Details

Time bar (total: 16.4s)

sample374.0ms

Algorithm
intervals
Results
49.0ms50×body1280valid
24.0ms163×body80valid
21.0ms34×body640valid
11.0ms28×body320valid
4.0ms37×body80nan
2.0ms6×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
02027
14326
28824
316424
434124
585224
6280424
done500024

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ F (sin B))
0.2b
(* x (/ 1.0 (tan B)))
9.7b
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.3b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite134.0ms

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:
2.0ms
(/ F (sin B))
8.0ms
(* x (/ 1.0 (tan B)))
87.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
26.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series597.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ F (sin B))
108.0ms
(* x (/ 1.0 (tan B)))
288.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
154.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify749.0ms

Counts
174 → 174
Iterations

Useful iterations: 2 (333.0ms)

IterNodesCost
03112820
17812540
221292283
done50002283

prune709.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1.0 (tan B)))
0.3b
(* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
0.4b
(/ (* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))) (sin B))
16.3b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
31×times-frac
30×pow-unpow
25×add-exp-log
21×associate-*r*
16×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
8×prod-exp
7×pow1 unpow-prod-down
6×associate-*l*
5×pow-neg associate-*r/ div-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv neg-sub0 pow-to-exp pow-exp associate-/r* associate-/l/ pow-sub sqr-pow
2×un-div-inv *-commutative
1×tan-quot neg-mul-1 pow-pow frac-2neg pow-prod-down clear-num associate-/r/ associate-/l*
Counts
4 → 141
Calls
4 calls:
8.0ms
(* x (/ 1.0 (tan B)))
6.0ms
(* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
5.0ms
(/ (* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))) (sin B))
4.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
107.0ms
(* x (/ 1.0 (tan B)))
220.0ms
(* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
364.0ms
(/ (* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))) (sin B))
326.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify704.0ms

Counts
153 → 153
Iterations

Useful iterations: 2 (327.0ms)

IterNodesCost
03192489
17952333
222462149
done50012149

prune614.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* x 1.0) (tan B))
0.3b
(* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
0.4b
(/ (* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))) (sin B))
16.3b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
30×pow-unpow
27×add-cube-cbrt *-un-lft-identity
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-*r* prod-exp
6×div-exp associate-/r*
5×pow1 pow-neg
4×cbrt-undiv expm1-log1p-u associate-*r/ log1p-expm1-u div-inv add-log-exp
3×neg-sub0 pow-to-exp associate-*l* pow-exp cbrt-unprod associate-/l/ pow-sub unswap-sqr sqr-pow
2×frac-2neg clear-num un-div-inv associate-/l*
1×tan-quot neg-mul-1 pow-pow associate-/r/ *-commutative
Counts
4 → 130
Calls
4 calls:
3.0ms
(/ (* x 1.0) (tan B))
6.0ms
(* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
5.0ms
(/ (* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))) (sin B))
8.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (* x 1.0) (tan B))
214.0ms
(* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))))
358.0ms
(/ (* F (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))) (sin B))
330.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify682.0ms

Counts
142 → 142
Iterations

Useful iterations: 2 (316.0ms)

IterNodesCost
03042391
17482245
222122061
done50002061

prune570.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)) 0)) (* (sin B) (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))))
0.3b
(* (sin B) (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
16.3b
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
28×prod-exp
23×add-cbrt-cube
22×add-sqr-sqrt
18×div-exp
17×add-cube-cbrt *-un-lft-identity
13×pow-unpow times-frac
10×pow-to-exp pow-exp
7×unpow-prod-down associate-*r*
6×cbrt-undiv cbrt-unprod
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×associate-*l* div-inv unswap-sqr sqr-pow
2×frac-2neg clear-num associate-/l*
1×tan-quot pow-pow associate-/r/ *-commutative
Counts
4 → 115
Calls
4 calls:
4.0ms
(/ (* x 1.0) (tan B))
7.0ms
(/ (* F (pow (fma 2.0 x (fma F F 2.0)) 0)) (* (sin B) (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))))
6.0ms
(* (sin B) (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
2.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (* x 1.0) (tan B))
365.0ms
(/ (* F (pow (fma 2.0 x (fma F F 2.0)) 0)) (* (sin B) (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))))
680.0ms
(* (sin B) (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
317.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify885.0ms

Counts
127 → 127
Iterations

Useful iterations: done (882.0ms)

IterNodesCost
02862798
17562265
226272017
done50001968

prune455.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes141.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.5b

bsearch307.0ms

Steps
ItersRangePoint
9
6.379368274952145e-05
22276.40736340321
16387.002115766478
10
-1.3782269510853453e+20
-4115381.757174666
-67836704772650.625

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03884
14984
25584
done5584

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.6s1647×body1280valid
845.0ms1328×body640valid
678.0ms4838×body80valid
298.0ms703×body320valid
167.0ms1625×body80nan
99.0ms350×body160valid