Average Error: 33.3 → 9.7
Time: 30.7s
Precision: 64
Internal Precision: 128
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.7715196556134555 \cdot 10^{+46}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \le -1.1090157738250754 \cdot 10^{-76}:\\ \;\;\;\;\frac{\left(a \cdot c\right) \cdot 4}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{(\left(-4 \cdot a\right) \cdot c + \left(b \cdot b\right))_*}\right)}\\ \mathbf{elif}\;b \le 5.973421650485517 \cdot 10^{+105}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{(-4 \cdot \left(a \cdot c\right) + \left(b \cdot b\right))_*}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Target

Original33.3
Target20.4
Herbie9.7
\[\begin{array}{l} \mathbf{if}\;b \lt 0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if b < -1.7715196556134555e+46

    1. Initial program 56.2

      \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]

    2. Taylor expanded around inf 56.2

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]

    3. Simplified56.2

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}{2 \cdot a}\]
    4. Using strategy rm

    5. Applied add-sqr-sqrt56.2

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*} \cdot \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}}{2 \cdot a}\]

    6. Applied sqrt-prod58.3

      \[\leadsto \frac{\left(-b\right) - \color{blue}{\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}}{2 \cdot a}\]

    7. Applied add-sqr-sqrt56.2

      \[\leadsto \frac{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}} - \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}{2 \cdot a}\]

    8. Applied prod-diff56.3

      \[\leadsto \frac{\color{blue}{(\left(\sqrt{-b}\right) \cdot \left(\sqrt{-b}\right) + \left(-\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right))_* + (\left(-\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) \cdot \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) + \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right))_*}}{2 \cdot a}\]

    9. Simplified60.6

      \[\leadsto \frac{\color{blue}{\left(\left(-b\right) - \sqrt{(-4 \cdot \left(a \cdot c\right) + \left(b \cdot b\right))_*}\right)} + (\left(-\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) \cdot \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) + \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right))_*}{2 \cdot a}\]

    10. Simplified56.2

      \[\leadsto \frac{\left(\left(-b\right) - \sqrt{(-4 \cdot \left(a \cdot c\right) + \left(b \cdot b\right))_*}\right) + \color{blue}{0}}{2 \cdot a}\]

    11. Taylor expanded around -inf 4.3

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]

    12. Simplified4.3

      \[\leadsto \color{blue}{\frac{-c}{b}}\]

    if -1.7715196556134555e+46 < b < -1.1090157738250754e-76

    1. Initial program 42.2

      \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]

    2. Taylor expanded around inf 42.2

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]

    3. Simplified42.2

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}{2 \cdot a}\]
    4. Using strategy rm

    5. Applied flip--42.3

      \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*} \cdot \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}{\left(-b\right) + \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}}{2 \cdot a}\]

    6. Applied associate-/l/45.0

      \[\leadsto \color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*} \cdot \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}\right)}}\]

    7. Simplified18.1

      \[\leadsto \frac{\color{blue}{\left(a \cdot c\right) \cdot 4}}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}\right)}\]

    if -1.1090157738250754e-76 < b < 5.973421650485517e+105

    1. Initial program 13.0

      \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]

    2. Taylor expanded around inf 13.0

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]

    3. Simplified13.0

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}{2 \cdot a}\]
    4. Using strategy rm

    5. Applied add-sqr-sqrt13.0

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*} \cdot \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}}{2 \cdot a}\]

    6. Applied sqrt-prod13.2

      \[\leadsto \frac{\left(-b\right) - \color{blue}{\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}}{2 \cdot a}\]

    7. Applied add-sqr-sqrt48.6

      \[\leadsto \frac{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}} - \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}{2 \cdot a}\]

    8. Applied prod-diff48.6

      \[\leadsto \frac{\color{blue}{(\left(\sqrt{-b}\right) \cdot \left(\sqrt{-b}\right) + \left(-\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right))_* + (\left(-\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) \cdot \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) + \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right))_*}}{2 \cdot a}\]

    9. Simplified13.1

      \[\leadsto \frac{\color{blue}{\left(\left(-b\right) - \sqrt{(-4 \cdot \left(a \cdot c\right) + \left(b \cdot b\right))_*}\right)} + (\left(-\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) \cdot \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) + \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right))_*}{2 \cdot a}\]

    10. Simplified13.0

      \[\leadsto \frac{\left(\left(-b\right) - \sqrt{(-4 \cdot \left(a \cdot c\right) + \left(b \cdot b\right))_*}\right) + \color{blue}{0}}{2 \cdot a}\]

    if 5.973421650485517e+105 < b

    1. Initial program 46.5

      \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]

    2. Taylor expanded around inf 46.5

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{{b}^{2} - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]

    3. Simplified46.4

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}{2 \cdot a}\]
    4. Using strategy rm

    5. Applied add-sqr-sqrt46.4

      \[\leadsto \frac{\left(-b\right) - \sqrt{\color{blue}{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*} \cdot \sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}}{2 \cdot a}\]

    6. Applied sqrt-prod46.5

      \[\leadsto \frac{\left(-b\right) - \color{blue}{\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}}{2 \cdot a}\]

    7. Applied add-sqr-sqrt62.3

      \[\leadsto \frac{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}} - \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}}{2 \cdot a}\]

    8. Applied prod-diff62.3

      \[\leadsto \frac{\color{blue}{(\left(\sqrt{-b}\right) \cdot \left(\sqrt{-b}\right) + \left(-\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right))_* + (\left(-\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) \cdot \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) + \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right))_*}}{2 \cdot a}\]

    9. Simplified47.6

      \[\leadsto \frac{\color{blue}{\left(\left(-b\right) - \sqrt{(-4 \cdot \left(a \cdot c\right) + \left(b \cdot b\right))_*}\right)} + (\left(-\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) \cdot \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right) + \left(\sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}} \cdot \sqrt{\sqrt{(\left(a \cdot -4\right) \cdot c + \left(b \cdot b\right))_*}}\right))_*}{2 \cdot a}\]

    10. Simplified46.5

      \[\leadsto \frac{\left(\left(-b\right) - \sqrt{(-4 \cdot \left(a \cdot c\right) + \left(b \cdot b\right))_*}\right) + \color{blue}{0}}{2 \cdot a}\]

    11. Taylor expanded around inf 3.8

      \[\leadsto \color{blue}{\frac{c}{b} - \frac{b}{a}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification9.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.7715196556134555 \cdot 10^{+46}:\\ \;\;\;\;\frac{-c}{b}\\ \mathbf{elif}\;b \le -1.1090157738250754 \cdot 10^{-76}:\\ \;\;\;\;\frac{\left(a \cdot c\right) \cdot 4}{\left(2 \cdot a\right) \cdot \left(\left(-b\right) + \sqrt{(\left(-4 \cdot a\right) \cdot c + \left(b \cdot b\right))_*}\right)}\\ \mathbf{elif}\;b \le 5.973421650485517 \cdot 10^{+105}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{(-4 \cdot \left(a \cdot c\right) + \left(b \cdot b\right))_*}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019002 +o rules:numerics
(FPCore (a b c)
  :name "The quadratic formula (r2)"

  :herbie-target
  (if (< b 0) (/ c (* 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 a)))

Details

Time bar (total: 29.9s)Debug log

sample130.0ms

Algorithm
intervals

simplify76.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

76.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.3b

localize51.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (- (* b b) (* 4 (* a c))))
1.9b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.6b
(- (* b b) (* 4 (* a c)))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite63.0ms

Algorithm
rewrite-expression-head
Counts
4 → 108
Calls

4 calls. Slowest were:

36.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
14.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
6.0ms
(sqrt (- (* b b) (* 4 (* a c))))

series197.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

79.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
46.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
41.0ms
(sqrt (- (* b b) (* 4 (* a c))))
31.0ms
(- (* b b) (* 4 (* a c)))

simplify6.6s

Counts
98 → 120
Calls

98 calls. Slowest were:

405.0ms
(- (* (- b) (- b)) (* (sqrt (- (* b b) (* 4 (* a c)))) (sqrt (- (* b b) (* 4 (* a c))))))
382.0ms
(sqrt (- (pow (* b b) 3) (pow (* 4 (* a c)) 3)))
346.0ms
(- (pow (- b) 3) (pow (sqrt (- (* b b) (* 4 (* a c)))) 3))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.0b

localize29.0ms

Local error

Found 3 expressions with local error:

22.2b
(sqrt (fma (* a -4) c (* b b)))
1.9b
(- (- b) (sqrt (fma (* a -4) c (* b b))))
0.1b
(/ (- (- b) (sqrt (fma (* a -4) c (* b b)))) (* 2 a))

rewrite38.0ms

Algorithm
rewrite-expression-head
Counts
3 → 90
Calls

3 calls. Slowest were:

24.0ms
(/ (- (- b) (sqrt (fma (* a -4) c (* b b)))) (* 2 a))
10.0ms
(- (- b) (sqrt (fma (* a -4) c (* b b))))
2.0ms
(sqrt (fma (* a -4) c (* b b)))

series208.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

70.0ms
(- (- b) (sqrt (fma (* a -4) c (* b b))))
69.0ms
(/ (- (- b) (sqrt (fma (* a -4) c (* b b)))) (* 2 a))
68.0ms
(sqrt (fma (* a -4) c (* b b)))

simplify3.4s

Counts
90 → 99
Calls

90 calls. Slowest were:

256.0ms
(- (* (- b) (- b)) (* (sqrt (fma (* a -4) c (* b b))) (sqrt (fma (* a -4) c (* b b)))))
221.0ms
(- (pow (- b) 3) (pow (sqrt (fma (* a -4) c (* b b))) 3))
106.0ms
(/ (* (* (- (- b) (sqrt (fma (* a -4) c (* b b)))) (- (- b) (sqrt (fma (* a -4) c (* b b))))) (- (- b) (sqrt (fma (* a -4) c (* b b))))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.0b

localize15.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma -4 (* a c) (* b b)))
1.9b
(- (- b) (sqrt (fma -4 (* a c) (* b b))))
0.6b
(fma -4 (* a c) (* b b))
0.1b
(/ (+ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 0) (* 2 a))

rewrite94.0ms

Algorithm
rewrite-expression-head
Counts
4 → 94
Calls

4 calls. Slowest were:

87.0ms
(/ (+ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 0) (* 2 a))
5.0ms
(- (- b) (sqrt (fma -4 (* a c) (* b b))))
1.0ms
(sqrt (fma -4 (* a c) (* b b)))

series199.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

62.0ms
(/ (+ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 0) (* 2 a))
62.0ms
(- (- b) (sqrt (fma -4 (* a c) (* b b))))
44.0ms
(sqrt (fma -4 (* a c) (* b b)))
30.0ms
(fma -4 (* a c) (* b b))

simplify3.4s

Counts
85 → 106
Calls

85 calls. Slowest were:

148.0ms
(- (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) (- (- b) (sqrt (fma -4 (* a c) (* b b))))) (* 0 0))
127.0ms
(/ (+ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 0) a)
125.0ms
(- (log (+ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 0)) (log (* 2 a)))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.0b

localize6.0ms

Local error

Found 4 expressions with local error:

22.2b
(sqrt (fma (* a -4) c (* b b)))
1.9b
(- (- b) (sqrt (fma (* a -4) c (* b b))))
0.2b
(/ 1 (/ (* 2 a) (- (- b) (sqrt (fma (* a -4) c (* b b))))))
0.1b
(/ (* 2 a) (- (- b) (sqrt (fma (* a -4) c (* b b)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Counts
4 → 118
Calls

4 calls. Slowest were:

8.0ms
(/ (* 2 a) (- (- b) (sqrt (fma (* a -4) c (* b b)))))
5.0ms
(- (- b) (sqrt (fma (* a -4) c (* b b))))
4.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (fma (* a -4) c (* b b))))))

series309.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

110.0ms
(/ (* 2 a) (- (- b) (sqrt (fma (* a -4) c (* b b)))))
81.0ms
(/ 1 (/ (* 2 a) (- (- b) (sqrt (fma (* a -4) c (* b b))))))
72.0ms
(- (- b) (sqrt (fma (* a -4) c (* b b))))
46.0ms
(sqrt (fma (* a -4) c (* b b)))

simplify4.5s

Counts
108 → 130
Calls

108 calls. Slowest were:

532.0ms
(+ (* (- b) (- b)) (+ (* (sqrt (fma (* a -4) c (* b b))) (sqrt (fma (* a -4) c (* b b)))) (* (- b) (sqrt (fma (* a -4) c (* b b))))))
406.0ms
(cbrt (/ (* 2 a) (- (- b) (sqrt (fma (* a -4) c (* b b))))))
404.0ms
(+ (* (- b) (- b)) (+ (* (sqrt (fma (* a -4) c (* b b))) (sqrt (fma (* a -4) c (* b b)))) (* (- b) (sqrt (fma (* a -4) c (* b b))))))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.0b

regimes230.0ms

Accuracy

85.3% (4.1b remaining)

Error of 9.7b against oracle of 5.7b and baseline of 33.3b

bsearch397.0ms

end0.0ms

sample4.7s

Algorithm
intervals