt 1.0))))
16.3b
(fma (/ x (/ (* 1.0 (sqrt 1.0)) x)) 0.25 (- 0.5 (fma 0.1875 (/ (* x x) (/ (pow (sqrt 1.0) 5) (* x x))) (/ 0.5 (sqrt 1.0)))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt *-un-lft-identity
17×add-exp-log add-cube-cbrt
12×unpow-prod-down
10×times-frac associate-/l*
9×add-cbrt-cube prod-diff
6×div-exp sqrt-prod add-log-exp
4×expm1-log1p-u pow1 log1p-expm1-u
3×fma-neg prod-exp fma-udef
2×pow-to-exp cbrt-undiv pow-exp sqr-pow
1×clear-num associate-/r* sub-neg frac-2neg flip3-- diff-log cbrt-unprod div-inv flip-- associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 90
Calls
4 calls:
1.0ms
(fma 0.1875 (/ (* x x) (/ (pow (sqrt 1.0) 5) (* x x))) (/ 0.5 (sqrt 1.0)))
25.0ms
(/ (pow (sqrt 1.0) 5) (* x x))
10.0ms
(- 0.5 (fma 0.1875 (/ (* x x) (/ (pow (sqrt 1.0) 5) (* x x))) (/ 0.5 (sqrt 1.0))))
1.0ms
(fma (/ x (/ (* 1.0 (sqrt 1.0)) x)) 0.25 (- 0.5 (fma 0.1875 (/ (* x x) (/ (pow (sqrt 1.0) 5) (* x x))) (/ 0.5 (sqrt 1.0)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
498.0ms
(fma 0.1875 (/ (* x x) (/ (pow (sqrt 1.0) 5) (* x x))) (/ 0.5 (sqrt 1.0)))
197.0ms
(/ (pow (sqrt 1.0) 5) (* x x))
575.0ms
(- 0.5 (fma 0.1875 (/ (* x x) (/ (pow (sqrt 1.0) 5) (* x x))) (/ 0.5 (sqrt 1.0))))
367.0ms
(fma (/ x (/ (* 1.0 (sqrt 1.0)) x)) 0.25 (- 0.5 (fma 0.1875 (/ (* x x) (/ (pow (sqrt 1.0) 5) (* x x))) (/ 0.5 (sqrt 1.0)))))

simplify1.5s

Counts
102 → 102
Iterations
IterNodes
done5002
21744
1375
0172

prune816.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes229.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.7b

bsearch2.0ms

simplify19.0ms

Iterations
IterNodes
done60
360
258
153
044

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.5s2843×body1280valid
281.0ms638×body640valid
258.0ms4049×body80valid
57.0ms335×body320valid
16.0ms135×body160valid