Details

simplify4.1m (37.7%)

sample3.8m (34.8%)

Algorithm
77×intervals
Results
1.2m43416×body1280valid
35.5s15711×body10240exit
27.9s31012×body640valid
19.0s202010×body80valid
15.0s152419×body80nan
13.0s27589×body320valid
9.3s35972×body160valid
6.4s152309×pre80true
1.6s3056×body2560valid
771.0ms7814×body160nan
594.0ms4140×pre10240exit
163.0ms8177×pre80false
138.0ms234×body5120valid
2.0ms2×body640nan

prune1.4m (12.6%)

series55.9s (8.6%)

Calls

437 calls:

752.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
727.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
722.0ms
(fma (cos phi2) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (cos phi1))
667.0ms
(* (hypot (pow (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) 1) (- phi1 phi2)) R)
575.0ms
(hypot (pow (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) 1) (- phi1 phi2))

rewrite23.5s (3.6%)

Algorithm
141×rewrite-expression-head
Calls

437 calls:

957.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))
829.0ms
(* (- (/ (* m (- (* 1.0 1.0) (* m m))) (/ (* v (+ (pow 1.0 3) (pow m 3))) (+ (* 1.0 1.0) (- (* m m) (* 1.0 m))))) 1.0) (- 1.0 m))
553.0ms
(* (- (- (* 1.0 (/ m v)) (/ (pow m 2) v)) 1.0) m)
517.0ms
(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))
472.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
Rules
12668×*-un-lft-identity
11841×times-frac
11303×add-sqr-sqrt
8117×add-cube-cbrt
5950×prod-diff
2095×add-exp-log
1711×add-cbrt-cube
1331×difference-of-squares
1266×distribute-lft-out
1184×sqrt-prod
1030×unpow-prod-down
956×distribute-lft-out--
940×distribute-rgt-in distribute-lft-in
882×pow1
845×associate-/r/
833×cube-prod
785×div-inv
707×cbrt-prod
666×log-pow
627×add-log-exp
622×div-exp
587×exp-prod
578×associate-*r*
563×associate-/l*
551×prod-exp
544×associate--l+
512×associate-/r*
439×log1p-expm1-u expm1-log1p-u
427×cbrt-unprod
426×cbrt-undiv
422×associate-*l*
379×fma-neg
369×flip--
368×flip3-- sqr-pow
323×distribute-rgt-neg-in
313×flip-+
312×flip3-+
266×unpow3
242×distribute-lft-neg-in
203×log-prod
180×fma-def
171×cube-mult
148×pow-prod-down
121×unswap-sqr associate-*r/
113×sqrt-div
111×clear-num frac-2neg
108×distribute-rgt-out
102×frac-times
91×sub-neg
85×associate-/l/
83×*-commutative
77×associate-*l/
73×1-exp diff-log
71×sqrt-pow1
69×pow1/2
66×swap-sqr
62×neg-mul-1
55×sin-sum
54×pow-unpow cbrt-div
49×cos-sum rec-exp
44×associate-+r+
42×pow-pow
37×div-sub
35×rem-sqrt-square
33×pow1/3
32×fma-udef log-div
30×sum-log
27×pow-exp
24×distribute-lft1-in
23×frac-sub
22×pow-to-exp
20×+-commutative
19×frac-add
18×rem-log-exp
17×rem-cube-cbrt
16×neg-sub0 pow-prod-up sin-diff
14×cube-div associate--l-
13×hypot-def
12×pow-sqr tan-quot associate-+l-
11×neg-log
10×difference-cubes cos-diff unpow2 sin-mult
9×sin-cos-mult cos-mult exp-sum
8×sum-cubes acos-asin
7×pow2 associate-+l+ pow-flip pow-plus rem-cbrt-cube
6×inv-pow
5×log1p-udef distribute-rgt1-in log1p-expm1
4×acos-neg sqrt-unprod associate-+r- expm1-log1p distribute-frac-neg asin-acos expm1-udef
3×exp-diff un-div-inv count-2 distribute-neg-frac
2×sin-neg exp-neg hypot-udef rem-square-sqrt distribute-rgt-out-- distribute-rgt-neg-out associate--r+
1×unpow-prod-up sub-div tanh-undef tanh-def

regimes12.8s (2.0%)

Accuracy

Total 46.5b remaining (31.4%)

Threshold costs 6.0b (4%)

7.7b45.1%Cubic critical, narrow range
6.1b14.3%Quadratic roots, medium range
5.9b14.4%Cubic critical, medium range
5.8b50.8%Quotient of products
4.6b83.7%Quadratic roots, full range

localize3.6s (0.6%)

bsearch689.0ms (0.1%)

end0.0ms (0.0%)