Details

simplify37.0m

Calls

17233 calls:

Slowest
4.8s
(/ (* (* (* 3 3) 3) (* (* (* c c) c) (* (* a a) a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
4.2s
(/ (* (* (* 3 3) 3) (* (* (* c a) (* c a)) (* c a))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
4.2s
(/ (* (* (* 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)))))))
2.9s
(- (+ (log 3) (log (* c a))) (+ (log 3) (log a)))
2.7s
(/ (* (* (* 4 4) 4) (* (* (* c a) (* c a)) (* c a))) (* (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))))

sample11.2m

Algorithm
70×intervals
Results
8.2m75988×body10240exit
55.3s31522×body1280valid
25.4s191996×body80valid
23.7s24299×body640valid
20.7s148659×body80nan
14.1s25059×body320valid
13.4s35060×body160valid
9.3s150254×pre80true
1.6s1885×body2560valid
1.2s7846×body160nan
1.2s4169×pre10240exit
136.0ms114×body5120valid

prune3.1m

series48.6s

Calls

405 calls:

Slowest
916.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R)
704.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))) R))
681.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
652.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
628.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))

regimes9.8s

Accuracy

Total 22.3b remaining (13.1%)

6.6b26.6%Cubic critical, narrow range
3.2b72.6%Quotient of products
2.5b29.6%Cubic critical, wide range
2.1b0%Cubic critical, medium range
1.3b94.3%Cubic critical

rewrite9.4s

Algorithm
123×rewrite-expression-head
Calls

405 calls:

Slowest
389.0ms
(* (* (* (- (/ (* m (- 1 m)) v) 1) (sqrt m)) (sqrt (sqrt m))) (sqrt (sqrt m)))
214.0ms
(+ (+ (/ -3 (* (* x x) x)) (/ -3 x)) (/ -1 (* x x)))
210.0ms
(cbrt (* (* (* (sin phi2) (sin phi1)) (* (sin phi2) (sin phi1))) (* (sin phi2) (sin phi1))))
201.0ms
(cbrt (* (* (* (/ 1 (fma x x -1)) -2) (* (/ 1 (fma x x -1)) -2)) (* (/ 1 (fma x x -1)) -2)))
177.0ms
(- (/ (exp x) (+ (exp x) (exp (- x)))) (/ (exp (- x)) (+ (exp x) (exp (- x)))))
Rules
18413×times-frac
13774×*-un-lft-identity
12908×add-sqr-sqrt
11236×add-cube-cbrt
6463×prod-diff
2904×sqrt-prod
1736×add-exp-log
1463×add-cbrt-cube
1057×div-inv
1021×pow1
764×distribute-lft-out
686×difference-of-squares
581×associate-/r/
562×add-log-exp
560×associate-/r*
481×div-exp
471×associate-*r*
462×associate-*l*
421×associate-/l*
410×unpow-prod-down
407×expm1-log1p-u
406×cube-prod log1p-expm1-u
405×insert-posit16 prod-exp
394×distribute-rgt-in distribute-lft-in
384×distribute-lft-out--
371×fma-neg
360×cbrt-unprod
328×cbrt-undiv
268×distribute-rgt-neg-in
264×cbrt-prod
249×flip-+
248×flip3-+
234×distribute-lft-neg-in
215×pow-prod-down
184×flip--
183×flip3--
152×difference-of-sqr-1
143×associate-*r/
139×unswap-sqr
120×swap-sqr
117×fma-def
102×sqrt-div
99×frac-2neg clear-num
89×*-commutative
88×log-prod
78×neg-mul-1
76×associate-*l/
71×sqrt-pow1 sub-neg
70×sqr-pow
66×fma-udef
63×pow1/2
62×pow-prod-up
58×associate-/l/
57×cube-mult
56×unpow3
55×1-exp rec-exp
50×diff-log
49×associate-+l+
47×associate-+r+ cbrt-div
46×exp-prod
43×pow1/3
42×pow-sqr
41×frac-times pow-plus
39×log-pow
36×rem-sqrt-square
33×sin-sum
30×sum-log
24×cos-sum
23×exp-sum pow2 +-commutative
22×frac-add
21×log-div
20×sin-mult
17×div-sub
16×pow-flip
15×rem-log-exp
14×neg-sub0 pow-pow inv-pow
12×tan-quot
11×distribute-rgt-out
10×neg-log pow-unpow
pow-exp pow3 associate--l- distribute-rgt-out-- quot-tan acos-asin
associate-+l-
rem-exp-log
unpow-prod-up distribute-lft-neg-out frac-sub associate--r+ rem-cbrt-cube associate--r- expm1-def log1p-udef
distribute-frac-neg cube-unmult associate--l+ log1p-expm1 sqrt-unprod pow-to-exp acos-neg rem-square-sqrt
expm1-log1p expm1-udef exp-diff rem-cube-cbrt distribute-rgt1-in sub-div difference-cubes cos-diff
cos-mult distribute-lft1-in unsub-neg cube-div tanh-def tanh-undef exp-neg asin-acos unpow1/3 sin-diff un-div-inv e-exp-1

localize4.3s

bsearch1.5s

end1.0ms