Details

Time bar (total: 3.7s)

sample34.0ms

Algorithm
intervals
Results
17.0ms89×body1280valid
4.0ms138×body80valid
2.0ms20×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series195.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
28.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms
(/ 1.0 (hypot 1.0 x))
86.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify69.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0221492
1697465
22325463
35001463

prune164.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 11.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 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))
0.6b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1 associate-*r/ associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-exp clear-num frac-sub flip-- div-inv
1×+-commutative flip3-+ diff-log sum-log flip-+ distribute-lft-out
Counts
4 → 84
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series122.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
33.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify139.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0306616
11080568
24851560
35001560

prune259.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
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)))
0.0b
(/ 1.0 (hypot 1.0 x))
0.6b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
14×*-un-lft-identity associate-*r/
12×add-sqr-sqrt add-cube-cbrt
10×times-frac associate-*l/
8×frac-sub add-log-exp
6×flip3-- flip3-+ flip-- flip-+ associate-/l/
5×cbrt-undiv div-exp
4×pow1 prod-exp associate-/r* cbrt-unprod associate-/l*
2×frac-2neg clear-num associate-/r/ div-inv associate--r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in diff-log sum-log distribute-lft-out
Counts
4 → 86
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
15.0ms
(/ (* 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)))
3.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series187.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
67.0ms
(/ (* 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)))
6.0ms
(/ 1.0 (hypot 1.0 x))
32.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify79.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06251165
13259984
25001984

prune354.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot 1.0 x))
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)))
0.5b
(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
0.6b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×add-exp-log
20×add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity associate-*r/
10×times-frac associate-*l/ sqrt-prod
9×pow1
8×frac-sub
6×flip3-- flip3-+ div-exp associate-*r* associate-*l* flip-- flip-+ associate-/l/ add-log-exp
5×cbrt-undiv prod-exp cbrt-unprod
4×associate-/r* associate-/l* unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 sqrt-div clear-num associate-/r/ div-inv associate--r+
1×distribute-rgt-in sub-neg rec-exp pow-flip distribute-lft-in sqrt-unprod diff-log 1-exp *-commutative inv-pow
Counts
4 → 110
Calls
4 calls:
3.0ms
(/ 1 (hypot 1.0 x))
14.0ms
(/ (* 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)))
11.0ms
(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
7.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series175.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1 (hypot 1.0 x))
58.0ms
(/ (* 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)))
76.0ms
(* (sqrt 0.5) (sqrt (+ (* 1.0 (/ 1 (hypot 1.0 x))) 1.0)))
35.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify97.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
06581344
136211158
250011144

prune567.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.1b

regimes261.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03422
13622
23622

end0.0ms

sample789.0ms

Algorithm
intervals
Results
453.0ms2835×body1280valid
115.0ms4065×body80valid
82.0ms647×body640valid
26.0ms305×body320valid
8.0ms148×body160valid