Details

Time bar (total: 5.8s)

sample58.0ms

Algorithm
intervals
Results
33.0ms93×body1280valid
7.0ms119×body80valid
7.0ms26×body640valid
2.0ms11×body320valid
1.0ms7×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: 18.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
2.2b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×times-frac
5×add-exp-log add-cbrt-cube add-log-exp
3×pow1 associate-/r* associate-/l*
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
3 → 48
Calls
3 calls:
0.0ms
(hypot 1.0 x)
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series93.0ms

Counts
3 → 9
Calls
3 calls:
1.0ms
(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))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0158331
1485306
21410304
35001304

prune131.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (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)))))))
1.6b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite31.0ms

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:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
18.0ms
(/ (- (* 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 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series206.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
162.0ms
(/ (- (* 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)))))))
33.0ms
(- (* 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 (41.0ms)

IterNodesCost
04071275
115941181
250011177

prune335.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.1b
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.7b
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
24×add-sqr-sqrt
22×add-cube-cbrt times-frac
17×add-exp-log add-cbrt-cube
10×associate-/r*
7×associate-/l*
6×cbrt-undiv div-exp associate-/r/ add-log-exp
5×div-inv
4×pow1
3×distribute-rgt-out-- frac-2neg flip3-+ clear-num flip-+
2×prod-exp cbrt-unprod distribute-lft-out
1×sub-neg flip3-- diff-log associate-*r/ frac-sub flip-- associate-/l/ distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 101
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
41.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series489.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
153.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
325.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04011320
117401175
250011148

prune333.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.7b
(- (/ (* 1.0 (- 1.0 0.5)) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
2.4b
(- (* (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)))))))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
78×associate-*r/
52×sqrt-div
28×flip3-+ flip-+
17×frac-sub
12×pow1 add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
8×frac-times unpow-prod-down pow-pow cube-prod add-log-exp
6×add-exp-log pow-unpow associate-*l/ add-cbrt-cube
5×sub-div
4×cube-div distribute-rgt-out-- sqrt-pow1 sqrt-prod associate-/r/
2×cube-mult pow-to-exp sub-neg flip3-- pow1/2 diff-log unpow3 pow-prod-down pow-exp sqrt-pow2 flip-- div-inv rem-cube-cbrt sqr-pow
1×distribute-lft-out-- difference-of-squares
Counts
4 → 114
Calls
4 calls:
8.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
9.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
184.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
59.0ms
(- (* (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)))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
145.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
139.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
809.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))))
277.0ms
(- (* (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)))))))

simplify112.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
06922604
128702284
250012276

prune462.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.5b

regimes155.0ms

Accuracy

0% (0.3b remaining)

Error of 15.0b against oracle of 14.7b and baseline of 15.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03426
13426

end0.0ms

sample1.5s

Algorithm
intervals
Results
908.0ms2856×body1280valid
239.0ms4062×body80valid
161.0ms616×body640valid
56.0ms314×body320valid
18.0ms152×body160valid