Details

Time bar (total: 10.8s)

sample76.0ms

Algorithm
intervals
Results
26.0ms85×body1280valid
17.0ms288×body80valid
12.0ms61×body640valid
3.0ms21×body320valid
1.0ms11×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

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))
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series346.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(fma a1 a1 (* a2 a2))
108.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
206.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0205467
11002399
25001393

prune183.0ms

Filtered
70 candidates to 49 candidates (70.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
36×add-exp-log cbrt-prod add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
23×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* fma-udef
2×frac-2neg clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
4 → 137
Calls
4 calls:
0.0ms
(fma a1 a1 (* a2 a2))
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
7.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
14.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
35.0ms
(fma a1 a1 (* a2 a2))
103.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
827.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
212.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify71.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04912250
125351935
250011905

prune413.0ms

Filtered
149 candidates to 104 candidates (69.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
0.2b
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
241×add-exp-log
180×cbrt-prod
171×times-frac
117×add-sqr-sqrt
100×div-exp
97×prod-exp
83×*-un-lft-identity
78×add-cube-cbrt
77×add-cbrt-cube
67×associate-*r*
52×cbrt-undiv
45×cbrt-unprod
36×sqrt-prod
29×div-inv
16×unswap-sqr
13×associate-/r*
12×rec-exp 1-exp
10×associate-*l*
8×pow1
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative fma-udef
1×distribute-rgt-in frac-times distribute-lft-in associate-*r/ associate-*l/ associate-/l/
Counts
4 → 305
Calls
4 calls:
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
7.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
12.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
78.0ms
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
632.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
776.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
220.0ms
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

simplify75.0ms

Algorithm
egg-herbie
Counts
317 → 317
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013317346
150016415

prune965.0ms

Filtered
317 candidates to 198 candidates (62.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b
(/ (/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
0.2b
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
5.8b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
360×add-exp-log
180×cbrt-prod
171×times-frac
161×prod-exp
142×div-exp
118×add-cbrt-cube
115×add-sqr-sqrt
82×*-un-lft-identity
77×add-cube-cbrt cbrt-unprod
74×cbrt-undiv
64×associate-*r*
39×sqrt-prod
29×div-inv
16×rec-exp 1-exp
15×unswap-sqr
13×associate-/r*
7×pow1 associate-*l*
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef hypot-def associate-/l/
Counts
4 → 327
Calls
4 calls:
11.0ms
(/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
18.0ms
(/ (/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
90.0ms
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
1.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
628.0ms
(/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
772.0ms
(/ (/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
265.0ms
(* (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (* (* (hypot a1 a2) (cos th)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))
49.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify94.0ms

Algorithm
egg-herbie
Counts
339 → 339
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
014779149
150017799

prune1.1s

Filtered
339 candidates to 202 candidates (59.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes205.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02626
12626

end0.0ms

sample2.2s

Algorithm
intervals
Results
796.0ms2494×body1280valid
466.0ms2151×body640valid
383.0ms8160×body80valid
156.0ms1039×body320valid
55.0ms504×body160valid