Details

simplify6.5m (43.4%)

sample5.0m (33.7%)

Algorithm
78×intervals
Results
1.7m20426×body10240exit
1.3m43746×body1280valid
31.2s30691×body640valid
19.1s202771×body80valid
14.7s153013×body80nan
12.4s27749×body320valid
8.6s158253×pre80true
8.3s35759×body160valid
2.7s3100×body2560valid
1.2s7869×body160nan
486.0ms4116×pre10240exit
170.0ms220×body5120valid
165.0ms8292×pre80false
2.0ms1×body640nan

series1.4m (9.4%)

Calls

450 calls:

27.6s
(* (hypot (* (- lambda1 lambda2) (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
1.1s
(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)))
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)))
838.0ms
(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))
818.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi2 phi1)))) (- phi1 phi2)) R)

prune1.2m (7.9%)

rewrite26.2s (2.9%)

Algorithm
147×rewrite-expression-head
Calls

450 calls:

1.9s
(+ (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x) x)
1.3s
(log (exp (/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (fma (/ x (+ x 1.0)) (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- x 1.0)) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))))))
913.0ms
(log (+ (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) x) x))
646.0ms
(* (- (* m (/ (- (* 1.0 1.0) (* m m)) (* v (+ 1.0 m)))) 1.0) m)
513.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
Rules
14980×*-un-lft-identity
11672×times-frac
10886×add-sqr-sqrt
8048×add-cube-cbrt
6739×prod-diff
2769×unpow-prod-down
2731×cube-prod
2523×add-exp-log
2158×distribute-lft-out
1592×add-cbrt-cube
1271×difference-of-squares
1237×distribute-lft-out--
1090×sqrt-prod
1088×associate-/r/
944×pow1
880×prod-exp
765×div-inv
750×log-prod
728×div-exp
657×add-log-exp
541×associate-*r*
511×exp-sum
462×associate-*l*
454×expm1-log1p-u
451×log1p-expm1-u
443×associate-/l*
439×associate-/r*
432×fma-neg
404×flip-+
403×flip3-+
401×cbrt-unprod
386×cbrt-prod
371×flip--
370×flip3--
338×pow-exp
336×cbrt-undiv
331×log-pow
279×exp-prod
265×sqr-pow
237×pow-to-exp
204×pow-prod-down
190×unpow3
184×cube-mult
152×distribute-rgt-in distribute-lft-in
143×fma-def
129×unswap-sqr
121×distribute-rgt-neg-in
112×clear-num frac-2neg
111×associate-*r/
103×sub-neg
93×*-commutative
91×distribute-lft-neg-in
81×associate-/l/
78×diff-log
68×associate-+r+
65×sqrt-div
61×associate-*l/
55×frac-times
52×cos-sum
51×div-sub
48×log-div
46×sqrt-pow1
40×pow1/2 swap-sqr
38×cbrt-div
35×sin-mult
33×sin-sum 1-exp rec-exp sum-log
32×fma-udef
30×neg-mul-1
28×rem-sqrt-square
27×pow-unpow rem-log-exp
24×+-commutative cos-mult
21×cube-div frac-sub
20×pow1/3
19×sin-diff
18×rem-cube-cbrt
17×pow-pow
16×pow-prod-up
15×associate-+l+ associate--l+
14×sin-cos-mult cos-diff pow-sqr tan-quot
12×acos-asin
9×exp-diff associate-+l- associate--r+
8×frac-add pow-plus
7×inv-pow pow-flip
6×acos-neg distribute-rgt-out-- associate--l- pow2 distribute-frac-neg
5×neg-sub0 associate--r-
4×difference-cubes un-div-inv log1p-udef associate-+r- log1p-expm1 sub-div neg-log rem-cbrt-cube
3×rem-exp-log sqrt-unprod distribute-neg-in log-rec asin-acos expm1-udef
2×expm1-log1p hypot-udef distribute-rgt-out distribute-rgt-neg-out
1×unsub-neg rem-square-sqrt tanh-undef exp-to-pow tanh-def

regimes16.2s (1.8%)

Accuracy

Total 51.4b remaining (34%)

Threshold costs 4.5b (3%)

7.6b45.5%Quadratic roots, narrow range
7.6b45.4%Cubic critical, narrow range
6.4b10.7%Cubic critical, medium range
6.0b82.2%Quadratic roots, full range
3.7b0%Cubic critical, wide range

bsearch4.8s (0.5%)

localize3.8s (0.4%)

end0.0ms (0.0%)