Details

sample28.7m (80.3%)

Algorithm
72×intervals
Results
7.6m81227×body10240exit
53.8s33195×body1280valid
26.0s198039×body80valid
20.9s152615×body80nan
19.9s24057×body640valid
13.1s25414×body320valid
11.4s34974×body160valid
9.9s153862×pre80true
3.0s3052×body2560valid
1.7s7875×body160nan
1.3s4165×pre10240exit
197.0ms224×body5120valid

simplify3.4m (9.5%)

prune2.5m (7.0%)

series37.2s (1.7%)

Calls

387 calls:

Slowest
686.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
593.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
588.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
584.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
578.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

regimes12.1s (0.6%)

Accuracy

Total 58.2b remaining (33.1%)

Threshold costs 4.3b (2.4%)

7.5b45.7%Quadratic roots, narrow range
7.2b47.1%Cubic critical, narrow range
6.8b0%Cubic critical, medium range
5.9b12.1%Quadratic roots, medium range
5.1b28.9%Quotient of products

rewrite12.0s (0.6%)

Algorithm
126×rewrite-expression-head
Calls

387 calls:

Slowest
436.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
329.0ms
(log (+ x (+ x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
287.0ms
(- (/ -1/16 (* (* x x) (* (* x x) x))) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))
200.0ms
(log (- (/ -1/16 (* (* x x) (* (* x x) x))) (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
177.0ms
(+ (* 3/40 (* (* x x) (* (* x x) x))) (- x (* (* (* x x) x) 1/6)))
Rules
3965×*-un-lft-identity
3743×times-frac
3737×add-sqr-sqrt
3255×add-exp-log
2375×add-cube-cbrt
1807×add-cbrt-cube
1301×prod-exp
1150×associate-*l/
1148×div-exp
1102×flip--
1101×flip3--
1033×pow1
797×associate-*r*
782×frac-times
723×sqrt-prod
694×pow-exp
620×associate-*l*
612×frac-add
593×add-log-exp
558×cbrt-unprod
556×sqrt-div
510×cbrt-prod
480×associate-*r/
452×cbrt-undiv
428×distribute-lft-out
387×insert-posit16
373×associate-/r*
353×difference-of-squares
349×pow-to-exp
337×associate-/l*
272×cbrt-div
271×div-inv
256×distribute-lft-out--
254×pow-prod-down
230×unswap-sqr
165×log-prod
159×1-exp
155×associate-/r/
154×rec-exp
143×flip-+
142×flip3-+
100×frac-2neg clear-num
95×*-commutative
94×sub-neg
89×swap-sqr
85×associate-/l/
76×cos-mult
69×diff-log
67×pow-prod-up
58×difference-of-sqr-1
48×log-pow
47×sqrt-pow1 frac-sub
45×unpow-prod-down
44×distribute-rgt-in distribute-lft-in
43×log-div
42×pow1/3
39×sum-log pow1/2
38×pow-plus
33×pow-sqr
30×exp-prod
28×+-commutative
27×tan-quot rem-sqrt-square
23×pow2
21×associate--l+
20×div-sub distribute-rgt-out rem-log-exp
17×associate-+r+
16×distribute-rgt-out--
13×distribute-rgt-neg-in distribute-lft-neg-in
12×sqr-pow
11×cos-sum cos-diff
10×pow-flip inv-pow
9×acos-asin
8×sin-mult
7×cube-prod pow-pow distribute-rgt1-in
6×associate-+l+ difference-of-sqr--1 pow-unpow neg-mul-1
5×distribute-lft-neg-out exp-diff associate--l- associate-+l-
4×associate-+r- pow3
3×exp-sum distribute-frac-neg associate--r+ distribute-neg-frac acos-neg
2×sin-sum cube-mult sqr-sin un-div-inv exp-to-pow rem-exp-log sub-div sqr-cos cos-PI/3
1×rem-cube-cbrt unsub-neg sqrt-unprod distribute-rgt-neg-out unpow3 tanh-undef tanh-def asin-acos sum-cubes rem-cbrt-cube cube-unmult associate--r- sin-diff

localize4.3s (0.2%)

bsearch1.6s (0.1%)

end1.0ms (0.0%)