Details

sample10.8m

Algorithm
72×intervals
Results
7.8m80216×body10240exit
51.1s32970×body1280valid
25.8s198789×body80valid
22.7s24408×body640valid
19.6s150219×body80nan
14.5s25264×body320valid
12.5s34806×body160valid
8.7s154414×pre80true
3.7s3177×body2560valid
1.4s8085×body160nan
1.0s4157×pre10240exit
311.0ms229×body5120valid

prune5.6m

simplify4.0m

series55.1s

Calls

448 calls:

Slowest
682.0ms
(/ (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (* 3 a))
645.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
632.0ms
(cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))
628.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
619.0ms
(* (fma (sqrt (sqrt (fma c (* -3 a) (* b b)))) (sqrt (sqrt (fma c (* -3 a) (* b b)))) (- b)) (/ 1/3 a))

regimes15.3s

Accuracy

Total 45.5b remaining (14.6%)

Threshold costs 4.1b (1.3%)

7.4b44.8%Quadratic roots, narrow range
7.3b46%Cubic critical, narrow range
4.8b52.4%Quotient of products
4.3b84.5%Quadratic roots, full range
3.9b81%Cubic critical

rewrite10.5s

Algorithm
135×rewrite-expression-head
Calls

448 calls:

Slowest
354.0ms
(cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
265.0ms
(* (- (/ m (/ v (- 1 m))) 1) (- 1 m))
178.0ms
(+ (+ (/ 1 (* x x)) (/ 3 x)) (/ 3 (* x (* x x))))
173.0ms
(* (- (/ m (/ v (- 1 m))) 1) m)
155.0ms
(/ (* (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)))
Rules
26940×times-frac
24645×*-un-lft-identity
20632×add-sqr-sqrt
14673×add-cube-cbrt
10014×prod-diff
8624×sqrt-prod
3106×distribute-lft-out
2952×add-exp-log
2517×difference-of-squares
2487×pow1
1870×associate-/r/
1535×add-cbrt-cube
1282×distribute-lft-out--
1185×div-inv
1174×prod-exp
966×div-exp
960×difference-of-sqr-1
760×pow-prod-up
715×associate-*r*
697×pow-exp
637×sqrt-div
636×associate-*l*
631×add-log-exp
577×fma-neg
566×flip-+
565×flip3-+
559×associate-/r*
534×flip--
533×flip3--
496×pow-plus
473×associate-/l*
459×cbrt-prod
453×expm1-log1p-u
452×log1p-expm1-u
448×insert-posit16
425×cbrt-unprod
413×pow-prod-down
375×swap-sqr
347×pow-to-exp
316×frac-times
304×cbrt-undiv
288×pow-sqr
241×associate-*l/
231×unswap-sqr
192×associate-*r/
190×log-prod
181×pow2
165×frac-sub
160×1-exp rec-exp
155×cbrt-div
153×fma-def
102×frac-2neg clear-num
95×distribute-rgt-out
94×*-commutative
91×distribute-rgt1-in
84×log-pow
80×sqrt-pow1 pow1/2
78×distribute-rgt-in distribute-lft-in
72×difference-of-sqr--1 pow1/3
65×fma-udef
64×sub-neg
61×exp-prod
60×unpow-prod-down
58×diff-log
57×pow3
52×rem-sqrt-square
49×associate-/l/
41×sum-log
39×pow-flip
33×sin-sum
29×tan-quot log-div
28×rem-log-exp
26×div-sub
25×+-commutative cos-sum
24×associate-+l+
22×inv-pow
21×exp-sum pow-pow
19×cube-prod
18×distribute-rgt-neg-in
15×frac-add
12×pow-unpow tanh-def
9×distribute-lft-neg-in acos-asin
8×associate--r+ log1p-udef
7×expm1-udef cos-mult un-div-inv associate-+l-
6×neg-sub0 exp-diff log1p-expm1 sqr-pow pow-div
5×expm1-log1p associate--l+ sin-mult rem-exp-log cube-mult
4×sqrt-unprod sum-cubes hypot-def rem-square-sqrt associate--r- expm1-def
3×associate-+r+ distribute-frac-neg cube-unmult log-rec neg-log neg-mul-1 distribute-rgt-out-- acos-neg rem-cbrt-cube
2×difference-cubes hypot-udef cos-diff
1×remove-posit16 rem-cube-cbrt unpow3 tanh-undef exp-to-pow asin-acos sin-diff unpow1/3

localize5.0s

bsearch1.6s

end1.0ms