Details

simplify7.1m (48.2%)

prune3.6m (24.6%)

sample2.0m (13.5%)

Algorithm
54×intervals
Results
47.1s11093×body10240exit
21.2s11192×body1280valid
9.9s10631×body640valid
8.2s89477×body80valid
7.6s90458×body80nan
5.4s109625×pre80true
4.8s18423×body160valid
4.7s13945×body320valid
773.0ms7869×body160nan
200.0ms8292×pre80false
45.0ms109×body2560valid
20.0ms127×pre10240exit
4.0msbody5120valid

series1.3m (8.8%)

Calls

487 calls:

6.3s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)) (+ (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (cos phi1))) (* (cos phi1) (cos phi1))))
2.1s
(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))
2.1s
(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))
2.1s
(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))
2.1s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))

rewrite34.5s (3.9%)

Algorithm
147×rewrite-expression-head
Calls

487 calls:

1.2s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
1.2s
(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
740.0ms
(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))
717.0ms
(sqrt (+ (- (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))
703.0ms
(sqrt (+ (- (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2) (+ (pow lambda1 2) (pow lambda2 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))
Rules
71066×times-frac
40557×add-sqr-sqrt
35549×*-un-lft-identity
28572×unpow-prod-down
23949×add-cube-cbrt
18406×sqrt-prod
6545×difference-of-squares
3741×sqr-pow
3482×distribute-lft-out--
3112×add-exp-log
2289×distribute-lft-out
1955×associate-/r/
1949×add-cbrt-cube
1820×div-inv
1039×prod-exp
1025×pow1
1013×flip-+
1012×flip3-+
991×div-exp
763×add-log-exp
754×associate-/r*
723×associate-*r*
689×associate-/l*
495×associate-*l*
492×cbrt-undiv
478×cbrt-unprod
456×flip--
455×flip3--
358×pow-exp
337×cbrt-prod
325×log-prod
253×pow-to-exp
248×sqrt-div
238×cube-prod
232×associate-*l/
223×associate-*r/
210×pow-prod-down
197×frac-times
158×log-pow
155×frac-add
148×distribute-rgt-neg-in
146×unswap-sqr
133×sub-neg
129×rem-sqrt-square
128×clear-num frac-2neg
112×associate-/l/
106×*-commutative
91×exp-prod
90×diff-log
73×associate-+r+
70×swap-sqr sqrt-pow1
64×distribute-rgt-in distribute-lft-in
58×log-div
55×pow1/2
54×sum-log
46×1-exp rec-exp
45×+-commutative
43×div-sub
40×frac-sub
37×unpow3
35×cube-mult
33×cbrt-div
31×rem-log-exp
30×pow-unpow
29×associate--l+
28×distribute-rgt-out tan-quot
24×pow1/3
23×cos-sum
22×exp-sum
21×sin-mult
20×pow-prod-up
19×sin-diff
18×pow-sqr
17×neg-sub0 cos-mult
15×cube-div cos-diff
14×sin-cos-mult associate-+l+ associate-+l- pow-pow
13×associate--l- pow-plus neg-log
12×pow2
11×rem-cube-cbrt
10×inv-pow pow-flip associate--r+
associate-+r- acos-asin
exp-diff sin-sum
unpow2
sum-cubes distribute-lft1-in associate--r-
distribute-frac-neg acos-neg sqrt-unprod distribute-neg-in distribute-rgt-out-- asin-acos log-rec rem-cbrt-cube
sub0-neg un-div-inv rem-exp-log distribute-rgt-neg-out
difference-cubes unsub-neg rem-square-sqrt sub-div tanh-undef exp-to-pow tanh-def

localize4.5s (0.5%)

regimes3.8s (0.4%)

Accuracy

Total 9.1b remaining (60.7%)

Threshold costs 1.6b (11%)

3.7b0%Cubic critical, wide range
3.7b0%Quadratic roots, wide range
0.4b0%Quadratic roots, medium range
0.4b0%Hyperbolic arc-(co)tangent
0.3b0%Quadratic roots, narrow range

bsearch9.0ms (0.0%)

end0.0ms (0.0%)