Details

Time bar (total: 9.2s)

sample77.0ms

Algorithm
intervals
Results
27.0ms83×body1280valid
15.0ms69×body640valid
13.0ms256×body80valid
5.0ms30×body320valid
1.0ms11×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.3b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))
0.4b
(* (cos th) (fma a1 a1 (* a2 a2)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* fma-udef log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 61
Calls
3 calls:
0.0ms
(fma a1 a1 (* a2 a2))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))
4.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))

series367.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(fma a1 a1 (* a2 a2))
215.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))
112.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))

simplify35.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0205467
11002399
25001393

prune200.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (hypot a1 a2))
0.1b
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
0.3b
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
6.6b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×pow1 sqrt-prod
9×associate-*r*
7×prod-exp cbrt-unprod
6×times-frac associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×*-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num fma-udef hypot-def div-inv associate-/l* unswap-sqr
Counts
4 → 90
Calls
4 calls:
3.0ms
(* (cos th) (hypot a1 a2))
9.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
10.0ms
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (cos th) (hypot a1 a2))
186.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
298.0ms
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (sqrt 2.0))
48.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify53.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0305785
11700625
25001573

prune497.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (hypot a1 a2))
0.2b
(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
0.2b
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-sqr-sqrt
59×times-frac
48×add-cube-cbrt *-un-lft-identity
44×cbrt-prod
43×add-cbrt-cube
34×associate-*r*
23×prod-exp cbrt-unprod
22×sqrt-prod
18×cbrt-undiv div-exp
10×associate-/r*
8×pow1 associate-*l*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative
1×frac-times associate-*r/ associate-*l/
Counts
4 → 170
Calls
4 calls:
3.0ms
(* (cos th) (hypot a1 a2))
4.0ms
(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
7.0ms
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
36.0ms
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (cos th) (hypot a1 a2))
287.0ms
(/ (hypot a1 a2) (cbrt (sqrt 2.0)))
567.0ms
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
245.0ms
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (hypot a1 a2) (cbrt (sqrt 2.0))))

simplify110.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
06362325
137671967
250011857

prune525.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b
(/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
0.3b
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
0.4b
(/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
235×cbrt-prod
144×add-sqr-sqrt
132×add-exp-log
118×add-cube-cbrt *-un-lft-identity
88×associate-*r*
80×add-cbrt-cube
52×cbrt-undiv div-exp
47×prod-exp sqrt-prod cbrt-unprod
30×div-inv
14×associate-/r*
11×associate-/l*
9×unswap-sqr
6×pow1
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 324
Calls
4 calls:
7.0ms
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
13.0ms
(/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
69.0ms
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
6.0ms
(/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
572.0ms
(/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
288.0ms
(/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))
259.0ms
(* (/ (* (cos th) (hypot a1 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
381.0ms
(/ (hypot a1 a2) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify77.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013217574
150016396

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes140.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01823
11823

end0.0ms

sample2.2s

Algorithm
intervals
Results
808.0ms2485×body1280valid
461.0ms2094×body640valid
420.0ms7973×body80valid
158.0ms1004×body320valid
56.0ms506×body160valid