Details

Time bar (total: 7.0s)

sample32.0ms

Algorithm
intervals
Results
16.0ms97×body1280valid
4.0ms132×body80valid
2.0ms16×body640valid
1.0ms9×body320valid
0.0ms2×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: 14.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(hypot 1.0 x)
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
6×add-exp-log add-cbrt-cube
4×pow1
3×associate-/r* associate-/l*
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num sum-log flip-- flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(hypot 1.0 x)
6.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
1.0ms
(hypot 1.0 x)
32.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
88.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
0204408
1643378
21990376
35001375

prune152.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.3b

localize13.0ms

Local error

Found 4 expressions with local error:

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)))))))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.3b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite30.0ms

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))
17.0ms
(/ (- (* 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)))))))
2.0ms
(+ 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))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
164.0ms
(/ (- (* 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)))))))
76.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
38.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify60.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04231277
116411179
250011174

prune288.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

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)))))))
1.3b
(- (/ (* 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
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:
2.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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))))))))

series640.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
73.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
154.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
331.0ms
(- (/ (* 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))))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03731324
115361171
250021142

prune220.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 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)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.5b
(/ (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (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)
1.3b
(- (/ (* 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))) (/ (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
149×*-un-lft-identity
118×times-frac
50×distribute-lft-out
49×add-sqr-sqrt
47×add-cube-cbrt
44×unpow-prod-down cube-prod
40×associate-/r*
28×add-exp-log add-cbrt-cube
27×associate-*r/
19×associate-/r/
14×flip3-+ sqrt-div flip-+
13×frac-sub
12×cbrt-undiv div-exp
10×sum-cubes associate-/l*
8×pow1
6×add-log-exp
4×flip3-- pow-pow prod-exp flip-- cbrt-unprod div-inv
3×pow-unpow associate-/l/
2×cube-div frac-2neg sqrt-pow1 clear-num sqrt-prod
1×cube-mult pow-to-exp sub-neg pow1/2 diff-log unpow3 pow-prod-down pow-exp sqrt-pow2 distribute-lft-out-- rem-cube-cbrt difference-of-squares sqr-pow
Counts
4 → 204
Calls
4 calls:
56.0ms
(/ (* 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)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
59.0ms
(/ (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
8.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
121.0ms
(- (/ (* 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))) (/ (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))

series3.0s

Counts
4 → 12
Calls
4 calls:
602.0ms
(/ (* 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)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
408.0ms
(/ (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
330.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.6s
(- (/ (* 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))) (/ (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))

simplify110.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
012117504
150017005

prune672.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.0b

regimes80.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.9b and baseline of 15.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037110
137110

end0.0ms

sample838.0ms

Algorithm
intervals
Results
486.0ms2884×body1280valid
120.0ms4073×body80valid
85.0ms599×body640valid
27.0ms302×body320valid
8.0ms142×body160valid