Details

simplify25.5m

Calls

12017 calls:

Slowest
2.8s
(/ (* (* (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (/ 1 (+ 1 (exp (- s)))) c_p)) (pow (/ 1 (+ 1 (exp (- s)))) c_p)) (* (* (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n))) (* (* (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n))) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n))))
2.7s
(/ (* (* (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n))) (* (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)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n))) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n))))
2.7s
(/ (* (* (* -2 -2) -2) (* (* (* a c) (* a c)) (* a c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
2.7s
(/ (* (* (* -2 (* a c)) (* -2 (* a c))) (* -2 (* a c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))
2.7s
(/ (* (* (* -2 -2) -2) (* (* (* a a) a) (* (* c c) c))) (* (* (* (* 2 a) b) (* (* 2 a) b)) (* (* 2 a) b)))

sample11.9m

Algorithm
72×intervals
Results
8.7m82064×body10240exit
58.0s33153×body1280valid
25.6s198514×body80valid
23.6s24490×body640valid
19.7s150895×body80nan
13.6s24944×body320valid
13.4s34925×body160valid
9.9s154039×pre80true
4.2s3128×body2560valid
1.5s7711×body160nan
938.0ms4173×pre10240exit
656.0ms227×body5120valid

prune2.6m

series39.2s

Calls

415 calls:

Slowest
584.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
550.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
546.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
542.0ms
(/ 1 (* (/ (+ 1 (* e (cos v))) (sin v)) (/ 1 e)))
536.0ms
(/ (* (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)))

rewrite16.0s

Algorithm
127×rewrite-expression-head
Calls

415 calls:

Slowest
590.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
570.0ms
(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
459.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
419.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
337.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
Rules
4449×*-un-lft-identity
4228×add-sqr-sqrt
4187×times-frac
3570×add-exp-log
2769×add-cube-cbrt
2006×add-cbrt-cube
1488×prod-exp
1297×pow1
1174×div-exp
881×associate-*l/
789×flip--
788×flip3--
696×pow-exp
692×frac-times
664×cbrt-unprod
653×add-log-exp
623×associate-*r*
607×difference-of-squares
557×associate-*l*
526×sqrt-div
504×associate-/r*
477×associate-*r/
452×cbrt-undiv
421×cbrt-prod
415×insert-posit16
395×frac-add
360×associate-/l*
353×distribute-lft-out
351×log-prod
348×pow-to-exp
332×distribute-lft-out--
329×pow-prod-down
316×sqrt-prod
276×div-inv
243×swap-sqr
240×associate-/r/
177×1-exp rec-exp
172×unswap-sqr
168×flip-+
167×flip3-+
166×cbrt-div
140×exp-prod
133×log-div
126×pow-prod-up
122×log-pow
106×tanh-def
104×frac-2neg clear-num
101×*-commutative
100×sub-neg
89×pow-sqr
88×difference-of-sqr-1
87×diff-log
85×frac-sub
84×exp-diff
80×unpow-prod-down
75×sqrt-pow1 pow1/2 associate-/l/
59×pow-plus
51×pow1/3
49×associate--r+
47×rem-log-exp
45×sum-log
43×pow2
39×distribute-rgt-in distribute-lft-in
36×div-sub
35×associate--l+
32×pow-flip
31×rem-sqrt-square
29×+-commutative
28×cube-prod
24×distribute-rgt-neg-in tan-quot
20×distribute-rgt-out-- distribute-lft-neg-in
15×un-div-inv
13×inv-pow acos-asin
12×cos-mult
11×exp-sum
10×sqr-pow associate-+l-
cos-diff
associate--l- distribute-frac-neg neg-mul-1 sin-mult cos-sum associate--r-
exp-neg sum-cubes acos-neg
neg-sub0 sin-sum pow-unpow pow3 sqrt-unprod pow-pow rem-exp-log
associate-+r+ sub-div rem-square-sqrt
associate-+l+ cube-unmult
difference-cubes
log-rec
quot-tan remove-posit16 sub0-neg tanh-undef sin-PI/3 asin-acos rem-cbrt-cube sin-diff

regimes14.7s

Accuracy

Total 53.9b remaining (33.2%)

7.7b44.1%Quadratic roots, narrow range
6.6b0%Cubic critical, medium range
6.6b26%Cubic critical, narrow range
6.4b6.5%Quadratic roots, medium range
4.5b84.2%Cubic critical

bsearch8.5s

localize4.6s

end1.0ms