Details

Time bar (total: 5.9s)

sample42.0ms

Algorithm
intervals
Results
21.0ms87×body1280valid
7.0ms132×body80valid
4.0ms23×body640valid
1.0ms9×body320valid
0.0ms5×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: 15.3b

localize9.0ms

Local error

Found 1 expressions with local error:

1.9b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 14
Calls
1 calls:
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series88.0ms

Counts
1 → 3
Calls
1 calls:
88.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 4 (57.0ms)

IterNodesCost
087169
1208156
2670154
32027154
45001152

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity add-log-exp
7×add-sqr-sqrt
3×diff-log distribute-lft-out--
2×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- associate--l+ frac-sub add-cbrt-cube flip-- difference-of-squares
1×+-commutative associate--l- flip3-+ times-frac sum-log flip-+ distribute-lft-out
Counts
2 → 34
Calls
2 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
22.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series117.0ms

Counts
2 → 6
Calls
2 calls:
82.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
36.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify67.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0223323
1595298
22572296
35001294

prune103.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b
(/ (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5)) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
1.4b
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*l/
8×add-exp-log frac-sub add-cbrt-cube
7×*-un-lft-identity add-log-exp
6×flip3-- flip3-+ flip-- flip-+ associate-/l/
5×add-sqr-sqrt add-cube-cbrt
3×pow1 times-frac associate-/l*
2×cbrt-undiv associate-*r/ div-exp associate-/r/
1×+-commutative sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* sum-log cbrt-unprod div-inv distribute-lft-out
Counts
3 → 58
Calls
3 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
64.0ms
(/ (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5)) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
28.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5))

series191.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
73.0ms
(/ (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5)) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
42.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5))

simplify91.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
05841396
130311212
250031211

prune330.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 14.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))) (+ (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5)))
0.2b
(* (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)))
1.4b
(- (* (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5)))
15.3b
(/ (- (* (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5))) (* (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))) (+ (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5))))

rewrite765.0ms

Algorithm
rewrite-expression-head
Rules
514×associate-*l/
156×frac-times
128×flip3-+ frac-sub flip-+
116×flip3-- flip--
106×associate-*r/
66×associate-/l/
48×pow1
30×add-exp-log add-cbrt-cube
24×frac-add
20×pow-prod-down associate-/r/
14×prod-exp cbrt-unprod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×times-frac associate-*r* pow-sqr pow-prod-up associate-/l*
3×cbrt-undiv div-exp difference-of-squares
2×pow-plus associate-*l* *-commutative
1×pow2 distribute-rgt-in sub-neg frac-2neg distribute-lft-in diff-log div-sub swap-sqr clear-num associate-/r* div-inv
Counts
4 → 271
Calls
4 calls:
87.0ms
(* (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))) (+ (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5)))
121.0ms
(* (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)))
145.0ms
(- (* (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5)))
384.0ms
(/ (- (* (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5))) (* (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))) (+ (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5))))

series343.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))) (+ (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5)))
38.0ms
(* (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)))
69.0ms
(- (* (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5)))
163.0ms
(/ (- (* (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x))) (* (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5))) (* (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))) (+ (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5))) 0.5))))

simplify176.0ms

Algorithm
egg-herbie
Counts
283 → 283
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0213714184
1500213703

prune2.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.5b

regimes60.0ms

Accuracy

0% (0.2b remaining)

Error of 14.9b against oracle of 14.6b and baseline of 14.9b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.1s

Algorithm
intervals
Results
583.0ms2839×body1280valid
214.0ms4052×body80valid
113.0ms642×body640valid
45.0ms314×body320valid
14.0ms153×body160valid