Details

Time bar (total: 38.3s)

sample864.0ms

Algorithm
intervals
Results
621.0ms44×body640valid
66.0ms52×body1280valid
37.0ms154×body80valid
15.0ms17×body320valid
9.0ms60×body80nan
4.0ms11×body160valid

simplify3.0s

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.2b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
0.3b
(* (/ 1.0 (tan B)) x)
0.4b
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
18.4b
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite105.0ms

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:
24.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
29.0ms
(* (/ 1.0 (tan B)) x)
10.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
9.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
439.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
121.0ms
(* (/ 1.0 (tan B)) x)
371.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
218.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify3.9s

Counts
274 → 274
Iterations
IterNodes
done5004
24220
11302
0497

prune2.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
0.2b
(/ F (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
0.3b
(* (/ 1.0 (tan B)) x)
18.4b
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
25×*-un-lft-identity add-exp-log add-cube-cbrt
22×times-frac
17×associate-*l*
16×add-cbrt-cube
13×pow-unpow
10×associate-*r*
8×prod-exp
7×pow1 unpow-prod-down
5×div-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×pow-to-exp cbrt-undiv pow-exp div-inv associate-/l* sqr-pow
2×*-commutative
1×clear-num associate-/r* pow-pow frac-2neg pow-prod-down associate-*l/ tan-quot associate-/r/
Counts
4 → 116
Calls
4 calls:
25.0ms
(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
17.0ms
(/ F (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
16.0ms
(* (/ 1.0 (tan B)) x)
7.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
490.0ms
(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
487.0ms
(/ F (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
142.0ms
(* (/ 1.0 (tan B)) x)
195.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify2.9s

Counts
128 → 128
Iterations
IterNodes
done5000
22186
1675
0273

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 1.0 x) (tan B))
0.2b
(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
0.2b
(/ F (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
18.4b
(pow (fma F F (fma x 2.0 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))
14.0ms
(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
16.0ms
(/ F (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
7.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ (* 1.0 x) (tan B))
386.0ms
(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
489.0ms
(/ F (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
179.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify2.4s

Counts
117 → 117
Iterations
IterNodes
done5000
22187
1665
0257

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
27×add-sqr-sqrt
20×*-un-lft-identity add-cbrt-cube add-cube-cbrt
15×times-frac
13×pow-unpow
10×associate-*r* associate-*l* prod-exp
7×pow1 unpow-prod-down
6×div-exp cbrt-unprod
4×expm1-log1p-u cbrt-undiv log1p-expm1-u add-log-exp unswap-sqr
3×pow-to-exp pow-exp div-inv associate-/l* sqr-pow
2×*-commutative
1×clear-num associate-/r* pow-pow frac-2neg pow-prod-down associate-*l/
Counts
4 → 110
Calls
4 calls:
24.0ms
(* (/ (* 1.0 x) (sin B)) (cos B))
17.0ms
(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
9.0ms
(/ F (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
3.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (/ (* 1.0 x) (sin B)) (cos B))
395.0ms
(* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
518.0ms
(/ F (* (sin B) (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
225.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify2.4s

Counts
122 → 122
Iterations
IterNodes
done5015
22667
1684
0267

prune959.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes498.0ms

Accuracy

98% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.3b

bsearch610.0ms

Steps
ItersRangePoint
10
0.019618473278136022
56593606606875.23
51126349.92642568
8
-2.4005474304550297e+53
-6.753921075725816e+49
-4.105717990897647e+51

simplify21.0ms

Iterations
IterNodes
done39
139
034

end0.0ms

sample10.4s

Algorithm
intervals
Results
3.8s1681×body1280valid
2.7s1374×body640valid
2.0s4727×body80valid
655.0ms721×body320valid
528.0ms1635×body80nan
248.0ms358×body160valid