Details

Time bar (total: 5.2s)

sample31.0ms

Algorithm
intervals
Results
16.0ms98×body1280valid
4.0ms123×body80valid
3.0ms21×body640valid
1.0ms10×body320valid
0.0ms4×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: 14.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.4b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×times-frac
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
3 → 54
Calls
3 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(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))))))

series178.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
72.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
100.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0200410
1601393
21997391
35001391

prune138.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 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 (- 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)))))))
0.9b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt times-frac
8×add-exp-log associate-*r/ add-cbrt-cube add-log-exp
7×associate-/r*
6×associate-/l*
5×distribute-lft-out
4×pow1 flip3-- associate--l+ frac-sub flip-- associate-/l/
3×sub-neg
2×cbrt-undiv distribute-rgt-in frac-2neg distribute-lft-in flip3-+ div-exp clear-num associate-/r/ flip-+ div-inv
1×+-commutative diff-log div-sub sum-log
Counts
4 → 95
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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))))

series278.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
80.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
159.0ms
(/ (- (* 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))))

simplify54.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04231277
116411179
250011174

prune275.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.4b

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 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.2b
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.0b
(- (/ (* 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))))))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
13×add-exp-log add-cbrt-cube
10×add-log-exp
8×add-sqr-sqrt
6×add-cube-cbrt associate-/r/
5×flip3-+ flip-+
4×pow1 cbrt-undiv times-frac div-exp associate-/r* distribute-lft-out
3×distribute-rgt-out-- div-inv
2×+-commutative prod-exp sum-log cbrt-unprod
1×sub-neg flip3-- frac-2neg diff-log associate-*r/ clear-num frac-sub flip-- associate-/l/ associate-/l* distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 71
Calls
4 calls:
3.0ms
(+ 1.0 (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))))))
9.0ms
(/ (* 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))))))))

series635.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
79.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
151.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
326.0ms
(- (/ (* 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))))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03731324
115361171
250021142

prune218.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.2b

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)
1.0b
(- (/ (* 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))))
1.7b
(- (* (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)))))))

rewrite284.0ms

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)
10.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
197.0ms
(- (/ (* 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))))
62.0ms
(- (* (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:
138.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
135.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
779.0ms
(- (/ (* 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))))
274.0ms
(- (* (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)))))))

simplify109.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
06922604
128702284
250012276

prune442.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.2b

regimes89.0ms

Accuracy

0% (0.3b remaining)

Error of 14.6b against oracle of 14.4b and baseline of 14.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04376
14376

end0.0ms

sample823.0ms

Algorithm
intervals
Results
478.0ms2909×body1280valid
117.0ms4022×body80valid
81.0ms621×body640valid
26.0ms293×body320valid
9.0ms155×body160valid