16368 calls:
| 1.7s | (re (+.c (+.c (+.c (+.c (+.c (+.c (*.c (*.c (*.c (*.c (*.c (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (*.c (*.c (*.c (*.c (*.c (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1))) (*.c (complex 6 0) (complex -1 1))) (complex 1 0))) |
| 1.6s | (im (+.c (+.c (+.c (+.c (+.c (+.c (*.c (*.c (*.c (*.c (*.c (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (*.c (*.c (*.c (*.c (*.c (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1))) (*.c (complex 6 0) (complex -1 1))) (complex 1 0))) |
| 1.4s | (/ (* (* (* (sin x) (/ (sin x) x)) (* (sin x) (/ (sin x) x))) (* (sin x) (/ (sin x) x))) (* (* (* (+ (cos x) 1) x) (* (+ (cos x) 1) x)) (* (+ (cos x) 1) x))) |
| 1.4s | (fma (sqrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (sqrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (- (* (sqrt (/ (sin x) (cos x))) (sqrt (/ (sin x) (cos x)))))) |
| 1.3s | (fma (sqrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (sqrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (- (* (cbrt (/ (sin x) (cos x))) (* (cbrt (/ (sin x) (cos x))) (cbrt (/ (sin x) (cos x))))))) |
| 56× | intervals |
| 16× | halfpoints |
| 1.1m | 66512× | body | 1280 | valid |
| 39.5s | 16978× | body | 2560 | valid |
| 26.2s | 42491× | body | 640 | valid |
| 13.1s | 12661× | body | 10240 | exit |
| 11.8s | 93713× | body | 80 | valid |
| 8.6s | 21110× | body | 320 | valid |
| 6.7s | 63554× | body | 80 | nan |
| 3.5s | 10954× | body | 160 | valid |
| 1.9s | 47441× | pre | 80 | true |
| 537.0ms | 478× | body | 5120 | valid |
| 498.0ms | 621× | body | 1280 | nan |
| 389.0ms | 679× | body | 640 | nan |
| 122.0ms | 388× | body | 320 | nan |
| 36.0ms | 196× | body | 160 | nan |
360 calls:
| 1.8s | (- (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))) (/ (sin x) (cos x))) |
| 1.1s | (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x))) |
| 825.0ms | (log (exp (* (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))) (cbrt (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))))) |
| 741.0ms | (/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))) |
| 653.0ms | (cbrt (* (/ (/ (expm1 (* (+ b a) eps)) (/ (expm1 (* eps a)) eps)) (expm1 (* eps b))) (* (/ (/ (expm1 (* (+ b a) eps)) (/ (expm1 (* eps a)) eps)) (expm1 (* eps b))) (/ (/ (expm1 (* (+ b a) eps)) (/ (expm1 (* eps a)) eps)) (expm1 (* eps b)))))) |
| 115× | rewrite-expression-head |
360 calls:
| 229.0ms | (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))) |
| 202.0ms | (cbrt (* (* (* (expm1 (* a x)) (expm1 (* a x))) (expm1 (* a x))) (* (exp (log (* (expm1 (* a x)) (expm1 (* a x))))) (expm1 (* a x))))) |
| 151.0ms | (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a)) |
| 149.0ms | (* (/ 1 a) (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))) |
| 131.0ms | (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) |
| 7841× | *-un-lft-identity |
| 7344× | add-sqr-sqrt |
| 7287× | times-frac |
| 5598× | add-cube-cbrt |
| 2920× | prod-diff |
| 2089× | sqrt-prod |
| 1567× | pow1 |
| 1284× | add-exp-log |
| 1139× | add-cbrt-cube |
| 668× | unpow-prod-down |
| 664× | distribute-lft-out |
| 638× | difference-of-squares |
| 580× | associate-*l* |
| 547× | add-log-exp |
| 472× | distribute-lft-out-- |
| 456× | associate-/r* |
| 455× | associate-*r* |
| 425× | div-inv |
| 373× | associate-/l* |
| 361× | fma-neg |
| 359× | log1p-expm1-u |
| 354× | expm1-log1p-u insert-posit16 |
| 324× | pow-prod-down |
| 323× | prod-exp |
| 295× | cbrt-unprod |
| 279× | div-exp |
| 274× | pow-prod-up |
| 258× | associate-+l+ |
| 257× | associate-/r/ |
| 247× | swap-sqr |
| 222× | sqr-pow |
| 202× | cbrt-undiv |
| 200× | log-prod |
| 194× | distribute-rgt-neg-in |
| 170× | unswap-sqr |
| 168× | cbrt-prod |
| 162× | pow-sqr |
| 148× | sqrt-pow1 |
| 145× | flip-+ flip3-+ |
| 127× | sqrt-div |
| 122× | pow-plus |
| 118× | flip3-- flip-- |
| 113× | distribute-lft-neg-in |
| 107× | fma-def |
| 105× | associate-*r/ |
| 103× | pow1/2 |
| 95× | tan-quot |
| 91× | pow2 |
| 88× | log-pow |
| 85× | *-commutative |
| 81× | frac-times |
| 75× | associate-*l/ |
| 71× | diff-log |
| 70× | sub-neg |
| 67× | exp-sum |
| 65× | pow-unpow |
| 64× | frac-2neg clear-num |
| 53× | exp-prod |
| 39× | associate-/l/ |
| 38× | pow-flip 1-exp |
| 37× | neg-mul-1 |
| 36× | pow1/3 |
| 35× | rec-exp rem-sqrt-square |
| 28× | sum-log |
| 27× | inv-pow |
| 23× | fma-udef |
| 22× | div-sub |
| 21× | log-div |
| 19× | +-commutative |
| 17× | cbrt-div |
| 16× | rem-log-exp |
| 15× | frac-add |
| 11× | associate--l+ |
| 10× | pow-exp distribute-rgt-in associate--l- pow-to-exp distribute-lft-in |
| 9× | neg-sub0 pow3 difference-of-sqr-1 sqrt-unprod rem-cbrt-cube |
| 8× | expm1-udef frac-sub distribute-neg-frac |
| 7× | exp-diff sin-mult associate--r+ |
| 5× | expm1-log1p neg-log sqr-sin pow-pow |
| 4× | exp-neg exp-to-pow rem-square-sqrt |
| 3× | associate-+r+ cube-unmult rem-exp-log associate-+l- hypot-def |
| 2× | sin-sum log1p-expm1 log1p-udef +.c-commutative un-div-inv tan-sum log1p-def cos-sum distribute-neg-in |
| 1× | distribute-lft-neg-out diff-atan cos-mult exp-sqrt distribute-rgt-neg-out hypot-udef diff-sin diff-cos expm1-def distribute-rgt-out-- |
Total 25.6b remaining (23%)
| 5.5b | 80.6% | quadp (p42, positive) |
| 4.1b | 85.4% | quadm (p42, negative) |
| 4.0b | 85.8% | quad2m (problem 3.2.1, negative) |
| 3.5b | 87.6% | quad2p (problem 3.2.1, positive) |
| 3.3b | -0.7% | expq3 (problem 3.4.2) |