Details

Time bar (total: 40.2s)

sample451.0ms

Algorithm
intervals
Results
169.0ms57×body1280valid
77.0ms42×body640valid
72.0ms31×body320valid
38.0ms140×body80valid
9.0ms42×body80nan
4.0ms8×body160valid

simplify3.4s

Counts
1 → 1
Iterations
IterNodes
done5001
62738
5849
4325
3161
290
143
020

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (tan B)) x)
0.3b
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
0.3b
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
20.8b
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
214×times-frac
133×add-sqr-sqrt
128×*-un-lft-identity add-cube-cbrt
51×unpow-prod-down
34×associate-/r*
30×pow-unpow
25×add-exp-log
17×sqr-pow
16×add-cbrt-cube
14×associate-*l*
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-*r* pow-exp
2×clear-num frac-2neg prod-exp cbrt-unprod unswap-sqr
1×neg-mul-1 pow-pow pow-prod-down associate-*l/ tan-quot *-commutative
Counts
4 → 262
Calls
4 calls:
22.0ms
(* (/ 1.0 (tan B)) x)
13.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
13.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
15.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (/ 1.0 (tan B)) x)
812.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
322.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
235.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify3.4s

Counts
274 → 274
Iterations
IterNodes
done5001
24165
11314
0497

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 1.0 x) (tan B))
0.3b
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
0.3b
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
20.8b
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
207×times-frac
122×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
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×neg-sub0 cbrt-undiv pow-neg pow-sub
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp clear-num frac-2neg pow-exp
1×neg-mul-1 pow-pow prod-exp tan-quot cbrt-unprod
Counts
4 → 251
Calls
4 calls:
25.0ms
(/ (* 1.0 x) (tan B))
17.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
9.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
6.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ (* 1.0 x) (tan B))
449.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
355.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
248.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify3.7s

Counts
263 → 263
Iterations
IterNodes
done5001
24316
11302
0481

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 1.0 x) (tan B))
0.2b
(* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0)))
0.6b
(* (/ 1 (sin B)) (* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))))
20.8b
(pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
42×add-sqr-sqrt times-frac
37×*-un-lft-identity add-cube-cbrt
34×pow-unpow
32×prod-exp
23×add-cbrt-cube
16×associate-*l*
10×div-exp
9×distribute-lft-neg-in distribute-rgt-neg-in associate-*r/
8×associate-*r* cbrt-unprod
7×pow1 pow-neg unpow-prod-down distribute-frac-neg
6×pow-to-exp pow-exp
4×neg-sub0 expm1-log1p-u cbrt-undiv rec-exp 1-exp div-sub log1p-expm1-u pow-sub add-log-exp
3×frac-times associate-/r* neg-mul-1 un-div-inv div-inv unswap-sqr sqr-pow
2×*-commutative
1×clear-num pow-pow frac-2neg pow-prod-down associate-*l/ tan-quot associate-/r/ associate-/l*
Counts
4 → 158
Calls
4 calls:
16.0ms
(/ (* 1.0 x) (tan B))
21.0ms
(* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0)))
65.0ms
(* (/ 1 (sin B)) (* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))))
6.0ms
(pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
170.0ms
(/ (* 1.0 x) (tan B))
368.0ms
(* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0)))
506.0ms
(* (/ 1 (sin B)) (* F (pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))))
219.0ms
(pow (fma F F (fma 2.0 x 2.0)) (/ (- 1.0) 2.0))

simplify2.4s

Counts
170 → 170
Iterations
IterNodes
done5001
22737
1899
0326

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 1.0 x) (tan B))
0.2b
(* (sin B) (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)))
0.3b
(/ F (* (sin B) (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))))
20.8b
(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
24×add-sqr-sqrt
19×*-un-lft-identity add-cube-cbrt
16×add-cbrt-cube
15×times-frac
13×pow-unpow
7×unpow-prod-down associate-*r* prod-exp
6×div-exp
5×pow1
4×expm1-log1p-u cbrt-undiv associate-/r* log1p-expm1-u associate-/l* add-log-exp
3×pow-to-exp associate-*l* pow-exp cbrt-unprod div-inv unswap-sqr sqr-pow
2×clear-num frac-2neg
1×pow-pow tan-quot associate-/r/ *-commutative
Counts
4 → 105
Calls
4 calls:
15.0ms
(/ (* 1.0 x) (tan B))
22.0ms
(* (sin B) (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)))
9.0ms
(/ F (* (sin B) (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))))
4.0ms
(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ (* 1.0 x) (tan B))
368.0ms
(* (sin B) (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0)))
491.0ms
(/ F (* (sin B) (pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))))
186.0ms
(pow (fma F F (fma 2.0 x 2.0)) (/ 1.0 2.0))

simplify2.4s

Counts
117 → 117
Iterations
IterNodes
done5002
22189
1665
0257

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes579.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 11.1b

bsearch617.0ms

Steps
ItersRangePoint
11
1.710610704328059e-08
5484521745298321.0
662194.5861720684
9
-5.854806215004893e+51
-6.062265789515972e+43
-6.178111444164113e+43

simplify12.0ms

Iterations
IterNodes
done40
140
035

end0.0ms

sample10.2s

Algorithm
intervals
Results
3.9s1618×body1280valid
2.6s1415×body640valid
1.5s4845×body80valid
1.0s670×body320valid
436.0ms1577×body80nan
239.0ms364×body160valid