Details

Time bar (total: 7.7s)

sample92.0ms

Algorithm
intervals
Results
37.0ms104×body1280valid
13.0ms279×body80valid
13.0ms61×body640valid
6.0ms39×body320valid
1.0ms13×body160valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune9.0ms

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))

rewrite26.0ms

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))
12.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
12.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series338.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(fma a1 a1 (* a2 a2))
101.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
205.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0205467
11002399
25001393

prune183.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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)))

rewrite58.0ms

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))
11.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
17.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
25.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series969.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(fma a1 a1 (* a2 a2))
102.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
628.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
207.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify82.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
04912250
125351935
250011905

prune426.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
0.2b
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
6.4b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
56×times-frac
40×add-cbrt-cube
36×cbrt-prod add-sqr-sqrt
35×add-cube-cbrt *-un-lft-identity
24×sqrt-prod
21×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
12×div-inv
10×pow1 associate-/r*
6×associate-*r* associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative fma-udef hypot-def associate-/l/
Counts
4 → 152
Calls
4 calls:
23.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
28.0ms
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
38.0ms
(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
2.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
382.0ms
(* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2))))
712.0ms
(/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
279.0ms
(/ (/ (* (* (cos th) (hypot a1 a2)) (sqrt (fma a1 a1 (* a2 a2)))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
40.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify92.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05682920
132202380
250012274

prune462.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
93×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×sqrt-prod
25×associate-/r*
10×add-exp-log add-cbrt-cube
9×associate-/l*
6×div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×associate-/r/ fma-udef
Counts
3 → 159
Calls
3 calls:
0.0ms
(fma a1 a1 (* a2 a2))
15.0ms
(/ (cos th) (/ (sqrt 2.0) (fma a1 a1 (* a2 a2))))
6.0ms
(/ (sqrt 2.0) (fma a1 a1 (* a2 a2)))

series299.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(fma a1 a1 (* a2 a2))
192.0ms
(/ (cos th) (/ (sqrt 2.0) (fma a1 a1 (* a2 a2))))
76.0ms
(/ (sqrt 2.0) (fma a1 a1 (* a2 a2)))

simplify67.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04801844
122331642
250011633

prune411.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes170.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01816
11816

end0.0ms

sample2.4s

Algorithm
intervals
Results
826.0ms2518×body1280valid
461.0ms2019×body640valid
399.0ms8000×body80valid
168.0ms1068×body320valid
56.0ms535×body160valid