Details

Time bar (total: 1.3m)

sample57.0ms

Algorithm
intervals
Results
32.0ms95×body1280valid
6.0ms127×body80valid
4.0ms24×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify34.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
1.4b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×times-frac
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
3 → 54
Calls
3 calls:
14.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series238.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms
(/ 1.0 (hypot 1.0 x))
134.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify930.0ms

Counts
63 → 63

prune213.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 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))
0.9b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt add-cube-cbrt
10×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
8×associate-*r/
6×add-log-exp
4×pow1 flip3-- associate--l+ frac-sub flip-- associate-/l/ distribute-lft-out
3×cbrt-undiv sub-neg frac-2neg div-exp clear-num div-inv
2×distribute-rgt-in distribute-lft-in associate-/r/
1×flip3-+ diff-log div-sub flip-+
Counts
4 → 110
Calls
4 calls:
60.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
23.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
13.0ms
(/ 1.0 (hypot 1.0 x))
18.0ms
(/ 1.0 (hypot 1.0 x))
51.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify682.0ms

Counts
122 → 122

prune453.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.2b

localize33.0ms

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 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.9b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
375×times-frac
292×*-un-lft-identity
208×sqrt-prod
188×add-sqr-sqrt add-cube-cbrt
52×distribute-lft-out
33×associate-/l*
18×sqrt-div associate-/r/
13×add-exp-log associate-/r* add-cbrt-cube
11×div-inv
9×flip3-+ flip-+
6×add-log-exp
5×cbrt-undiv div-exp
4×pow1 associate-*r/ associate--l+
3×sub-neg frac-2neg clear-num
2×distribute-rgt-in flip3-- distribute-lft-in div-sub frac-sub flip--
1×diff-log associate-/l/
Counts
4 → 313
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
117.0ms
(/ (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
32.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(/ 1.0 (hypot 1.0 x))
235.0ms
(/ (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
40.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify1.4s

Counts
325 → 325

prune993.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 15.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (/ (/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.1b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
0.9b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
14677×associate-*r/
12588×times-frac
7415×*-un-lft-identity
6328×sqrt-prod
5824×frac-add
4589×add-sqr-sqrt
4162×associate-/r/
3922×flip3-- flip--
3913×add-cube-cbrt
3808×frac-times
1582×distribute-lft-out
1456×associate-*l/
961×flip3-+ flip-+
744×associate-/l*
677×sqr-pow
676×difference-of-squares
169×difference-cubes distribute-lft-out--
66×div-inv
21×add-exp-log add-cbrt-cube
18×sqrt-div
10×associate-/r*
8×cbrt-undiv div-exp
7×pow1
6×add-log-exp
5×cube-div
3×pow-unpow div-sub pow-exp rem-cube-cbrt
2×pow-pow frac-2neg prod-exp clear-num frac-sub cbrt-unprod
1×cube-mult pow-to-exp sub-neg unpow-prod-down diff-log unpow3 cube-prod pow-prod-down associate-/l/
Counts
4 → 6027
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
677.0ms
(/ (/ (/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
9.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
30.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series587.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ 1.0 (hypot 1.0 x))
436.0ms
(/ (/ (/ (- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (+ (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5)))) (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
49.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
88.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify22.3s

Counts
6039 → 6039

prune46.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

regimes92.0ms

Accuracy

-187.7% (0.7b remaining)

Error of 14.9b against oracle of 14.2b and baseline of 14.4b

bsearch0.0ms

simplify634.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.4s2873×body1280valid
393.0ms4094×body80valid
203.0ms615×body640valid
46.0ms262×body320valid
17.0ms156×body160valid