Details

sample696.0ms

Algorithm

intervals

Results

275.0ms	63×	body	1280	valid
95.0ms	43×	body	640	valid
82.0ms	44×	body	80	nan
74.0ms	140×	body	80	valid
32.0ms	21×	body	320	valid
12.0ms	11×	body	160	valid

simplify302.0ms

Calls

1 calls:

Slowest

301.0ms

(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize78.0ms

Local error

Found 4 expressions with local error:

15.9b	(pow (fma 2 x (fma F F 2)) -1/2)
6.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
0.2b	(/ x (tan B))
0.2b	(/ F (sin B))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
6×	`associate-/r` `unpow-prod-down` `add-cbrt-cube` `associate-l*`
5×	`pow1`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `div-inv`
2×	`pow-to-exp` `clear-num` `frac-2neg` `pow-exp`
1×	`pow-pow` `tan-quot` `associate-r/` `associate-/r/` `-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

12.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
5.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms	(/ x (tan B))
1.0ms	(/ F (sin B))

series695.0ms

Calls

4 calls:

Slowest

282.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
167.0ms	(/ x (tan B))
164.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
82.0ms	(/ F (sin B))

simplify2.8s

Calls

38 calls:

Slowest

417.0ms	(- (+ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (* 3/8 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (pow x 2)))) (* 1/2 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) x)))
338.0ms	(* (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (* (* (/ F (sin B)) (/ F (sin B))) (/ F (sin B))))
314.0ms	(- (+ (* 3/8 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) (pow x 2))) (exp (* -1/2 (- (log 2) (log (/ 1 x)))))) (* 1/2 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) x)))
290.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
197.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 9.0b

localize21.0ms

Local error

Found 4 expressions with local error:

15.9b	(pow (fma 2 x (fma F F 2)) -1/2)
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
0.2b	(/ x (tan B))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
7×	`pow1` `associate-l`
6×	`unpow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`prod-exp` `*-commutative` `div-inv`
1×	`pow-to-exp` `rec-exp` `clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `pow-exp` `tan-quot` `associate-*r/` `associate-/r/` `un-div-inv` `cbrt-unprod`

Calls

4 calls:

Slowest

22.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
8.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms	(/ x (tan B))

series638.0ms

Calls

4 calls:

Slowest

231.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
172.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
162.0ms	(/ x (tan B))
73.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify4.6s

Calls

37 calls:

Slowest

904.0ms	(* (* (* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (* (pow (fma 2 x (fma F F 2)) -1/2) F)) (* (pow (fma 2 x (fma F F 2)) -1/2) F)) (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))))
882.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
458.0ms	(- (+ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (* 3/8 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (pow x 2)))) (* 1/2 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) x)))
411.0ms	(- (+ (* 3/8 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) (pow x 2))) (exp (* -1/2 (- (log 2) (log (/ 1 x)))))) (* 1/2 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) x)))
285.0ms	(- (+ (* 3/2 (* (sqrt 1/32) (* (pow x 2) F))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))

prune4.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.0b

localize45.0ms

Local error

Found 4 expressions with local error:

15.9b	(pow (fma 2 x (fma F F 2)) -1/2)
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
0.2b	(* (/ x (sin B)) (cos B))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

11×	`associate-l` `add-exp-log`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
8×	`add-cbrt-cube`
7×	`associate-r`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `*-commutative`
2×	`pow-prod-down` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rec-exp` `pow-pow` `associate-l/` `pow-exp` `associate-r/` `un-div-inv`

Calls

4 calls:

Slowest

42.0ms	(* (/ x (sin B)) (cos B))
22.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
14.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
9.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series1.1s

Calls

4 calls:

Slowest

479.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
299.0ms	(* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (/ 1 (sin B)))
262.0ms	(* (/ x (sin B)) (cos B))
77.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify7.4s

Calls

42 calls:

Slowest

2.3s	(* (* (* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (* (pow (fma 2 x (fma F F 2)) -1/2) F)) (* (pow (fma 2 x (fma F F 2)) -1/2) F)) (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))))
698.0ms	(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
570.0ms	(+ (log (* (pow (fma 2 x (fma F F 2)) -1/2) F)) (log (/ 1 (sin B))))
493.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
465.0ms	(- (+ (* 3/2 (* (sqrt 1/32) (* (pow x 2) F))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.0b

localize18.0ms

Local error

Found 4 expressions with local error:

15.9b	(pow (fma 2 x (fma F F 2)) -1/2)
0.3b	(* x (* (/ 1 (sin B)) (cos B)))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(* (/ 1 (sin B)) (cos B))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-l`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
7×	`pow1`
6×	`unpow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`associate-*l/` `prod-exp`
1×	`pow-to-exp` `rec-exp` `pow-pow` `pow-prod-down` `pow-exp` `associate-*r/` `cbrt-unprod` `div-inv`

Calls

4 calls:

Slowest

11.0ms	(* (/ 1 (sin B)) (cos B))
10.0ms	(* x (* (/ 1 (sin B)) (cos B)))
9.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series587.0ms

Calls

4 calls:

Slowest

266.0ms	(* x (* (/ 1 (sin B)) (cos B)))
222.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
72.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
27.0ms	(* (/ 1 (sin B)) (cos B))

simplify5.1s

Calls

34 calls:

Slowest

1.1s	(* (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))) (* (* (cos B) (cos B)) (cos B)))
963.0ms	(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
803.0ms	(- (+ (* 3/8 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) (pow x 2))) (exp (* -1/2 (- (log 2) (log (/ 1 x)))))) (* 1/2 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) x)))
495.0ms	(- (+ (* 3/2 (* (sqrt 1/32) (* (pow x 2) F))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))
486.0ms	(- (+ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (* 3/8 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (pow x 2)))) (* 1/2 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) x)))

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.0b

regimes1.4s

Accuracy

0% (0.7b remaining)

Error of 10.6b against oracle of 10.0b and baseline of 10.6b

bsearch11.0ms

end27.0ms

sample35.4s

Algorithm

intervals

Results

13.3s	1682×	body	1280	valid
10.9s	1316×	body	640	valid
4.7s	4835×	body	80	valid
3.3s	726×	body	320	valid
1.7s	363×	body	160	valid
935.0ms	1703×	body	80	nan