Details

simplify7.1m (57.0%)

sample2.0m (16.4%)

Algorithm
54×intervals
Results
49.7s13530×body10240exit
22.2s12832×body1280valid
11.5s11655×body640valid
7.8s93154×body80valid
7.7s82016×body80nan
5.1s101183×pre80true
4.7s11165×body320valid
3.4s15954×body160valid
849.0ms7869×body160nan
210.0ms8292×pre80false
55.0ms109×body2560valid
16.0ms127×pre10240exit
4.0ms8×body5120valid

prune1.8m (14.2%)

series59.8s (8.1%)

Calls

465 calls:

860.0ms
(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))
850.0ms
(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))
782.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
716.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
691.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)

rewrite25.2s (3.4%)

Algorithm
147×rewrite-expression-head
Calls

465 calls:

731.0ms
(* (- (/ (* m (- (* 1.0 1.0) (* m m))) (* (sqrt (* v (+ 1.0 m))) (sqrt (* v (+ 1.0 m))))) 1.0) m)
554.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
485.0ms
(* (- (/ (- (* 1.0 m) (pow m 3)) (* v (+ 1.0 m))) 1.0) (- 1.0 m))
358.0ms
(* (/ (/ 1.0 (+ x 1.0)) (- x 1.0)) (cbrt (pow (- (- 0 1.0) 1.0) 3)))
323.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))
Rules
36231×times-frac
22067×*-un-lft-identity
19570×add-sqr-sqrt
15305×add-cube-cbrt
4829×prod-diff
3005×add-exp-log
1979×difference-of-squares
1905×distribute-lft-out--
1756×sqrt-prod
1746×add-cbrt-cube
1509×div-inv
1434×distribute-lft-out
1204×associate-/r/
1098×div-exp
972×pow1
945×prod-exp
922×associate-/r*
809×distribute-rgt-neg-in
774×log-prod
688×add-log-exp
627×associate-*r*
583×cbrt-prod
578×associate-/l*
511×exp-sum
478×associate-*l*
469×expm1-log1p-u
466×log1p-expm1-u
442×cbrt-undiv
441×flip--
440×flip3--
422×fma-neg
415×cbrt-unprod
358×unpow-prod-down
332×flip-+
331×flip3-+ pow-exp
308×cube-prod
235×pow-to-exp
224×pow-prod-down
199×distribute-lft-neg-in
168×fma-def
160×distribute-rgt-in distribute-lft-in
146×unswap-sqr
130×associate-*r/
123×sqr-pow
121×clear-num frac-2neg
105×log-pow
104×sub-neg
102×1-exp
101×associate-/l/
93×sqrt-div
92×*-commutative
87×unpow3
83×diff-log
81×cube-mult
76×sqrt-pow1
68×associate-+r+
66×neg-mul-1
63×associate-*l/
62×rec-exp
57×frac-times
53×exp-prod
52×pow1/2
51×div-sub
50×cos-sum
45×log-div
44×cbrt-div
42×swap-sqr
34×sum-log
33×sin-sum fma-udef
31×rem-log-exp
30×rem-sqrt-square
26×+-commutative
20×pow1/3
19×cube-div sin-mult sin-diff
18×pow-unpow pow-prod-up
16×neg-sub0 frac-sub
15×associate--l+
14×sin-cos-mult cos-diff associate-+l+ tan-quot
13×associate-+l-
12×pow-sqr acos-asin neg-log
11×associate--l-
9×associate--r+ pow-pow
8×exp-diff frac-add
7×rem-cube-cbrt cos-mult
6×acos-neg distribute-rgt-out-- distribute-frac-neg
5×un-div-inv inv-pow pow2 pow-flip pow-plus associate--r-
4×log1p-udef sqrt-unprod associate-+r- log1p-expm1 rem-cbrt-cube rem-exp-log
3×distribute-neg-in asin-acos expm1-udef log-rec
2×e-exp-1 expm1-log1p hypot-udef rem-square-sqrt distribute-rgt-out
1×unsub-neg tanh-undef exp-to-pow tanh-def

localize4.0s (0.5%)

regimes3.0s (0.4%)

Accuracy

Total 2.2b remaining (69.9%)

Threshold costs 2.2b (69.9%)

0.4b0%Cubic critical, narrow range
0.4b0%Hyperbolic arc-(co)tangent
0.4b0%Quadratic roots, medium range
0.3b0%Trigonometry A
0.2b0%a parameter of renormalized beta distribution

bsearch8.0ms (0.0%)

end0.0ms (0.0%)