5937 calls:
| 3.3s | (/ (* (* (* 4 (* c a)) (* 4 (* c a))) (* 4 (* c a))) (* (* (* (* 2 a) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (* (* 2 a) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))) (* (* 2 a) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))))) |
| 2.4s | (/ (/ (* (* (* 4 (* c a)) (* 4 (* c a))) (* 4 (* c a))) (* (* (* 2 a) (* 2 a)) (* 2 a))) (* (* (- (- b) (sqrt (fma c (* -4 a) (* b b)))) (- (- b) (sqrt (fma c (* -4 a) (* b b))))) (- (- b) (sqrt (fma c (* -4 a) (* b b)))))) |
| 2.0s | (/ (* (* (fma -9/2 (* (* b c) a) (* 27/8 (/ (* (* a c) (* a c)) b))) (fma -9/2 (* (* b c) a) (* 27/8 (/ (* (* a c) (* a c)) b)))) (fma -9/2 (* (* b c) a) (* 27/8 (/ (* (* a c) (* a c)) b)))) (* (* (* (* 3 a) (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b)))) (* (* 3 a) (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b))))) (* (* 3 a) (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b)))))) |
| 1.5s | (/ (* (* (/ (* 4 (* c a)) (* 2 a)) (/ (* 4 (* c a)) (* 2 a))) (/ (* 4 (* c a)) (* 2 a))) (* (* (- (- b) (sqrt (fma c (* -4 a) (* b b)))) (- (- b) (sqrt (fma c (* -4 a) (* b b))))) (- (- b) (sqrt (fma c (* -4 a) (* b b)))))) |
| 1.3s | (/ (* (* (- (* (sqrt (fma b b (* (* a c) -3))) (fma b b (* (* a c) -3))) (* b (* b b))) (- (* (sqrt (fma b b (* (* a c) -3))) (fma b b (* (* a c) -3))) (* b (* b b)))) (- (* (sqrt (fma b b (* (* a c) -3))) (fma b b (* (* a c) -3))) (* b (* b b)))) (* (* (* (* 3 a) (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b)))) (* (* 3 a) (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b))))) (* (* 3 a) (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b)))))) |
| 72× | intervals |
| 7.6m | 79291× | body | 10240 | exit |
| 54.2s | 33327× | body | 1280 | valid |
| 26.2s | 197651× | body | 80 | valid |
| 21.9s | 24490× | body | 640 | valid |
| 20.9s | 152095× | body | 80 | nan |
| 13.2s | 24979× | body | 320 | valid |
| 11.6s | 34866× | body | 160 | valid |
| 9.2s | 152859× | pre | 80 | true |
| 3.3s | 3032× | body | 2560 | valid |
| 1.9s | 7999× | body | 160 | nan |
| 1.1s | 4071× | pre | 10240 | exit |
| 693.0ms | 210× | body | 5120 | valid |
448 calls:
| 751.0ms | (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R) |
| 498.0ms | (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))) R)) |
| 497.0ms | (* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R) |
| 488.0ms | (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)) |
| 476.0ms | (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a) |
Total 36.6b remaining (14%)
| 6.8b | 22.3% | Cubic critical, narrow range |
| 5.1b | 53.1% | Quotient of products |
| 4.5b | 83.5% | Cubic critical |
| 3.9b | 81.5% | Quadratic roots, full range |
| 2.9b | 0% | Quadratic roots, narrow range |
| 132× | rewrite-expression-head |
448 calls:
| 83.0ms | (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))) |
| 76.0ms | (/ (- (pow (log (+ 1 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y))))) |
| 72.0ms | (cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x)))) |
| 70.0ms | (* (sqrt (fma 2/3 (* x x) 2)) (* (cbrt (* (* (sqrt (fma 2/3 (* x x) 2)) (sqrt (fma 2/3 (* x x) 2))) (sqrt (fma 2/3 (* x x) 2)))) x)) |
| 55.0ms | (- (+ (log (sqrt (+ 1 (exp x)))) (log (sqrt (+ 1 (exp x))))) (* x y)) |
| 1356× | *-un-lft-identity |
| 1344× | add-sqr-sqrt |
| 1308× | add-exp-log |
| 1191× | pow1 |
| 1179× | add-cube-cbrt |
| 785× | add-cbrt-cube |
| 548× | add-log-exp |
| 469× | prod-exp |
| 456× | tan-quot |
| 454× | expm1-log1p-u |
| 450× | log1p-expm1-u |
| 448× | insert-posit16 |
| 430× | prod-diff |
| 371× | frac-times |
| 366× | times-frac |
| 279× | associate-*l* associate-*l/ |
| 273× | pow-exp |
| 272× | pow-prod-up |
| 266× | sqrt-prod |
| 258× | div-inv |
| 252× | associate-*r* associate-*r/ |
| 249× | associate-/r/ |
| 223× | div-exp |
| 214× | fma-neg |
| 203× | associate-/r* |
| 202× | pow-plus |
| 190× | pow-prod-down |
| 187× | pow-to-exp |
| 180× | flip-- |
| 179× | flip3-- |
| 155× | flip-+ |
| 154× | flip3-+ |
| 149× | cbrt-unprod |
| 144× | associate-/l* |
| 140× | cbrt-div |
| 128× | cbrt-prod |
| 97× | pow2 |
| 95× | *-commutative |
| 93× | rec-exp |
| 88× | frac-2neg clear-num |
| 84× | fma-udef |
| 82× | log-prod |
| 74× | sub-neg |
| 68× | difference-of-squares |
| 65× | fma-def |
| 61× | distribute-lft-out associate-/l/ |
| 58× | pow1/3 distribute-rgt-in distribute-lft-in |
| 57× | cbrt-undiv pow1/2 |
| 53× | log-pow |
| 49× | frac-sub |
| 42× | log-div |
| 41× | diff-log |
| 40× | distribute-lft-out-- |
| 39× | pow3 |
| 38× | sqrt-div neg-mul-1 |
| 36× | pow-pow |
| 35× | rem-sqrt-square |
| 26× | div-sub |
| 22× | +-commutative |
| 20× | log1p-udef |
| 19× | unpow-prod-down |
| 18× | distribute-rgt-out |
| 17× | sum-log |
| 16× | rem-log-exp |
| 14× | difference-of-sqr-1 |
| 12× | pow-flip inv-pow cos-sum |
| 11× | associate--l+ rem-cbrt-cube |
| 10× | neg-sub0 |
| 9× | associate--l- exp-prod associate-+l- acos-asin frac-add expm1-def |
| 8× | log1p-expm1 |
| 7× | difference-cubes un-div-inv |
| 6× | sin-sum distribute-rgt1-in cube-unmult associate--r+ |
| 5× | cos-mult distribute-rgt-out-- |
| 4× | distribute-lft1-in cube-prod log1p-def sin-mult cos-diff |
| 3× | exp-diff associate-+r- associate-+r+ distribute-frac-neg sqrt-unprod acos-neg unpow1/3 rem-square-sqrt |
| 2× | expm1-log1p expm1-udef hypot-udef sub-div associate--r- |
| 1× | associate-+l+ tanh-undef tanh-def asin-acos rem-exp-log sqr-cos sin-diff |