Details

sample943.0ms

Algorithm

intervals

Results

165.0ms	56×	body	640	valid
120.0ms	45×	body	1280	valid
105.0ms	158×	body	80	valid
31.0ms	23×	body	320	valid
27.0ms	60×	body	80	nan
11.0ms	11×	body	160	valid

simplify205.0ms

Calls

1 calls:

Slowest

204.0ms

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize62.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (fma 2 x (fma F F 2)) -1/2)
5.5b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
0.2b	(/ F (sin B))
0.1b	(/ x (tan B))

rewrite21.0ms

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

11.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
6.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms	(/ F (sin B))
1.0ms	(/ x (tan B))

series777.0ms

Calls

4 calls:

Slowest

312.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
266.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
123.0ms	(/ x (tan B))
74.0ms	(/ F (sin B))

simplify2.3s

Calls

38 calls:

Slowest

353.0ms	(- (+ (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)))
283.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
277.0ms	(- (+ (* 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)))
240.0ms	(* (* (* (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))))
210.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.8b

localize8.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (fma 2 x (fma F F 2)) -1/2)
0.4b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.1b	(/ x (tan B))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

7.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
4.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
1.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms	(/ x (tan B))

series731.0ms

Calls

4 calls:

Slowest

259.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
229.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
126.0ms	(/ x (tan B))
117.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify2.3s

Calls

38 calls:

Slowest

323.0ms	(- (+ (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)))
317.0ms	(- (+ (* 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)))
236.0ms	(- (+ (* 3/2 (* (sqrt 1/32) (* (pow x 2) F))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))
221.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
217.0ms	(/ (* (* (* (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)) (* (* (sin B) (sin B)) (sin B)))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.8b

localize17.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (fma 2 x (fma F F 2)) -1/2)
0.4b	(/ (sin B) (* (pow (fma 2 x (fma F F 2)) -1/2) F))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(/ 1 (/ (sin B) (* (pow (fma 2 x (fma F F 2)) -1/2) F)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

7.0ms	(/ (sin B) (* (pow (fma 2 x (fma F F 2)) -1/2) F))
4.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
3.0ms	(/ 1 (/ (sin B) (* (pow (fma 2 x (fma F F 2)) -1/2) F)))
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series672.0ms

Calls

4 calls:

Slowest

234.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
164.0ms	(/ (sin B) (* (pow (fma 2 x (fma F F 2)) -1/2) F))
146.0ms	(/ 1 (/ (sin B) (* (pow (fma 2 x (fma F F 2)) -1/2) F)))
128.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify3.0s

Calls

41 calls:

Slowest

345.0ms	(- (+ (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)))
324.0ms	(- (+ (* 1/6 (* F (* B (sqrt 1/2)))) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
307.0ms	(- (+ (* 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)))
227.0ms	(- (+ (* 3/2 (* (sqrt 1/32) (* (pow x 2) F))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))
213.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.8b

localize14.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (fma 2 x (fma F F 2)) -1/2)
0.4b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(* (/ x (sin B)) (cos B))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

15.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
10.0ms	(* (/ x (sin B)) (cos 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)

series789.0ms

Calls

4 calls:

Slowest

315.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
207.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
149.0ms	(* (/ x (sin B)) (cos B))
118.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify2.6s

Calls

43 calls:

Slowest

318.0ms	(- (+ (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)))
304.0ms	(- (+ (* 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)))
270.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
267.0ms	(/ (* (* (* (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)) (* (* (sin B) (sin B)) (sin B)))
181.0ms	(- (+ (* 3/2 (* (sqrt 1/32) (* (pow x 2) F))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))

prune1.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.8b

regimes433.0ms

Accuracy

0% (0.7b remaining)

Error of 10.7b against oracle of 10.0b and baseline of 10.7b

bsearch4.0ms

end0.0ms

sample14.2s

Algorithm

intervals

Results

5.4s	1675×	body	1280	valid
3.4s	1421×	body	640	valid
2.2s	4754×	body	80	valid
1.3s	1679×	body	80	nan
1.1s	684×	body	320	valid
341.0ms	352×	body	160	valid