Details

simplify20.8m

Calls

11506 calls:

Slowest
1.9s
(/ (* (* (* -2 -2) -2) (* (* (* (/ a (sqrt b)) (/ c (sqrt b))) (* (/ a (sqrt b)) (/ c (sqrt b)))) (* (/ a (sqrt b)) (/ c (sqrt b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.8s
(/ (* (* (* -2 -2) -2) (* (/ (* (* a a) a) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (/ c (sqrt b)) (/ c (sqrt b))) (/ c (sqrt b))))) (* (* (* 2 2) 2) (* (* a a) a)))
1.8s
(/ (* (* (* -2 -2) -2) (/ (/ (* (* (* a a) a) (* (* c c) c)) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 2 2) 2) (* (* a a) a)))
1.8s
(/ (* (* (* -2 -2) -2) (* (* (* (/ a (sqrt b)) (/ a (sqrt b))) (/ a (sqrt b))) (/ (* (* c c) c) (* (* (sqrt b) (sqrt b)) (sqrt b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.7s
(/ (* (* (* -2 -2) -2) (* (/ (* (* a a) a) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (/ c (sqrt b)) (/ c (sqrt b))) (/ c (sqrt b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

sample10.5m

Algorithm
71×intervals
Results
7.5m76939×body10240exit
52.8s32577×body1280valid
26.5s197973×body80valid
25.0s24655×body640valid
20.6s151721×body80nan
15.1s25151×body320valid
11.9s34899×body160valid
10.4s149916×pre80true
3.0s2896×body2560valid
1.5s7756×body160nan
902.0ms4175×pre10240exit
207.0ms197×body5120valid

prune2.6m

series32.2s

Calls

388 calls:

Slowest
624.0ms
(/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
605.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
602.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
575.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (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))))

regimes13.5s

Accuracy

Total 57.8b remaining (33.4%)

7.7b44.7%Quadratic roots, narrow range
7.1b47.9%Cubic critical, narrow range
7.0b0%Cubic critical, medium range
5.9b13.4%Quadratic roots, medium range
4.8b82.9%Cubic critical

rewrite12.4s

Algorithm
124×rewrite-expression-head
Calls

388 calls:

Slowest
419.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
419.0ms
(* (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))
349.0ms
(/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
313.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
295.0ms
(+ (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15))
Rules
5353×times-frac
4783×*-un-lft-identity
4613×add-sqr-sqrt
3212×add-cube-cbrt
1952×add-exp-log
1657×add-cbrt-cube
1000×sqrt-prod
952×pow1
698×flip--
697×flip3--
655×associate-*r*
589×add-log-exp
588×difference-of-squares
573×associate-*l/
568×prod-exp
535×associate-*r/
531×frac-times
519×sqrt-div
518×cbrt-prod
503×associate-*l*
496×div-exp
485×associate-/r*
458×cbrt-unprod
388×insert-posit16
387×distribute-lft-out
384×cbrt-undiv
383×frac-add
377×associate-/l*
336×div-inv
325×distribute-lft-out--
249×log-prod
225×pow-prod-down
169×flip-+
168×flip3-+
166×unswap-sqr
165×associate-/r/
117×swap-sqr
114×unpow-prod-down
106×*-commutative
103×associate-/l/
97×frac-2neg clear-num
95×sub-neg
82×difference-of-sqr-1
72×cube-prod
66×cos-mult
60×diff-log
54×1-exp rec-exp
53×log-pow
51×exp-prod distribute-rgt-in distribute-lft-in
50×sqrt-pow1
46×pow1/2
45×sum-log
44×sin-mult
41×pow-prod-up
39×rem-sqrt-square
38×distribute-rgt-neg-in
36×log-div
35×frac-sub
31×+-commutative pow-sqr
28×pow-plus
27×div-sub
25×pow1/3
22×rem-log-exp
21×cbrt-div
20×sqr-pow associate--l+
19×tan-quot
18×pow-flip sum-cubes
17×pow2 inv-pow cube-mult
14×distribute-rgt-out--
12×sub-div
11×associate-+l- acos-asin cos-diff
10×exp-sum cos-sum
associate-+l+
associate--l- associate-+r+ pow-exp pow-to-exp
un-div-inv associate--r-
neg-sub0
sqrt-unprod associate--r+
associate-+r- distribute-frac-neg neg-log sin-PI/3 exp-to-pow rem-exp-log acos-neg
exp-diff sin-sum pow3 asin-acos
remove-posit16 sin-cos-mult tanh-undef tanh-def neg-mul-1 distribute-lft-neg-out sin-diff distribute-lft-neg-in

localize4.2s

bsearch1.3s

end1.0ms