Details

Time bar (total: 4.4s)

sample35.0ms

Algorithm
intervals
Results
18.0ms93×body1280valid
4.0ms132×body80valid
3.0ms20×body640valid
1.0ms9×body320valid
0.0ms2×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: 15.1b

localize8.0ms

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:
5.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series90.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
85.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify44.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0157308
1484286
21409284
35001284

prune104.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize13.0ms

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))))

rewrite71.0ms

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:
41.0ms
(/ (- (* 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)))))))
8.0ms
(/ 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))))

series196.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (- (* 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)))))))
6.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
35.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify57.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04071275
115941181
250011177

prune328.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.6b

localize20.0ms

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)))

rewrite77.0ms

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:
36.0ms
(/ (/ (* 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))))))
7.0ms
(/ 1.0 (hypot 1.0 x))
24.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(/ (/ (* 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)))))))
78.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (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)))

simplify111.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07822521
142462222
250012222

prune440.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.8b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))
1.6b
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
94×associate-*r/
62×sqrt-div
57×pow1
33×flip3-+ flip-+
30×sqrt-pow1
21×pow-prod-down
20×frac-sub
13×add-sqr-sqrt
12×frac-times associate-*l/
11×add-cube-cbrt *-un-lft-identity pow1/2
10×pow-prod-up
8×add-log-exp
7×add-exp-log add-cbrt-cube
6×sqrt-prod pow-sqr
4×unpow-prod-down flip3-- pow-pow cube-prod swap-sqr associate-*r* associate-*l* flip-- sub-div
3×pow-unpow
2×cube-div sub-neg diff-log associate--r+
1×pow2 distribute-rgt-in cube-mult pow-to-exp distribute-rgt-out-- distribute-lft-in pow-plus sqrt-unprod unpow3 pow-exp prod-exp rem-square-sqrt *-commutative sqrt-pow2 cbrt-unprod rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 139
Calls
4 calls:
88.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
14.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
24.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))
108.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series531.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
146.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
30.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))
275.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify160.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (129.0ms)

IterNodesCost
07782336
140881998
250031985

prune603.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 14.5b

regimes77.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03943
14143
24143

end0.0ms

sample859.0ms

Algorithm
intervals
Results
469.0ms2858×body1280valid
123.0ms4057×body80valid
88.0ms626×body640valid
28.0ms318×body320valid
8.0ms141×body160valid