Details

Time bar (total: 35.9s)

sample524.0ms

Algorithm
intervals
Results
107.0ms42×body1280valid
83.0ms177×body80valid
64.0ms65×body80nan
50.0ms43×body640valid
18.0ms21×body320valid
5.0ms8×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
02027
14326
29124
317024
438524
5175824
done500024

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize77.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 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))))
16.8b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite479.0ms

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:
9.0ms
(/ 1.0 (tan B))
22.0ms
(* x (/ 1.0 (tan B)))
320.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
113.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series856.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ 1.0 (tan B))
148.0ms
(* x (/ 1.0 (tan B)))
439.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
195.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.4s

Counts
175 → 175
Iterations

Useful iterations: 2 (790.0ms)

IterNodesCost
03142836
18832565
238722305
done50002305

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
0.3b
(* x (/ 1.0 (tan B)))
0.4b
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
16.8b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite85.0ms

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
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×cbrt-undiv neg-sub0 pow-to-exp pow-neg pow-exp associate-/r* pow-sub sqr-pow
2×*-commutative associate-/l/
1×tan-quot neg-mul-1 pow-pow frac-2neg associate-*r/ pow-prod-down clear-num associate-/r/ associate-/l*
Counts
4 → 139
Calls
4 calls:
14.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
26.0ms
(* x (/ 1.0 (tan B)))
24.0ms
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
13.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series2.6s

Counts
4 → 12
Calls
4 calls:
911.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
161.0ms
(* x (/ 1.0 (tan B)))
1.0s
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
489.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.5s

Counts
151 → 151
Iterations

Useful iterations: done (2.5s)

IterNodesCost
03412633
19302510
238892318
done50022314

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* x 1.0) (tan B))
0.3b
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
0.4b
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
16.8b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite77.0ms

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-*l* prod-exp
6×div-exp associate-/r*
5×pow1
4×cbrt-undiv expm1-log1p-u 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×frac-2neg clear-num associate-/l/ associate-/l*
1×tan-quot neg-mul-1 pow-pow associate-/r/ *-commutative
Counts
4 → 128
Calls
4 calls:
13.0ms
(/ (* x 1.0) (tan B))
19.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
27.0ms
(/ (* (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)))

series2.8s

Counts
4 → 12
Calls
4 calls:
174.0ms
(/ (* x 1.0) (tan B))
932.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
1.2s
(/ (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (sin B))
483.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify2.9s

Counts
140 → 140
Iterations

Useful iterations: done (2.9s)

IterNodesCost
03262535
18792418
239152232
done50022224

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* x 1.0) (tan B))
0.3b
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
0.4b
(* (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (/ 1 (sin B)))
16.8b
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
37×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity prod-exp
30×pow-unpow times-frac
23×add-cbrt-cube
16×associate-*r*
13×distribute-lft-neg-in distribute-rgt-neg-in
10×div-exp
8×associate-*l* associate-*l/ cbrt-unprod
7×pow1 unpow-prod-down
6×pow-to-exp pow-exp
4×cbrt-undiv neg-sub0 expm1-log1p-u pow-neg rec-exp 1-exp log1p-expm1-u div-inv pow-sub add-log-exp
3×associate-/r* unswap-sqr sqr-pow
2×frac-times *-commutative
1×tan-quot neg-mul-1 pow-pow frac-2neg associate-*r/ pow-prod-down clear-num associate-/r/ un-div-inv associate-/l*
Counts
4 → 152
Calls
4 calls:
23.0ms
(/ (* x 1.0) (tan B))
26.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
76.0ms
(* (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (/ 1 (sin B)))
14.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

series2.6s

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ (* x 1.0) (tan B))
957.0ms
(* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F)
960.0ms
(* (* (pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0))) F) (/ 1 (sin B)))
478.0ms
(pow (fma 2.0 x (fma F F 2.0)) (- (/ 1.0 2.0)))

simplify680.0ms

Counts
164 → 164
Iterations

Useful iterations: done (674.0ms)

IterNodesCost
03653157
110522924
done50002618

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes370.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.9b

bsearch560.0ms

Steps
ItersRangePoint
11
8.931192701332034e-10
453861013356227.3
12064.689062358544
7
-2.3990535726943103e+72
-1.13694984016438e+70
-2.906001815670825e+71

simplify17.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03674
15174
25974
done5974

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.3s1635×body1280valid
2.1s1412×body640valid
1.2s4845×body80valid
969.0ms654×body320valid
437.0ms1704×body80nan
205.0ms347×body160valid