Details

Time bar (total: 6.7s)

sample29.0ms

Algorithm
intervals
Results
14.0ms84×body1280valid
4.0ms143×body80valid
3.0ms20×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify10.0ms

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: 14.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(hypot 1.0 x)
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.7b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity add-log-exp
7×pow1
6×add-sqr-sqrt
4×add-exp-log add-cube-cbrt add-cbrt-cube
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×+-commutative sub-neg flip3-- pow1/2 diff-log pow-prod-down sum-log sqrt-prod flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 46
Calls
4 calls:
5.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.0ms
(hypot 1.0 x)
6.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series188.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.0ms
(hypot 1.0 x)
74.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
86.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0167381
1423355
21736353
35002352

prune127.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
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
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.2b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
13×add-sqr-sqrt add-cube-cbrt
12×times-frac
10×associate-*r/
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
4×flip3-- associate--l+ associate-/r* frac-sub flip-- associate-/l/ distribute-lft-out
3×sub-neg associate-/l*
2×distribute-rgt-in distribute-lft-in sqrt-pow1 flip3-+ sqrt-div associate-/r/ flip-+
1×cbrt-undiv frac-2neg pow1/2 diff-log div-sub div-exp pow-prod-down clear-num sqrt-prod div-inv
Counts
4 → 76
Calls
4 calls:
1.0ms
(hypot 1.0 x)
11.0ms
(/ (- (* 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
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1.0 x)
164.0ms
(/ (- (* 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)))))))
72.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
38.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify49.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03961127
114031048
250011044

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
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)))))
0.1b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.1b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
288×associate-*r/
108×frac-add
76×flip3-- flip--
74×associate-/r/
72×frac-times
40×add-sqr-sqrt
30×*-un-lft-identity
27×times-frac associate-*l/
21×add-exp-log add-cbrt-cube sqr-pow
20×add-cube-cbrt difference-of-squares
19×flip3-+ flip-+
12×pow1
9×cube-div associate-/l*
7×prod-exp cbrt-unprod
6×add-log-exp
5×difference-cubes distribute-lft-out--
4×pow-prod-down frac-sub associate-/l/
3×cbrt-undiv pow-unpow div-exp associate-*r* pow-exp associate-/r* rem-cube-cbrt
2×pow-pow
1×distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down frac-2neg distribute-lft-in diff-log unpow3 div-sub cube-prod associate-*l* clear-num *-commutative div-inv
Counts
4 → 206
Calls
4 calls:
12.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
33.0ms
(/ (- (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)))))
5.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
8.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

series350.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
185.0ms
(/ (- (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)))))
33.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
73.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))

simplify104.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
019676759
150016583

prune980.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) (pow (* 1.0 (- 1.0 0.5)) 3))) (* (+ 1.0 0.5) (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5)))))
1.1b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
1.2b
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
1.2b
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
497×associate-*r/
220×frac-times
122×flip3-- flip--
82×frac-sub
78×flip3-+ associate-*l/ flip-+
76×cube-div
36×add-exp-log distribute-rgt-in distribute-lft-in frac-add add-cbrt-cube
25×pow1
22×prod-exp cbrt-unprod
19×sub-neg
16×associate--l+ associate--r+
15×pow-prod-down
10×add-log-exp
8×add-sqr-sqrt sub-div
6×*-un-lft-identity
4×add-cube-cbrt difference-of-squares sqr-pow
3×diff-log
2×cbrt-undiv distribute-rgt-out-- div-exp
1×difference-cubes associate-*r* associate-*l* *-commutative distribute-lft-out--
Counts
4 → 291
Calls
4 calls:
28.0ms
(* (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) (pow (* 1.0 (- 1.0 0.5)) 3))) (* (+ 1.0 0.5) (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5)))))
8.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
20.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
16.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3) (pow (* 1.0 (- 1.0 0.5)) 3))) (* (+ 1.0 0.5) (+ (* 1.0 1.0) (+ (* 0.5 0.5) (* 1.0 0.5)))))
86.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3))
37.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))
44.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 1.0 (- 1.0 0.5))))

simplify138.0ms

Algorithm
egg-herbie
Counts
303 → 303
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
023918772
150028629

prune2.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.0b

regimes75.0ms

Accuracy

0% (0.2b remaining)

Error of 14.3b against oracle of 14.0b and baseline of 14.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06696
16696

end0.0ms

sample838.0ms

Algorithm
intervals
Results
489.0ms2888×body1280valid
123.0ms4085×body80valid
80.0ms604×body640valid
25.0ms279×body320valid
10.0ms144×body160valid