Details

Time bar (total: 3.9s)

sample31.0ms

Algorithm
intervals
Results
15.0ms90×body1280valid
4.0ms131×body80valid
2.0ms16×body640valid
1.0ms10×body320valid
1.0ms9×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: 14.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(hypot 1.0 x)
2.5b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
7×pow1
6×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
4 → 61
Calls
4 calls:
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(hypot 1.0 x)
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series165.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(/ 1.0 (hypot 1.0 x))
1.0ms
(hypot 1.0 x)
86.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0201433
1602413
22000411
35001411

prune180.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.0b

localize16.0ms

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)))))))
2.0b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite33.0ms

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))
19.0ms
(/ (- (* 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))))

series205.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
160.0ms
(/ (- (* 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)))))))
34.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify52.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04071275
115941181
250011177

prune337.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
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 (- (* (- (* 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)))
2.0b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
36×add-exp-log add-cbrt-cube
35×*-un-lft-identity
34×times-frac
22×associate-*l/
21×add-sqr-sqrt
19×add-cube-cbrt
14×associate-*r/ associate-/r/
13×cbrt-undiv div-exp
11×flip3-+ flip-+
9×prod-exp cbrt-unprod
8×frac-sub distribute-lft-out associate-/l*
7×flip3-- flip-- div-inv associate-/l/
6×pow1 add-log-exp
5×associate-/r*
4×associate-*l*
3×associate-*r*
2×frac-2neg clear-num associate--r+
1×distribute-rgt-in sub-neg distribute-lft-in diff-log pow-prod-down *-commutative difference-of-squares unswap-sqr
Counts
4 → 130
Calls
4 calls:
10.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
19.0ms
(/ (/ (* 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)))))))
21.0ms
(/ (* 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)))
8.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
215.0ms
(/ (/ (* 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)))))))
63.0ms
(/ (* 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)))
32.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify119.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
08072954
144222532
250032532

prune455.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
0.0b
(* (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))) (/ (- 1.0 0.5) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)))
2.0b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log add-cbrt-cube
35×*-un-lft-identity
32×add-sqr-sqrt
29×associate-*r*
23×times-frac prod-exp cbrt-unprod
17×cbrt-undiv add-cube-cbrt div-exp
15×associate-*r/ associate-*l/
11×associate-*l*
9×flip3-- flip--
8×pow1 frac-sub
6×associate-/r/ associate-/l/ add-log-exp
5×flip3-+ flip-+ distribute-lft-out difference-of-squares
4×distribute-lft-out--
3×div-inv unswap-sqr
2×pow-prod-down *-commutative associate--r+
1×distribute-rgt-in frac-times sub-neg frac-2neg distribute-lft-in diff-log clear-num associate-/r* associate-/l*
Counts
4 → 135
Calls
4 calls:
10.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
59.0ms
(* (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))) (/ (- 1.0 0.5) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
22.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)))
9.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
216.0ms
(* (/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))) (/ (- 1.0 0.5) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
64.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)))
32.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08883276
150012608

prune425.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.0b

regimes62.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03022
13222
23222

end0.0ms

sample798.0ms

Algorithm
intervals
Results
439.0ms2741×body1280valid
123.0ms4105×body80valid
90.0ms665×body640valid
28.0ms318×body320valid
10.0ms171×body160valid