Details

sample928.0ms

Algorithm

intervals

Results

183.0ms	61×	body	1280	valid
115.0ms	41×	body	640	valid
67.0ms	152×	body	80	valid
26.0ms	20×	body	320	valid
20.0ms	46×	body	80	nan
10.0ms	10×	body	160	valid

simplify201.0ms

Calls

1 calls:

Slowest

200.0ms

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize47.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (fma 2 x (fma F F 2)) -1/2)
6.5b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
0.2b	(/ x (tan B))
0.1b	(/ F (sin B))

rewrite12.0ms

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

6.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms	(/ x (tan B))
1.0ms	(/ F (sin B))

series762.0ms

Calls

4 calls:

Slowest

296.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
244.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
153.0ms	(/ x (tan B))
68.0ms	(/ F (sin B))

simplify2.3s

Calls

38 calls:

Slowest

300.0ms	(- (+ (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)))
297.0ms	(- (+ (* 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)))
266.0ms	(* (* (* (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))))
246.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
172.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.6b

localize17.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (fma 2 x (fma F F 2)) -1/2)
0.3b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(/ x (tan B))

rewrite28.0ms

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

15.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (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))

series838.0ms

Calls

4 calls:

Slowest

299.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
210.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
186.0ms	(/ x (tan B))
142.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify2.4s

Calls

38 calls:

Slowest

331.0ms	(- (+ (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)))
299.0ms	(- (+ (* 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)))
254.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
250.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
219.0ms	(/ (* (* (* (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)))

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.6b

localize11.0ms

Local error

Found 4 expressions with local error:

16.7b	(pow (fma 2 x (fma F F 2)) -1/2)
0.3b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(* (/ x (sin B)) (cos B))

rewrite31.0ms

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

11.0ms	(/ (* (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)
1.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series778.0ms

Calls

4 calls:

Slowest

273.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
244.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
144.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
117.0ms	(* (/ x (sin B)) (cos B))

simplify2.8s

Calls

43 calls:

Slowest

340.0ms	(- (+ (* 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)))
312.0ms	(- (+ (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)))
276.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
247.0ms	(- (+ (* 3/2 (* (sqrt 1/32) (* (pow x 2) F))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))
229.0ms	(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))

prune1.5s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.6b

localize32.0ms

Local error

Found 4 expressions with local error:

16.6b	(sqrt (fma 2 x (fma F F 2)))
16.6b	(sqrt (fma 2 x (fma F F 2)))
0.3b	(/ (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F)) (sin B))
0.3b	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

37.0ms	(/ (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F)) (sin B))
27.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F))
2.0ms	(sqrt (fma 2 x (fma F F 2)))
2.0ms	(sqrt (fma 2 x (fma F F 2)))

series687.0ms

Calls

4 calls:

Slowest

233.0ms	(/ (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F)) (sin B))
162.0ms	(sqrt (fma 2 x (fma F F 2)))
147.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F))
145.0ms	(sqrt (fma 2 x (fma F F 2)))

simplify4.3s

Calls

48 calls:

Slowest

364.0ms	(/ (* (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F)) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F))) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F))) (* (* (sin B) (sin B)) (sin B)))
361.0ms	(/ (* (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (* (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F)) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F))) (* (* (sin B) (sin B)) (sin B)))
317.0ms	(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))
301.0ms	(* (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (* (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F)) (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) F)))
283.0ms	(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))

prune1.6s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 9.6b

regimes423.0ms

Accuracy

0% (0.6b remaining)

Error of 10.7b against oracle of 10.1b and baseline of 10.7b

bsearch3.0ms

end0.0ms

sample14.5s

Algorithm

intervals

Results

4.9s	1665×	body	1280	valid
3.3s	1415×	body	640	valid
3.1s	4759×	body	80	valid
1.5s	696×	body	320	valid
727.0ms	345×	body	160	valid
647.0ms	1631×	body	80	nan