Details

simplify1.3hr

Calls

36219 calls:

Slowest
33.6s
(+ (- (log -2) (+ (log (+ x 1)) (log (- (* x x) (* 1 1))))) (log (+ x 1)))
33.4s
(/ (* (cbrt -2) (cbrt -2)) (* (+ x 1) (+ x (sqrt (* 1 1)))))
32.9s
(- (* 1 (/ (- x 1) (cbrt 1))) (* (/ (+ x 1) 1) (* (cbrt 1) (cbrt 1))))
32.6s
(/ (/ (* a c) b) a)
32.6s
(/ (* -3/2 (/ (* (sqrt a) (sqrt c)) (* (cbrt b) (cbrt b)))) (* 3 1))

sample11.9m

Algorithm
66×intervals
Results
9.3m79696×body10240exit
46.8s26530×body1280valid
21.4s144884×body80nan
20.4s170329×body80valid
19.4s18669×body640valid
12.0s18754×body320valid
10.0s30843×body160valid
8.1s137936×pre80true
2.6s2246×body2560valid
1.5s8034×body160nan
854.0ms4067×pre10240exit
243.0ms217×body5120valid

rewrite5.4m

Algorithm
123×rewrite-expression-head
Calls

375 calls:

Slowest
33.9s
(cbrt (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))))
12.5s
(cbrt (cbrt (* (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))))))
3.9s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
3.7s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
3.5s
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
Rules
4719408×tan-quot
4210713×frac-times
2103639×associate-*l/
1974684×add-sqr-sqrt
1850692×unswap-sqr
1430595×associate-*r/
807685×cbrt-div
278471×cbrt-prod
261840×swap-sqr
190609×*-commutative
56966×times-frac
56225×*-un-lft-identity
39339×add-cube-cbrt
39113×associate-/l*
30979×associate-*r*
26161×associate-/r*
23425×frac-add
20732×associate-*l*
18721×frac-sub
12797×associate-/l/
9795×log-div
9643×unpow-prod-down
6873×difference-of-squares
5973×flip--
5972×flip3--
5401×clear-num
5177×frac-2neg
3377×distribute-lft-out--
3318×distribute-lft-out
2748×sqrt-div
2671×add-exp-log
2595×pow1
2571×sqr-pow
2325×sqrt-prod
2043×div-inv
1420×add-cbrt-cube
1180×flip-+
1179×flip3-+
1113×prod-exp
969×pow-prod-up
881×pow-prod-down
874×div-exp
829×log-prod
701×pow-exp
662×pow3
643×pow-plus
624×un-div-inv add-log-exp
574×associate-/r/
419×cbrt-unprod
417×pow-unpow
411×cube-prod
408×sum-cubes
375×insert-posit16
352×pow-to-exp
351×associate-+r-
308×pow-sqr
266×cbrt-undiv
211×difference-of-sqr-1
191×pow2
141×distribute-rgt-out--
127×1-exp
126×rec-exp
125×distribute-rgt-neg-in
115×log-pow
104×rem-cbrt-cube
99×diff-log
92×sub-neg
90×exp-prod cube-mult
54×associate-+r+
51×distribute-lft-neg-in
50×pow1/3 +-commutative
48×sqrt-pow1
43×sum-log
42×rem-sqrt-square
40×cube-unmult
38×associate-+l+ distribute-rgt-in pow1/2 distribute-lft-in
31×div-sub
26×associate--l+ associate-+l-
25×rem-log-exp
21×associate--r+ sub-div
17×neg-mul-1
16×cos-diff
14×log-rec
13×associate--l-
12×pow-flip cos-sum
11×associate--r-
10×sin-sum pow-pow
9×neg-sub0
8×sin-mult inv-pow acos-asin
7×neg-log asin-acos distribute-rgt-out
6×exp-diff exp-sum
3×cos-mult distribute-frac-neg sin-PI/3 rem-exp-log acos-neg
2×distribute-rgt1-in
1×rem-cube-cbrt sqrt-undiv sin-cos-mult unpow3 sqrt-unprod tanh-undef tanh-def exp-to-pow sin-diff

prune5.3m

series36.9s

Calls

375 calls:

Slowest
786.0ms
(/ (* (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)))
646.0ms
(cbrt x)
640.0ms
(+ (* (cos (/ (/ PI 2) 3)) (cos (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))) (* (sin (* (sqrt PI) (/ (sqrt PI) 6))) (sin (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))))
633.0ms
(+ (* (cos (/ (/ PI 2) 3)) (cos (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))) (* (sin (/ (/ PI 2) 3)) (sin (+ (/ (asin (/ g h)) 3) (/ PI 3/2)))))
589.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (cbrt (- lambda1 lambda2)) (cbrt (- lambda1 lambda2)))) (* (cbrt (- lambda1 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

regimes12.3s

Accuracy

Total 43.7b remaining (33.2%)

7.4b46.6%Cubic critical, narrow range
7.2b47.2%Quadratic roots, narrow range
6.7b0%Quadratic roots, medium range
5.9b12.6%Cubic critical, medium range
4.1b85.2%Cubic critical

localize4.0s

bsearch1.1s

end1.0ms