Details

Time bar (total: 49.4s)

sample605.0ms

Algorithm
intervals
Results
134.0ms52×body1280valid
81.0ms63×body80nan
72.0ms59×body640valid
39.0ms139×body80valid
13.0ms16×body320valid
5.0ms10×body160valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
020850
143825
291760
3169760
4384760
51755760
done5000760

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.4b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
0.3b
(* x (/ 1.0 (tan B)))
0.3b
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
14.4b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
31×times-frac
30×pow-unpow
25×add-exp-log
17×associate-*r*
16×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-*l*
8×prod-exp
7×pow1 unpow-prod-down
5×div-exp unswap-sqr
4×expm1-log1p-u associate-*l/ cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×neg-sub0 pow-to-exp cbrt-undiv pow-neg associate-/r* pow-exp pow-sub sqr-pow
2×*-commutative associate-/l/
1×clear-num neg-mul-1 pow-pow frac-2neg pow-prod-down tan-quot associate-*r/ associate-/r/ associate-/l*
Counts
4 → 139
Calls
4 calls:
31.0ms
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
28.0ms
(* x (/ 1.0 (tan B)))
20.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
15.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series2.7s

Counts
4 → 12
Calls
4 calls:
1.2s
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
165.0ms
(* x (/ 1.0 (tan B)))
890.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
485.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify3.1s

Counts
151 → 151
Iterations

Useful iterations: done (3.1s)

IterNodesCost
034174475
193268666
2399267808
done500267512

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.9b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* x 1.0) (tan B))
0.2b
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
0.3b
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
14.4b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
30×pow-unpow
27×*-un-lft-identity add-cube-cbrt
25×add-exp-log
24×times-frac
16×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
7×unpow-prod-down associate-*l* prod-exp
6×associate-/r* div-exp
5×pow1
4×expm1-log1p-u cbrt-undiv associate-*l/ log1p-expm1-u div-inv add-log-exp
3×neg-sub0 pow-to-exp pow-neg associate-*r* pow-exp cbrt-unprod pow-sub unswap-sqr sqr-pow
2×clear-num frac-2neg associate-/l* associate-/l/
1×neg-mul-1 pow-pow tan-quot associate-/r/ *-commutative
Counts
4 → 128
Calls
4 calls:
9.0ms
(/ (* x 1.0) (tan B))
10.0ms
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
14.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
20.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series2.9s

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (* x 1.0) (tan B))
1.1s
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
1.0s
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
539.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify3.2s

Counts
140 → 140
Iterations

Useful iterations: done (3.2s)

IterNodesCost
032671889
188166242
2391065466
done500265130

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* x 1.0) (tan B))
0.2b
(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
0.2b
(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
14.4b
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
112×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
51×unpow-prod-down
29×associate-/l*
25×add-exp-log
17×sqr-pow
16×add-cbrt-cube
13×pow-unpow associate-/r*
12×div-exp
8×div-inv
6×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp clear-num frac-2neg pow-exp
1×pow-pow prod-exp tan-quot associate-/r/ cbrt-unprod associate-/l/
Counts
4 → 222
Calls
4 calls:
13.0ms
(/ (* x 1.0) (tan B))
18.0ms
(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
12.0ms
(/ F (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (* x 1.0) (tan B))
608.0ms
(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
307.0ms
(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
475.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify3.4s

Counts
234 → 234
Iterations

Useful iterations: 2 (2.1s)

IterNodesCost
0437172875
11112163789
24911162747
done5000162747

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F)
0.2b
(/ (/ 1 (/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F)) (sin B))
0.4b
(/ 1 (/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F))
14.4b
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
981×times-frac
463×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
159×unpow-prod-down
90×associate-/l*
68×add-exp-log
53×sqr-pow
50×div-exp
31×associate-/r*
24×div-inv
20×add-cbrt-cube
13×pow-unpow
10×cbrt-undiv
8×pow-to-exp rec-exp 1-exp pow-exp
6×pow1
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×pow-pow pow-flip inv-pow associate-/l/
Counts
4 → 560
Calls
4 calls:
13.0ms
(/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F)
65.0ms
(/ (/ 1 (/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F)) (sin B))
26.0ms
(/ 1 (/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F))
7.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series5.9s

Counts
4 → 12
Calls
4 calls:
2.0s
(/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F)
1.9s
(/ (/ 1 (/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F)) (sin B))
1.5s
(/ 1 (/ (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) F))
507.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify4.1s

Counts
572 → 572
Iterations

Useful iterations: done (4.0s)

IterNodesCost
0947553307
12622490166
done5001485751

prune3.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes311.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.4b

bsearch404.0ms

Steps
ItersRangePoint
8
383123.6636286385
488997712.5877659
40253580.93657249
9
-2.8555728020291845e+22
-29272228678884.97
-29785009876925.473

simplify9.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0331344
1401344
done401344

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.3s1698×body1280valid
1.6s1407×body640valid
1.6s4690×body80valid
675.0ms711×body320valid
500.0ms351×body160valid
413.0ms1650×body80nan