Details

Time bar (total: 19.2s)

sample464.0ms

Algorithm
intervals
Results
74.0ms52×body1280valid
27.0ms42×body640valid
22.0ms156×body80valid
9.0ms20×body320valid
5.0ms50×body80nan
4.0ms14×body160valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
02027
14326
29124
316924
436624
591524
6321924
done500124

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (tan B))
0.3b
(* x (/ 1.0 (tan B)))
7.0b
(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
18.6b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
37×times-frac
36×add-cube-cbrt *-un-lft-identity
30×pow-unpow
14×associate-*r*
13×distribute-lft-neg-in distribute-rgt-neg-in
12×add-exp-log
11×add-cbrt-cube
7×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×unpow-prod-down associate-*l* associate-/r* associate-/l*
2×tan-quot cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×neg-sub0 pow-to-exp pow-neg neg-mul-1 pow-pow frac-2neg associate-*r/ pow-prod-down pow-exp clear-num *-commutative fma-udef pow-sub sqr-pow
Counts
4 → 123
Calls
4 calls:
6.0ms
(/ 1.0 (tan B))
18.0ms
(* x (/ 1.0 (tan B)))
0.0ms
(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
9.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series863.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 1.0 (tan B))
122.0ms
(* x (/ 1.0 (tan B)))
356.0ms
(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* x (/ 1.0 (tan B)))))
347.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.2s

Counts
135 → 135
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
02851919
16901835
217681712
348561677
done50001677

prune658.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 13.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ F (sin B))
0.2b
(/ (* x (cos B)) (sin B))
7.0b
(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
18.6b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity times-frac
13×distribute-lft-neg-in distribute-rgt-neg-in
12×add-exp-log
11×add-cbrt-cube
6×associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×cbrt-undiv unpow-prod-down div-exp
2×frac-2neg clear-num
1×neg-sub0 pow-to-exp pow-neg neg-mul-1 pow-pow pow-exp prod-exp cbrt-unprod fma-udef pow-sub sqr-pow
Counts
4 → 110
Calls
4 calls:
5.0ms
(/ F (sin B))
12.0ms
(/ (* x (cos B)) (sin B))
0.0ms
(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
9.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series849.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ F (sin B))
104.0ms
(/ (* x (cos B)) (sin B))
365.0ms
(fma (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
328.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify921.0ms

Counts
122 → 122
Iterations

Useful iterations: done (912.0ms)

IterNodesCost
02801858
16611785
217751651
done50001615

prune636.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* x (cos B)) (sin B))
0.2b
(pow (fma 2.0 x (fma F F 2.0)) -1)
7.0b
(fma (pow (pow (fma 2.0 x (fma F F 2.0)) -1) (/ 1.0 2.0)) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
18.4b
(pow (pow (fma 2.0 x (fma F F 2.0)) -1) (/ 1.0 2.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×pow-unpow
13×unpow-prod-down
12×add-exp-log times-frac
9×add-cbrt-cube
5×pow1 pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp associate-/r* sqr-pow
2×cbrt-undiv pow-pow div-exp div-inv
1×unpow-1 frac-2neg prod-exp clear-num cbrt-unprod fma-udef associate-/l*
Counts
4 → 88
Calls
4 calls:
12.0ms
(/ (* x (cos B)) (sin B))
6.0ms
(pow (fma 2.0 x (fma F F 2.0)) -1)
0.0ms
(fma (pow (pow (fma 2.0 x (fma F F 2.0)) -1) (/ 1.0 2.0)) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
7.0ms
(pow (pow (fma 2.0 x (fma F F 2.0)) -1) (/ 1.0 2.0))

series832.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (* x (cos B)) (sin B))
92.0ms
(pow (fma 2.0 x (fma F F 2.0)) -1)
325.0ms
(fma (pow (pow (fma 2.0 x (fma F F 2.0)) -1) (/ 1.0 2.0)) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
311.0ms
(pow (pow (fma 2.0 x (fma F F 2.0)) -1) (/ 1.0 2.0))

simplify837.0ms

Counts
100 → 100
Iterations

Useful iterations: done (834.0ms)

IterNodesCost
02361802
15811723
216171592
done50001549

prune515.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* x (cos B)) (sin B))
0.4b
(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
7.0b
(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
18.6b
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
30×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
19×add-exp-log
15×unpow-prod-down
13×pow-unpow
11×add-cbrt-cube
10×associate-/r*
8×div-exp
5×pow1 sqr-pow
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u associate-/l* add-log-exp
3×cbrt-undiv rec-exp 1-exp div-inv
2×frac-2neg clear-num
1×pow-flip pow-pow prod-exp cbrt-unprod fma-udef inv-pow
Counts
4 → 117
Calls
4 calls:
12.0ms
(/ (* x (cos B)) (sin B))
12.0ms
(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
0.0ms
(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
4.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (* x (cos B)) (sin B))
868.0ms
(/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
451.0ms
(fma (/ 1 (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (/ F (sin B)) (- (* 1.0 (/ (* x (cos B)) (sin B)))))
322.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.1s

Counts
129 → 129
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03172723
17482557
220312324
done50002280

prune456.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.6b

regimes282.0ms

Accuracy

0% (0.4b remaining)

Error of 14.0b against oracle of 13.5b and baseline of 14.0b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01827
12627
23427
33527
done3527

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s1673×body1280valid
869.0ms1364×body640valid
632.0ms4733×body80valid
301.0ms709×body320valid
160.0ms1641×body80nan
102.0ms350×body160valid