Details

simplify35.2m

Calls

16250 calls:

Slowest
5.0s
(/ (* (* (* 3 3) 3) (* (* (* c c) c) (* (* a a) a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
4.5s
(/ (* (* (* 3 3) 3) (* (* (* c c) c) (* (* a a) a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
3.9s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (- (- b) (sqrt (- (* b b) (* (* 3 a) c)))))))
3.9s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
3.8s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

sample12.5m

Algorithm
71×intervals
Results
9.4m81618×body10240exit
55.2s31882×body1280valid
26.6s192246×body80valid
24.2s24229×body640valid
20.5s149726×body80nan
14.2s24692×body320valid
11.4s34873×body160valid
9.1s152999×pre80true
1.8s7978×body160nan
1.8s1980×body2560valid
1.1s4125×pre10240exit
168.0ms130×body5120valid

prune3.1m

series1.2m

Calls

419 calls:

Slowest
21.9s
(* (hypot (* (- lambda1 lambda2) (fma (cos (* phi1 1/2)) (cos (* phi2 1/2)) (- (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))) (- phi1 phi2)) R)
829.0ms
(fma (sqrt (sqrt (cbrt (* (* (fma c (* -4 a) (* b b)) (fma c (* -4 a) (* b b))) (fma c (* -4 a) (* b b)))))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
813.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
676.0ms
(cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))
638.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 1/2 (+ phi1 phi2)))) (- phi1 phi2)) R)

regimes11.8s

Accuracy

Total 20.2b remaining (9.6%)

3.9b58.3%Quotient of products
3.1b0%Cubic critical, wide range
3.0b0%Quadratic roots, medium range
1.7b0%Quadratic roots, wide range
1.4b64.7%2-ancestry mixing, positive discriminant

rewrite9.5s

Algorithm
125×rewrite-expression-head
Calls

419 calls:

Slowest
416.0ms
(- (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))) (/ 1/4 (* x x)))
297.0ms
(* (- lambda1 lambda2) (- (* (cos (* phi1 1/2)) (cos (* phi2 1/2))) (* (sin (* phi1 1/2)) (sin (* phi2 1/2)))))
182.0ms
(exp (+ (/ 1 (- x 1)) (/ x (+ x 1))))
168.0ms
(* (- (/ m (/ v (- 1 m))) 1) (- 1 m))
160.0ms
(cbrt (* (* (- (exp x) (exp (- x))) (- (exp x) (exp (- x)))) (- (exp x) (exp (- x)))))
Rules
16594×times-frac
13161×*-un-lft-identity
12440×add-sqr-sqrt
10414×add-cube-cbrt
6361×prod-diff
2801×add-exp-log
2284×sqrt-prod
1427×add-cbrt-cube
1091×prod-exp
989×pow1
972×div-exp
925×div-inv
923×difference-of-squares
696×pow-exp
638×add-log-exp
635×distribute-lft-out
570×distribute-lft-out--
516×associate-*r*
497×fma-neg
451×associate-/r*
448×associate-/l*
426×expm1-log1p-u
420×log1p-expm1-u
419×insert-posit16
404×distribute-rgt-neg-in
396×associate-/r/
371×cbrt-unprod
362×distribute-rgt-in distribute-lft-in
346×pow-to-exp
327×distribute-lft-neg-in
319×associate-*l*
311×cbrt-undiv
257×cbrt-prod
234×flip--
233×flip3--
187×pow-prod-down
179×fma-def
164×difference-of-sqr-1
163×flip-+
162×flip3-+
142×1-exp rec-exp
109×neg-mul-1
107×unswap-sqr
96×sub-neg
91×frac-2neg clear-num
88×diff-log
87×*-commutative
84×fma-udef
83×associate-*r/
77×log-prod
75×frac-times
68×pow-prod-up
61×associate-*l/
60×swap-sqr
57×cbrt-div
49×unpow-prod-down
48×exp-sum pow-plus
47×associate--l+
42×associate-/l/ pow-sqr
37×log-pow
36×pow1/3
33×sin-sum
32×sum-log
31×exp-prod
30×pow2 cos-sum
28×sqrt-div
25×sqrt-pow1 pow1/2
24×+-commutative rem-sqrt-square
23×div-sub log1p-udef
20×pow-flip
19×difference-of-sqr--1 log-div
18×pow-pow
17×neg-sub0 frac-add
16×associate--r+
15×frac-sub
14×tan-quot
13×neg-log distribute-rgt-out
12×inv-pow sin-mult
10×cos-mult associate--l- expm1-def
pow-unpow acos-asin
log1p-expm1 pow3 rem-exp-log
sqr-pow associate-+l- rem-log-exp
associate--r-
distribute-lft1-in sub-div rem-cbrt-cube
exp-diff un-div-inv distribute-rgt-out--
associate-+l+ distribute-frac-neg hypot-udef acos-neg
expm1-log1p expm1-udef log1p-def cos-diff
distribute-rgt1-in associate-+r+ tanh-def tanh-undef asin-acos unpow1/3 sin-diff

localize4.6s

bsearch1.4s

end1.0ms