Details

Time bar (total: 5.4s)

sample35.0ms

Algorithm
intervals
Results
17.0ms87×body1280valid
4.0ms131×body80valid
3.0ms23×body640valid
1.0ms10×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: 15.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×add-exp-log add-cube-cbrt sqrt-pow1 sqrt-div associate-*r/ add-cbrt-cube
1×sub-neg flip3-- flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
2 → 27
Calls
2 calls:
11.0ms
(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))))))

series146.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(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))))))

simplify43.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0137276
1348263
21405261
35002261

prune72.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.8b

localize14.0ms

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

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
13×add-sqr-sqrt add-cube-cbrt
12×times-frac
10×associate-*r/
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
5×distribute-lft-out
4×flip3-- associate--l+ associate-/r* frac-sub flip-- associate-/l/
3×sub-neg flip3-+ flip-+ associate-/l*
2×distribute-rgt-in distribute-lft-in sqrt-pow1 sqrt-div associate-/r/
1×cbrt-undiv +-commutative frac-2neg pow1/2 diff-log div-sub div-exp pow-prod-down clear-num sum-log sqrt-prod div-inv
Counts
4 → 81
Calls
4 calls:
5.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
11.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
42.0ms
(/ (- (* 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)))))))
15.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
68.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
144.0ms
(/ (- (* 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)))))))
32.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify52.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04031245
114281156
250011151

prune237.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log add-cbrt-cube
12×*-un-lft-identity
10×pow1
8×add-sqr-sqrt
6×add-cube-cbrt associate-/r/ add-log-exp
5×flip3-+ associate-*r/ flip-+
4×cbrt-undiv sqrt-pow1 times-frac sqrt-div div-exp associate-/r*
3×distribute-rgt-out-- div-inv
2×pow1/2 pow-prod-down prod-exp sqrt-prod cbrt-unprod distribute-lft-out
1×sub-neg flip3-- frac-2neg diff-log clear-num frac-sub flip-- associate-/l/ associate-/l* distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 73
Calls
4 calls:
11.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
19.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
69.0ms
(- (/ (* 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))))))))

series575.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
71.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
143.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
297.0ms
(- (/ (* 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))))))))

simplify55.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04001251
116341129
250011102

prune234.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize25.0ms

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))))
2.5b
(- (* (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)))))))

rewrite386.0ms

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:
13.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
14.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
248.0ms
(- (/ (* 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))))
105.0ms
(- (* (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)))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
132.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
128.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
742.0ms
(- (/ (* 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))))
257.0ms
(- (* (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)))))))

simplify108.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
06922604
128702284
250012276

prune449.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.6b

regimes261.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04376
14376

end0.0ms

sample872.0ms

Algorithm
intervals
Results
492.0ms2911×body1280valid
120.0ms4038×body80valid
76.0ms587×body640valid
28.0ms318×body320valid
8.0ms146×body160valid