317 calls:
| 55.6s | (/ (+ (* (- a (+ b e)) (+ (pow d 3) (pow c 3))) (* (+ (* (- d c) d) (* c c)) (- (* a a) (* (+ b e) (+ b e))))) (* (- a (+ b e)) (+ (* (- d c) d) (* c c)))) |
| 694.0ms | (cbrt (+ (* x1 (* x1 (- (* 4.0 (/ (- (+ (* 3.0 (pow x1 2)) (* x2 2.0)) x1) (+ (pow x1 2) 1.0))) 6.0))) (* (* (* 2.0 x1) (/ (- (+ (* 3.0 (pow x1 2)) (* x2 2.0)) x1) (+ (pow x1 2) 1.0))) (- (/ (- (+ (* 3.0 (pow x1 2)) (* x2 2.0)) x1) (+ (pow x1 2) 1.0)) 3.0)))) |
| 668.0ms | (cbrt (+ (* x1 (* x1 (- (* 4.0 (/ (- (+ (* 3.0 (pow x1 2)) (* x2 2.0)) x1) (+ (pow x1 2) 1.0))) 6.0))) (* (* (* 2.0 x1) (/ (- (+ (* 3.0 (pow x1 2)) (* x2 2.0)) x1) (+ (pow x1 2) 1.0))) (- (/ (- (+ (* 3.0 (pow x1 2)) (* x2 2.0)) x1) (+ (pow x1 2) 1.0)) 3.0)))) |
| 649.0ms | (- (* (pow x 4.0) 9.0) (pow y 4.0)) |
| 630.0ms | (cbrt (pow (- (* (pow x 4.0) 9.0) (pow y 4.0)) 3)) |
| 73× | intervals |
| 26.3s | 285416× | body | 80 | valid |
| 10.0s | 25113× | body | 160 | valid |
| 8.2s | 13589× | body | 1280 | valid |
| 5.2s | 3866× | body | 2560 | valid |
| 3.9s | 9505× | body | 640 | valid |
| 3.5s | 100646× | pre | 80 | true |
| 2.6s | 2153× | body | 10240 | exit |
| 1.7s | 6916× | body | 320 | valid |
| 1.2s | 19387× | body | 80 | nan |
| 199.0ms | 235× | body | 5120 | valid |
| 7.0ms | 100× | pre | 80 | false |
| 108× | rewrite-expression-head |
317 calls:
| 3.4s | (+ (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y))) |
| 3.3s | (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) |
| 1.2s | (+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0))) |
| 1.1s | (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (+ (* x1 (* (* x1 4.0) (/ (- (+ (* 3.0 (pow x1 2)) (* x2 2.0)) x1) (+ (pow x1 2) 1.0)))) (* 6.0 (- (pow x1 2))))) |
| 963.0ms | (- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x))))))) |
| 30363× | frac-times |
| 29826× | times-frac |
| 24372× | cbrt-div |
| 14898× | exp-neg |
| 14187× | *-un-lft-identity |
| 14020× | add-sqr-sqrt |
| 11181× | neg-sub0 |
| 11178× | exp-diff |
| 10833× | add-cube-cbrt |
| 9252× | associate-*l/ |
| 9092× | frac-sub |
| 8631× | flip3-- flip-- |
| 8611× | associate-*r/ |
| 3727× | un-div-inv |
| 3325× | flip-+ flip3-+ |
| 1875× | add-exp-log |
| 1523× | add-cbrt-cube |
| 1449× | div-inv |
| 1368× | difference-of-squares |
| 1250× | distribute-lft-out-- |
| 979× | associate-*r* |
| 784× | associate-/r/ |
| 731× | pow1 |
| 677× | add-log-exp |
| 649× | div-exp |
| 561× | associate-/r* |
| 549× | associate-/l* |
| 476× | distribute-lft-out |
| 468× | associate-*l* |
| 453× | prod-exp |
| 451× | cbrt-undiv |
| 419× | unpow-prod-down |
| 369× | cbrt-unprod |
| 351× | sqrt-prod |
| 190× | pow-prod-down |
| 160× | frac-add |
| 158× | associate-/l/ |
| 145× | cbrt-prod |
| 140× | cube-prod |
| 127× | sum-log |
| 123× | distribute-rgt-neg-in |
| 116× | unswap-sqr |
| 113× | distribute-lft-neg-in |
| 101× | sqr-pow |
| 92× | sub-neg |
| 81× | frac-2neg clear-num |
| 77× | diff-log |
| 74× | sqrt-div *-commutative |
| 73× | exp-prod |
| 64× | log-pow |
| 56× | sqrt-pow1 |
| 49× | swap-sqr |
| 46× | 1-exp rec-exp |
| 43× | log-prod +-commutative |
| 41× | distribute-rgt-in distribute-lft-in |
| 40× | pow-unpow |
| 35× | neg-mul-1 |
| 33× | pow1/2 |
| 32× | pow-exp |
| 30× | associate-+l+ |
| 28× | div-sub |
| 26× | pow-pow |
| 23× | pow-to-exp |
| 21× | distribute-rgt-neg-out |
| 20× | log-div |
| 19× | unpow3 cube-mult |
| 18× | associate-+r+ |
| 16× | pow-prod-up |
| 14× | rem-sqrt-square |
| 13× | pow1/3 |
| 11× | cube-div pow-sqr |
| 10× | rem-cube-cbrt rem-log-exp |
| 9× | distribute-frac-neg |
| 8× | pow-flip distribute-lft-neg-out |
| 7× | associate--l- associate-+r- pow-plus rem-exp-log |
| 6× | pow2 neg-log associate--r+ inv-pow unsub-neg |
| 5× | exp-sum rem-cbrt-cube |
| 4× | sqrt-pow2 |
| 3× | unpow-prod-up unpow2 sum-cubes |
| 2× | associate--l+ sqrt-unprod difference-cubes exp-to-pow |
| 1× | pow3 sub-div distribute-rgt-out-- associate-+l- rem-square-sqrt associate--r- |
Total 31.1b remaining (8.4%)
Threshold costs 3.3b (0.9%)
| 10.9b | 52.8% | Compound Interest |
| 4.8b | 83.2% | The quadratic formula (r1) |
| 4.7b | 77.5% | Kahan p9 Example |
| 3.2b | 88.9% | The quadratic formula (r2) |
| 3.0b | 0% | Complex division, real part |