Details

simplify8.6m (69.7%)

sample1.3m (10.6%)

Algorithm
73×intervals
Results
28.9s293544×body80valid
10.3s13804×body1280valid
5.1s16942×body160valid
5.1s3830×body2560valid
4.6s9450×body640valid
3.5s2195×body10240exit
2.4s100652×pre80true
1.8s6699×body320valid
1.3s19194×body80nan
218.0ms217×body5120valid
6.0ms100×pre80false

prune1.0m (8.4%)

series48.1s (6.5%)

Calls

296 calls:

2.1s
(+ (pow y 6.0) (fma (pow y 4.0) 121.0 2.0))
1.6s
(fma (sqrt (pow x 4.0)) (sqrt (pow x 4.0)) (- (pow y 4.0)))
1.3s
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (fma (/ (* (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1))) 1) (/ (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (+ (* x1 x1) 1.0)) (- (* (sqrt 3.0) (sqrt 3.0))))) (fma x1 (* x1 (- (* 4.0 (/ (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))) 6.0)) (* (+ (- 3.0) 3.0) (/ (* (- (fma (* 3.0 x1) x1 (* 2.0 x2)) x1) (* 2.0 x1)) (fma x1 x1 1.0)))))
1.2s
(fma (sqrt (+ (+ e d) c)) (sqrt (+ (+ e d) c)) (+ b a))
771.0ms
(expm1 (log1p (* (pow y 6.0) 333.75)))

rewrite26.3s (3.6%)

Algorithm
103×rewrite-expression-head
Calls

296 calls:

1.7s
(+ (+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0))) (/ 77617.0 (* 2.0 33096.0)))
1.5s
(+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0)))
1.2s
(+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0)))
1.0s
(- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)
804.0ms
(/ (* x (- (pow 0.954929658551372 3) (pow (* (* 0.12900613773279798 x) x) 3))) (+ (* 0.954929658551372 0.954929658551372) (+ (* (* (* 0.12900613773279798 x) x) (* (* 0.12900613773279798 x) x)) (* 0.954929658551372 (* (* 0.12900613773279798 x) x)))))
Rules
9222×times-frac
8611×*-un-lft-identity
8100×add-sqr-sqrt
6789×add-cube-cbrt
4477×prod-diff
1693×add-exp-log
1409×add-cbrt-cube
917×unpow-prod-down
912×associate-*r*
741×pow1
654×distribute-lft-out
650×distribute-rgt-in distribute-lft-in
641×div-inv
578×sqrt-prod
566×add-log-exp
550×prod-exp
534×associate-*l*
461×difference-of-squares
426×cbrt-unprod
419×div-exp
342×sqr-pow
337×associate-/l*
328×cbrt-undiv
299×log1p-expm1-u
297×expm1-log1p-u
282×distribute-lft-out--
264×associate-/r*
259×cube-prod
243×fma-neg
230×flip-+ flip3-+
219×associate-/r/
206×frac-times associate-*r/
200×pow-prod-down
169×flip3-- flip--
167×distribute-rgt-neg-in
162×sqrt-div
158×unswap-sqr
147×associate-*l/
146×associate-+l+
143×distribute-lft-neg-in
103×sum-log
96×frac-sub
93×fma-def
84×unpow3 cube-mult swap-sqr
79×*-commutative
78×exp-neg
70×exp-prod sub-neg
67×neg-sub0
66×associate-/l/
62×clear-num frac-2neg
59×cbrt-prod exp-diff
50×diff-log
49×neg-mul-1
48×log-pow
44×fma-udef associate-+r+
39×rec-exp 1-exp
37×log-prod
35×sqrt-pow1
30×pow1/2 +-commutative
28×pow-exp
26×rem-sqrt-square pow-prod-up pow-to-exp
25×un-div-inv
24×frac-add
23×pow-sqr
19×div-sub
17×pow-unpow
15×unpow2
14×pow-plus
12×pow2 pow1/3
11×distribute-lft-neg-out pow-pow
neg-log log-div
distribute-frac-neg rem-log-exp
associate--l- expm1-udef
rem-exp-log inv-pow unpow-prod-up expm1-log1p pow-flip
unsub-neg
rem-cube-cbrt hypot-def associate--l+
cbrt-div cube-div sqrt-pow2 log1p-udef associate-+r- log1p-expm1 rem-cbrt-cube
sqrt-unprod rem-square-sqrt associate-+l- exp-to-pow

regimes4.5s (0.6%)

Accuracy

Total 47.6b remaining (19.3%)

Threshold costs 3.3b (1.4%)

12.6b42.3%Compound Interest
10.9b24.3%Complex division, real part
10.3b29.8%Complex division, imag part
4.6b83.9%The quadratic formula (r2)
4.3b84.5%The quadratic formula (r1)

localize2.7s (0.4%)

bsearch1.5s (0.2%)

end1.0ms (0.0%)