Details

Time bar (total: 3.7s)

sample35.0ms

Algorithm
intervals
Results
18.0ms93×body1280valid
4.0ms132×body80valid
3.0ms20×body640valid
1.0ms9×body320valid
0.0ms2×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
1.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
4.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series93.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
86.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify45.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0157308
1484286
21409284
35001284

prune101.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize12.0ms

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))
0.8b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite69.0ms

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:
40.0ms
(/ (- (* 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)))))))
7.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
15.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series206.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(/ (- (* 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)))))))
7.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
36.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify54.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04071275
115941181
250011177

prune298.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
42×times-frac
25×add-sqr-sqrt add-cube-cbrt
24×add-exp-log add-cbrt-cube
14×associate-*l/
12×associate-/r/
10×cbrt-undiv div-exp associate-/l*
9×flip3-+ flip-+ distribute-lft-out
8×add-log-exp
7×associate-/r* div-inv
4×pow1 associate-*r/ prod-exp frac-sub cbrt-unprod
3×flip3-- flip--
2×frac-2neg clear-num associate--r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in diff-log sum-log associate-/l/
Counts
4 → 119
Calls
4 calls:
35.0ms
(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (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))))))
5.0ms
(/ 1.0 (hypot 1.0 x))
26.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(/ (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
81.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms
(/ 1.0 (hypot 1.0 x))
35.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify109.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07822521
142462222
250012222

prune411.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.5b

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)))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
0.1b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
0.8b
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
103×associate-*r/
45×pow1
44×add-exp-log add-cbrt-cube
29×frac-times
24×frac-sub
22×flip3-- prod-exp flip-- cbrt-unprod
18×pow-prod-down
17×associate-*l/
16×add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt
9×distribute-rgt-in distribute-lft-in times-frac
8×flip3-+ associate--l+ flip-+
7×cbrt-undiv div-exp
6×frac-add add-log-exp
5×sub-neg associate-*l*
4×associate-*r* pow-sqr pow-prod-up
3×associate-/r* associate-/l*
2×pow-plus *-commutative
1×pow2 frac-2neg diff-log swap-sqr clear-num div-inv distribute-lft-out difference-of-squares unswap-sqr
Counts
4 → 154
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
55.0ms
(* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
43.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
74.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

series219.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
127.0ms
(* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))))
25.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
60.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010462339
150012129

prune397.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.4b

regimes75.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.9b and baseline of 15.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02926
12926

end0.0ms

sample837.0ms

Algorithm
intervals
Results
463.0ms2858×body1280valid
119.0ms4057×body80valid
80.0ms626×body640valid
28.0ms318×body320valid
8.0ms141×body160valid