Details

Time bar (total: 38.6s)

sample400.0ms

Algorithm
intervals
Results
128.0ms44×body1280valid
61.0ms51×body640valid
40.0ms140×body80valid
28.0ms35×body320valid
12.0ms59×body80nan
7.0ms14×body160valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
02027
14326
29124
316924
436624
591524
6321924
done500124

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ F (sin B))
0.3b
(* x (/ 1.0 (tan B)))
5.5b
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
14.3b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite484.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
49×times-frac
45×add-cube-cbrt *-un-lft-identity
30×pow-unpow
25×add-exp-log
21×associate-*r*
16×associate-*l* add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
8×unpow-prod-down prod-exp unswap-sqr
7×pow1
5×div-exp div-inv
4×expm1-log1p-u pow-neg cbrt-unprod log1p-expm1-u add-log-exp sqr-pow
3×cbrt-undiv neg-sub0 pow-to-exp associate-*r/ pow-exp associate-/r* associate-/l* pow-sub
2×frac-times *-commutative
1×tan-quot neg-mul-1 pow-pow frac-2neg pow-prod-down associate-*l/ clear-num associate-/r/ un-div-inv
Counts
4 → 162
Calls
4 calls:
11.0ms
(/ F (sin B))
38.0ms
(* x (/ 1.0 (tan B)))
330.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
96.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series994.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ F (sin B))
170.0ms
(* x (/ 1.0 (tan B)))
502.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
242.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.6s

Counts
174 → 174
Iterations

Useful iterations: 2 (526.0ms)

IterNodesCost
03112820
17602540
221072283
done50002283

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ F (/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))))
0.3b
(* x (/ 1.0 (tan B)))
0.4b
(/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
14.3b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
214×times-frac
133×add-sqr-sqrt
128×add-cube-cbrt *-un-lft-identity
51×unpow-prod-down
34×associate-/r*
30×pow-unpow
25×add-exp-log
17×sqr-pow
16×add-cbrt-cube
14×associate-*r*
13×distribute-lft-neg-in distribute-rgt-neg-in
12×associate-/r/
11×div-exp
9×div-inv
7×pow1
6×neg-sub0 pow-neg associate-/l* pow-sub
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp associate-*l* pow-exp
2×frac-2neg prod-exp clear-num cbrt-unprod unswap-sqr
1×tan-quot neg-mul-1 pow-pow associate-*r/ pow-prod-down *-commutative
Counts
4 → 262
Calls
4 calls:
20.0ms
(/ F (/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))))
35.0ms
(* x (/ 1.0 (tan B)))
19.0ms
(/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
7.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series2.3s

Counts
4 → 12
Calls
4 calls:
511.0ms
(/ F (/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))))
178.0ms
(* x (/ 1.0 (tan B)))
1.1s
(/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
555.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.3s

Counts
274 → 274
Iterations

Useful iterations: done (2.3s)

IterNodesCost
05256848
111986454
236866220
done50016216

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* x 1.0) (tan B))
0.2b
(/ F (/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))))
0.4b
(/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
14.3b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
207×times-frac
122×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
51×unpow-prod-down
37×associate-/r*
30×pow-unpow
25×add-exp-log
17×sqr-pow
16×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
12×div-exp associate-/r/
9×div-inv
7×associate-/l*
6×cbrt-undiv neg-sub0 pow-neg pow-sub
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp frac-2neg pow-exp clear-num
1×tan-quot neg-mul-1 pow-pow prod-exp cbrt-unprod
Counts
4 → 251
Calls
4 calls:
11.0ms
(/ (* x 1.0) (tan B))
34.0ms
(/ F (/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))))
11.0ms
(/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
7.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series2.5s

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (* x 1.0) (tan B))
480.0ms
(/ F (/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))))
1.0s
(/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
835.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.4s

Counts
263 → 263
Iterations

Useful iterations: done (2.4s)

IterNodesCost
05106750
111546366
236476132
done50006128

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ F (/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))))
0.2b
(* (/ (* x 1.0) (sin B)) (cos B))
0.4b
(/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
14.3b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
207×times-frac
125×add-sqr-sqrt
123×add-cube-cbrt *-un-lft-identity
51×unpow-prod-down
34×associate-/r*
30×pow-unpow
29×add-exp-log
20×add-cbrt-cube
17×sqr-pow
13×distribute-lft-neg-in distribute-rgt-neg-in
12×div-exp
11×associate-/r/
9×div-inv
7×pow1 associate-*l*
6×cbrt-undiv neg-sub0 pow-neg associate-/l* pow-sub
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-to-exp associate-*r* pow-exp
2×frac-2neg clear-num
1×neg-mul-1 pow-pow pow-prod-down associate-*l/ *-commutative unswap-sqr
Counts
4 → 256
Calls
4 calls:
31.0ms
(/ F (/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))))
44.0ms
(* (/ (* x 1.0) (sin B)) (cos B))
21.0ms
(/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
15.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series2.2s

Counts
4 → 12
Calls
4 calls:
488.0ms
(/ F (/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))))
150.0ms
(* (/ (* x 1.0) (sin B)) (cos B))
1.0s
(/ (sin B) (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
540.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.4s

Counts
268 → 268
Iterations

Useful iterations: done (2.4s)

IterNodesCost
05206899
112036514
238796242
done50006238

prune1.9s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes355.0ms

Accuracy

98% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.4b

bsearch490.0ms

Steps
ItersRangePoint
6
1791.5919577634695
9556.682540875734
9401.995455885359
9
-5.063582918003288e+31
-5.452804783141298e+22
-1.4125977831190179e+23

simplify22.0ms

Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
04490
16484
27278
done7278

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.4s1688×body1280valid
2.0s1354×body640valid
1.8s4868×body80valid
700.0ms670×body320valid
285.0ms1632×body80nan
251.0ms346×body160valid