Details

Time bar (total: 36.1s)

sample517.0ms

Algorithm
intervals
Results
193.0ms55×body1280valid
71.0ms50×body640valid
47.0ms144×body80valid
29.0ms24×body320valid
15.0ms59×body80nan
7.0ms11×body160valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02027
14326
29124
316924
436624
591524
6321924
done500124

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (tan B))
0.3b
(* x (/ 1.0 (tan B)))
7.4b
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.6b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite374.0ms

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×tan-quot frac-times associate-/r/ *-commutative
1×neg-mul-1 pow-pow frac-2neg pow-prod-down associate-*l/ clear-num un-div-inv
Counts
4 → 163
Calls
4 calls:
6.0ms
(/ 1.0 (tan B))
19.0ms
(* x (/ 1.0 (tan B)))
267.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
74.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series928.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ 1.0 (tan B))
223.0ms
(* x (/ 1.0 (tan B)))
427.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
217.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.7s

Counts
175 → 175
Iterations

Useful iterations: 2 (602.0ms)

IterNodesCost
03142836
17642557
221042297
done50002297

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (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)) (sin B))
16.6b
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
25×add-exp-log add-cube-cbrt *-un-lft-identity
22×times-frac
17×associate-*r*
16×add-cbrt-cube
13×pow-unpow
10×associate-*l*
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×cbrt-undiv pow-to-exp pow-exp div-inv associate-/l* sqr-pow
2×*-commutative
1×tan-quot pow-pow frac-2neg associate-*r/ pow-prod-down clear-num associate-/r* associate-/r/
Counts
4 → 116
Calls
4 calls:
22.0ms
(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
36.0ms
(* x (/ 1.0 (tan B)))
33.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
5.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

series2.6s

Counts
4 → 12
Calls
4 calls:
560.0ms
(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
147.0ms
(* x (/ 1.0 (tan B)))
1.4s
(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
519.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.5s

Counts
128 → 128
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02832182
16922070
220481897
done50001843

prune851.0ms

Pruning

11 alts after pruning (11 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))
0.3b
(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
0.3b
(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
16.6b
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
16×add-cbrt-cube
15×times-frac
13×pow-unpow
7×unpow-prod-down associate-*l* prod-exp
6×div-exp
5×pow1
4×cbrt-undiv expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
3×pow-to-exp associate-*r* pow-exp cbrt-unprod div-inv unswap-sqr sqr-pow
2×frac-2neg clear-num
1×tan-quot pow-pow associate-/r/ *-commutative
Counts
4 → 105
Calls
4 calls:
19.0ms
(/ (* x 1.0) (tan B))
19.0ms
(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
15.0ms
(* (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))

series3.2s

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ (* x 1.0) (tan B))
618.0ms
(/ F (* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B)))
1.5s
(* (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)) (sin B))
891.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify1.7s

Counts
117 → 117
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02682084
16491982
220181809
done50011755

prune752.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
0.2b
(/ (* x 1.0) (tan B))
0.2b
(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
16.6b
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
112×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
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 frac-2neg pow-exp clear-num
1×tan-quot pow-pow prod-exp associate-/r/ cbrt-unprod associate-/l/
Counts
4 → 222
Calls
4 calls:
8.0ms
(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
11.0ms
(/ (* x 1.0) (tan B))
45.0ms
(/ (/ 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))

series1.7s

Counts
4 → 12
Calls
4 calls:
414.0ms
(/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0)))
209.0ms
(/ (* x 1.0) (tan B))
628.0ms
(/ (/ F (pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))) (sin B))
489.0ms
(pow (fma 2.0 x (fma F F 2.0)) (/ 1.0 2.0))

simplify2.2s

Counts
234 → 234
Iterations

Useful iterations: done (2.2s)

IterNodesCost
04375816
110015583
226845386
done50015363

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes229.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.6b

bsearch574.0ms

Steps
ItersRangePoint
8
5162834274.222523
99213418183057.05
5282018286.626188
10
-5.567720691877046e+23
-6045414056204.408
-6123727708692.632

simplify19.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03695
14795
25395
done5395

end0.0ms

sample10.3s

Algorithm
intervals
Results
3.6s1667×body1280valid
2.4s1344×body640valid
1.9s4897×body80valid
1.2s711×body320valid
399.0ms1629×body80nan
183.0ms333×body160valid