Details

simplify10.0m (56.2%)

sample4.7m (26.3%)

Algorithm

77×

intervals

Results

1.7m	42973×	body	1280	valid
42.9s	31301×	body	640	valid
28.2s	201437×	body	80	valid
27.0s	14854×	body	10240	exit
19.7s	27952×	body	320	valid
19.3s	152623×	body	80	nan
14.0s	36233×	body	160	valid
9.4s	150526×	pre	80	true
3.7s	2949×	body	2560	valid
1.3s	8027×	body	160	nan
1.1s	4101×	pre	10240	exit
223.0ms	192×	body	5120	valid
2.0ms	1×	body	320	nan
1.0ms	1×	body	640	nan

prune1.5m (8.6%)

series59.3s (5.5%)

Calls

442 calls:

1.6s	(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
1.2s	(/ (/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (sqrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))) a)
1.2s	(/ (- (* (cos delta) (cos delta)) (fma (* (* (* (* (cos theta) (cos phi1)) (* (cos theta) (cos phi1))) (sin delta)) (sin delta)) (* (sin phi1) (sin phi1)) (fma (* (cos delta) (cos delta)) (* (* (sin phi1) (sin phi1)) (* (sin phi1) (sin phi1))) (* (* (* (sin phi1) (* (sin phi1) (sin phi1))) (sin delta)) (+ (* (* (cos delta) (cos phi1)) (cos theta)) (* (* (cos delta) (cos phi1)) (cos theta))))))) (fma (* (sin phi1) (sin phi1)) (cos delta) (fma (* (sin delta) (* (cos phi1) (cos theta))) (sin phi1) (cos delta))))
1.2s	(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))
949.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (fma (cos theta) (* (cos phi1) (sin delta)) (* (cos delta) (sin phi1))))))))

regimes19.2s (1.8%)

Accuracy

Total 52.9b remaining (20.8%)

Threshold costs 4.0b (1.6%)

7.7b	44%	Quadratic roots, narrow range
6.3b	6.2%	Quadratic roots, medium range
6.2b	22.4%	Cubic critical, narrow range
5.4b	46.9%	Quotient of products
4.3b	84.2%	Quadratic roots, full range

rewrite9.1s (0.9%)

Algorithm

138×	rewrite-expression-head

Calls

442 calls:

189.0ms	(* (/ (sqrt 2) (* (cbrt (+ (exp x) (exp (- x)))) (cbrt (+ (exp x) (exp (- x)))))) (/ (sqrt 2) (cbrt (+ (exp x) (exp (- x))))))
187.0ms	(* (* (* (/ (sin v) (fma (cos v) e 1)) (sqrt e)) (sqrt (sqrt e))) (sqrt (sqrt e)))
138.0ms	(* (* (* (/ a1 b1) (cbrt a2)) (cbrt a2)) (/ (cbrt a2) b2))
133.0ms	(- (/ -3 (* x (* x x))) (+ (/ 1 (* x x)) (/ 3 x)))
121.0ms	(* (- (/ (* m (- 1 m)) v) 1) (- 1 m))

Rules

7002×	`*-un-lft-identity`
6497×	`add-sqr-sqrt`
6388×	`times-frac`
4740×	`add-cube-cbrt`
2418×	`prod-diff`
1646×	`add-exp-log`
1418×	`add-cbrt-cube`
1379×	`pow1`
714×	`difference-of-squares`
631×	`sqrt-prod`
626×	`distribute-lft-out`
608×	`add-log-exp`
536×	`associate-r`
497×	`associate-l`
475×	`div-inv`
468×	`associate-/r*`
445×	`expm1-log1p-u`
443×	`log1p-expm1-u`
442×	`insert-posit16`
416×	`prod-exp`
390×	`associate-/r/`
387×	`associate-/l*`
379×	`distribute-lft-out--`
376×	`cbrt-unprod`
365×	`cbrt-prod`
362×	`div-exp`
302×	`fma-neg`
290×	`pow-prod-down`
284×	`cbrt-undiv`
213×	`frac-times`
185×	`difference-of-sqr-1`
181×	`flip-+`
180×	`flip3-+`
175×	`fma-def`
170×	`log-prod`
163×	`flip--`
162×	`flip3--`
157×	`unswap-sqr`
151×	`distribute-rgt-in` `distribute-lft-in`
149×	`pow-prod-up`
131×	`associate-*l/`
119×	`associate-*r/`
114×	`associate-+l+`
113×	`cbrt-div`
101×	`pow-plus`
99×	`tanh-def`
97×	`frac-2neg` `clear-num`
95×	`*-commutative`
84×	`swap-sqr`
81×	`pow-sqr`
79×	`associate-+r+`
69×	`sub-neg`
67×	`fma-udef`
64×	`associate-/l/`
60×	`unpow-prod-down`
55×	`pow2`
53×	`diff-log`
50×	`cos-sum`
49×	`log-pow`
48×	`pow1/3` `sqrt-pow1`
45×	`exp-sum`
40×	`pow1/2` `sin-mult`
39×	`exp-prod`
36×	`associate--l+` `pow3` `div-sub`
35×	`sum-log`
34×	`1-exp` `rem-sqrt-square` `frac-add`
33×	`sin-sum`
32×	`cos-mult`
26×	`pow-flip`
25×	`log-div`
24×	`sqrt-div` `rec-exp`
22×	`frac-sub` `sqr-pow` `+-commutative`
20×	`tan-quot`
18×	`distribute-rgt-neg-in` `cos-diff`
16×	`distribute-rgt-out`
15×	`distribute-lft-neg-in`
14×	`inv-pow`
13×	`rem-log-exp`
12×	`cube-prod` `pow-pow`
11×	`difference-cubes` `sin-diff`
10×	`expm1-def`
9×	`sin-cos-mult` `associate--r+` `acos-asin`
8×	`rem-exp-log`
5×	`associate-+r-` `sub-div` `neg-mul-1` `distribute-rgt-out--` `associate-+l-` `log1p-udef`
4×	`neg-sub0` `exp-diff` `cube-unmult` `log1p-expm1` `pow-exp` `unpow3` `neg-log` `cube-mult` `rem-cbrt-cube` `associate--r-`
3×	`expm1-log1p` `expm1-udef` `distribute-lft-neg-out` `distribute-frac-neg` `pow-unpow` `acos-neg` `sqr-cos`
2×	`distribute-rgt1-in` `log1p-def` `un-div-inv` `hypot-udef` `pow-to-exp`
1×	`quot-tan` `associate--l-` `sqrt-undiv` `unsub-neg` `tanh-undef` `asin-acos` `unpow1/3`

Details

simplify10.0m (56.2%)

sample4.7m (26.3%)

prune1.5m (8.6%)

series59.3s (5.5%)

regimes19.2s (1.8%)

rewrite9.1s (0.9%)

localize6.6s (0.6%)

bsearch766.0ms (0.1%)

end1.0ms (0.0%)