Details

prune35.0s (27.2%)

sample32.7s (25.4%)

Algorithm

73×

intervals

Results

9.1s	294754×	body	80	valid
4.6s	13607×	body	1280	valid
2.6s	3981×	body	2560	valid
1.7s	9368×	body	640	valid
1.7s	16718×	body	160	valid
1.3s	100594×	pre	80	true
1.0s	2210×	body	10240	exit
715.0ms	7042×	body	320	valid
526.0ms	19273×	body	80	nan
85.0ms	240×	body	5120	valid
3.0ms	100×	pre	80	false

series30.2s (23.5%)

Calls

290 calls:

1.2s	(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
917.0ms	(+ (fma (sqrt (+ e (+ d c))) (sqrt (+ e (+ d c))) b) a)
486.0ms	(fma (sqrt (+ e (+ d c))) (sqrt (+ e (+ d c))) b)
483.0ms	(fma x (* (- (* (* (* (* 11.0 x) x) y) y) (+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))) x) (+ (* 333.75 (pow y 6.0)) (fma (pow y 8.0) 5.5 (/ x (* 2.0 y)))))
415.0ms	(- (* 9.0 (pow x 4.0)) (pow y 4.0))

rewrite15.5s (12.1%)

Algorithm

106×	rewrite-expression-head

Calls

290 calls:

637.0ms	(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
635.0ms	(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
634.0ms	(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
555.0ms	(+ (+ (+ (+ e d) c) b) a)
515.0ms	(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)

Rules

10871×	`times-frac`
10392×	`*-un-lft-identity`
9424×	`add-sqr-sqrt`
7738×	`add-cube-cbrt`
5600×	`prod-diff`
2372×	`add-exp-log`
2036×	`add-cbrt-cube`
1318×	`unpow-prod-down`
987×	`distribute-lft-out`
970×	`prod-exp`
896×	`distribute-rgt-in` `distribute-lft-in`
785×	`cbrt-unprod`
760×	`pow1`
743×	`associate-r`
712×	`difference-of-squares`
702×	`div-inv`
683×	`cube-prod`
649×	`div-exp`
598×	`associate-l`
560×	`add-log-exp`
544×	`cbrt-undiv`
527×	`sqr-pow`
373×	`associate-/l*`
372×	`sqrt-prod`
352×	`distribute-lft-out--`
291×	`log1p-expm1-u` `expm1-log1p-u`
284×	`distribute-rgt-neg-in`
282×	`associate-/r/`
252×	`fma-neg`
249×	`distribute-lft-neg-in`
241×	`flip-+` `flip3-+`
236×	`cbrt-prod`
205×	`frac-times`
204×	`associate-/r*`
167×	`associate-*r/`
163×	`flip--` `flip3--`
159×	`unswap-sqr`
149×	`swap-sqr`
148×	`pow-prod-down`
138×	`associate-*l/`
122×	`unpow3` `cube-mult` `log-prod`
105×	`sum-log`
103×	`fma-def`
101×	`frac-sub`
95×	`associate-/l/`
83×	`neg-mul-1`
82×	`exp-sum`
76×	`exp-neg`
73×	`pow-prod-up`
72×	`*-commutative`
70×	`1-exp`
67×	`neg-sub0`
64×	`sub-neg`
60×	`sqrt-div`
57×	`exp-diff`
54×	`clear-num` `frac-2neg` `sqrt-pow1`
53×	`diff-log`
48×	`fma-udef`
47×	`pow-sqr` `pow-exp`
41×	`pow-to-exp`
40×	`pow-plus`
35×	`unpow2`
34×	`rec-exp`
33×	`pow1/2`
32×	`pow2`
30×	`pow1/3`
28×	`+-commutative`
27×	`pow-unpow`
25×	`un-div-inv`
20×	`div-sub`
18×	`difference-cubes` `frac-add` `pow-pow`
17×	`rem-sqrt-square` `log-pow`
12×	`associate--r+`
11×	`cube-div` `associate-+l+` `sum-cubes`
10×	`cbrt-div` `associate-+r+` `log-div`
9×	`exp-prod`
8×	`associate--l-`
7×	`rem-cube-cbrt` `neg-log`
6×	`distribute-frac-neg` `rem-cbrt-cube` `distribute-neg-frac`
5×	`distribute-lft-neg-out` `rem-log-exp`
4×	`hypot-def`
3×	`expm1-log1p` `expm1-udef` `associate-+l-`
2×	`log1p-udef` `inv-pow` `log1p-expm1` `pow-flip` `distribute-rgt-neg-out`
1×	`sqrt-unprod` `pow3` `cube-unmult` `unsub-neg` `rem-square-sqrt` `distribute-rgt-out` `distribute-rgt-out--`

simplify9.8s (7.7%)

regimes3.1s (2.4%)

Accuracy

Total 47.4b remaining (15.6%)

Threshold costs 2.5b (0.8%)

11.7b	49.5%	Compound Interest
9.0b	26.4%	Complex division, imag part
8.2b	24.7%	Complex division, real part
5.0b	76.5%	Kahan p9 Example
4.3b	83.8%	The quadratic formula (r1)

Details

prune35.0s (27.2%)

sample32.7s (25.4%)

series30.2s (23.5%)

rewrite15.5s (12.1%)

simplify9.8s (7.7%)

regimes3.1s (2.4%)

localize1.4s (1.1%)

bsearch853.0ms (0.7%)

end1.0ms (0.0%)