Average Error: 42.7 → 10.1
Time: 39.5s
Precision: 64
Internal Precision: 128
\[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.805590925906621 \cdot 10^{+75}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\left(-t\right) \cdot \sqrt{2} + -2 \cdot \frac{t}{x \cdot \sqrt{2}}}\\ \mathbf{elif}\;t \le -2.999571694817558 \cdot 10^{-156}:\\ \;\;\;\;\frac{\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot t\right)}{\sqrt{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\frac{t}{x} \cdot \left(t \cdot 4\right)\right))_*}}\\ \mathbf{elif}\;t \le -5.850506967033837 \cdot 10^{-251}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\left(-t\right) \cdot \sqrt{2} + -2 \cdot \frac{t}{x \cdot \sqrt{2}}}\\ \mathbf{elif}\;t \le 6.269988539509832 \cdot 10^{-184}:\\ \;\;\;\;\frac{\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot t\right)}{\sqrt{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\frac{t}{x} \cdot \left(t \cdot 4\right)\right))_*}}\\ \mathbf{elif}\;t \le 1.1645529092085739 \cdot 10^{-138} \lor \neg \left(t \le 5.2972532669470574 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{(\left(\frac{\frac{2}{x}}{\sqrt{2}}\right) \cdot t + \left(\sqrt{2} \cdot t\right))_*}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\sqrt{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\frac{t}{x} \cdot \left(t \cdot 4\right)\right))_*}}\\ \end{array}\]

Error

Bits error versus x

Bits error versus l

Bits error versus t

Derivation

  1. Split input into 4 regimes

  2. if t < -3.805590925906621e+75 or -2.999571694817558e-156 < t < -5.850506967033837e-251

    1. Initial program 49.7

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]

    2. Simplified49.7

      \[\leadsto \color{blue}{\frac{t \cdot \sqrt{2}}{\sqrt{(\left((\left(2 \cdot t\right) \cdot t + \left(\ell \cdot \ell\right))_*\right) \cdot \left(\frac{1 + x}{-1 + x}\right) + \left(\ell \cdot \left(-\ell\right)\right))_*}}}\]

    3. Taylor expanded around -inf 10.6

      \[\leadsto \frac{t \cdot \sqrt{2}}{\color{blue}{-\left(t \cdot \sqrt{2} + 2 \cdot \frac{t}{\sqrt{2} \cdot x}\right)}}\]

    if -3.805590925906621e+75 < t < -2.999571694817558e-156 or -5.850506967033837e-251 < t < 6.269988539509832e-184

    1. Initial program 40.9

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]

    2. Simplified40.9

      \[\leadsto \color{blue}{\frac{t \cdot \sqrt{2}}{\sqrt{(\left((\left(2 \cdot t\right) \cdot t + \left(\ell \cdot \ell\right))_*\right) \cdot \left(\frac{1 + x}{-1 + x}\right) + \left(\ell \cdot \left(-\ell\right)\right))_*}}}\]

    3. Taylor expanded around inf 18.9

      \[\leadsto \frac{t \cdot \sqrt{2}}{\sqrt{\color{blue}{2 \cdot {t}^{2} + \left(4 \cdot \frac{{t}^{2}}{x} + 2 \cdot \frac{{\ell}^{2}}{x}\right)}}}\]

    4. Simplified15.2

      \[\leadsto \frac{t \cdot \sqrt{2}}{\sqrt{\color{blue}{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\left(t \cdot 4\right) \cdot \frac{t}{x}\right))_*}}}\]
    5. Using strategy rm

    6. Applied add-sqr-sqrt15.4

      \[\leadsto \frac{t \cdot \color{blue}{\left(\sqrt{\sqrt{2}} \cdot \sqrt{\sqrt{2}}\right)}}{\sqrt{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\left(t \cdot 4\right) \cdot \frac{t}{x}\right))_*}}\]

    7. Applied associate-*r*15.3

      \[\leadsto \frac{\color{blue}{\left(t \cdot \sqrt{\sqrt{2}}\right) \cdot \sqrt{\sqrt{2}}}}{\sqrt{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\left(t \cdot 4\right) \cdot \frac{t}{x}\right))_*}}\]

    if 6.269988539509832e-184 < t < 1.1645529092085739e-138 or 5.2972532669470574e+36 < t

    1. Initial program 43.8

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]

    2. Simplified43.8

      \[\leadsto \color{blue}{\frac{t \cdot \sqrt{2}}{\sqrt{(\left((\left(2 \cdot t\right) \cdot t + \left(\ell \cdot \ell\right))_*\right) \cdot \left(\frac{1 + x}{-1 + x}\right) + \left(\ell \cdot \left(-\ell\right)\right))_*}}}\]

    3. Taylor expanded around inf 7.2

      \[\leadsto \frac{t \cdot \sqrt{2}}{\color{blue}{t \cdot \sqrt{2} + 2 \cdot \frac{t}{\sqrt{2} \cdot x}}}\]

    4. Simplified7.2

      \[\leadsto \frac{t \cdot \sqrt{2}}{\color{blue}{(\left(\frac{\frac{2}{x}}{\sqrt{2}}\right) \cdot t + \left(t \cdot \sqrt{2}\right))_*}}\]

    if 1.1645529092085739e-138 < t < 5.2972532669470574e+36

    1. Initial program 28.8

      \[\frac{\sqrt{2} \cdot t}{\sqrt{\frac{x + 1}{x - 1} \cdot \left(\ell \cdot \ell + 2 \cdot \left(t \cdot t\right)\right) - \ell \cdot \ell}}\]

    2. Simplified28.8

      \[\leadsto \color{blue}{\frac{t \cdot \sqrt{2}}{\sqrt{(\left((\left(2 \cdot t\right) \cdot t + \left(\ell \cdot \ell\right))_*\right) \cdot \left(\frac{1 + x}{-1 + x}\right) + \left(\ell \cdot \left(-\ell\right)\right))_*}}}\]

    3. Taylor expanded around inf 9.7

      \[\leadsto \frac{t \cdot \sqrt{2}}{\sqrt{\color{blue}{2 \cdot {t}^{2} + \left(4 \cdot \frac{{t}^{2}}{x} + 2 \cdot \frac{{\ell}^{2}}{x}\right)}}}\]

    4. Simplified4.6

      \[\leadsto \frac{t \cdot \sqrt{2}}{\sqrt{\color{blue}{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\left(t \cdot 4\right) \cdot \frac{t}{x}\right))_*}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification10.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.805590925906621 \cdot 10^{+75}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\left(-t\right) \cdot \sqrt{2} + -2 \cdot \frac{t}{x \cdot \sqrt{2}}}\\ \mathbf{elif}\;t \le -2.999571694817558 \cdot 10^{-156}:\\ \;\;\;\;\frac{\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot t\right)}{\sqrt{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\frac{t}{x} \cdot \left(t \cdot 4\right)\right))_*}}\\ \mathbf{elif}\;t \le -5.850506967033837 \cdot 10^{-251}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\left(-t\right) \cdot \sqrt{2} + -2 \cdot \frac{t}{x \cdot \sqrt{2}}}\\ \mathbf{elif}\;t \le 6.269988539509832 \cdot 10^{-184}:\\ \;\;\;\;\frac{\sqrt{\sqrt{2}} \cdot \left(\sqrt{\sqrt{2}} \cdot t\right)}{\sqrt{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\frac{t}{x} \cdot \left(t \cdot 4\right)\right))_*}}\\ \mathbf{elif}\;t \le 1.1645529092085739 \cdot 10^{-138} \lor \neg \left(t \le 5.2972532669470574 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{(\left(\frac{\frac{2}{x}}{\sqrt{2}}\right) \cdot t + \left(\sqrt{2} \cdot t\right))_*}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{2} \cdot t}{\sqrt{(2 \cdot \left((\left(\frac{\ell}{x}\right) \cdot \ell + \left(t \cdot t\right))_*\right) + \left(\frac{t}{x} \cdot \left(t \cdot 4\right)\right))_*}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (x l t)
  :name "Toniolo and Linder, Equation (7)"
  (/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))

Details

Time bar (total: 38.5s)Debug log

sample679.0ms

Algorithm
intervals
Results
631×(pre true 80)
310×(body nan 80)
161×(body real 80)
38×(body real 640)
24×(body nan 1280)
24×(body real 1280)
23×(body real 320)
20×(body nan 640)
12×(body nan 320)
11×(body real 160)
8×(body nan 160)

simplify560.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
559.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.3b

localize76.0ms

Local error

Found 4 expressions with local error:

23.8b
(sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l))))
14.5b
(fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l)))
0.5b
(* t (sqrt 2))
0.0b
(/ (* t (sqrt 2)) (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l)))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-cube-cbrt
10×*-un-lft-identity
9×sqrt-prod
6×add-exp-log
6×add-cbrt-cube
6×times-frac
6×associate-/r*
4×add-log-exp
4×log1p-expm1-u
4×pow1
4×expm1-log1p-u
3×associate-*r*
1×associate-/l*
1×div-inv
1×fma-udef
1×*-commutative
1×div-exp
1×pow1/2
1×frac-2neg
1×clear-num
1×rem-sqrt-square
1×cbrt-undiv
Counts
4 → 64
Calls
4 calls:
Slowest
9.0ms
(/ (* t (sqrt 2)) (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l)))))
5.0ms
(sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l))))
2.0ms
(* t (sqrt 2))
0.0ms
(fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l)))

series678.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
314.0ms
(/ (* t (sqrt 2)) (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l)))))
216.0ms
(sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l))))
109.0ms
(fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l)))
39.0ms
(* t (sqrt 2))

simplify11.9s

Counts
39 → 76
Calls
39 calls:
Slowest
659.0ms
(/ (* (* (* t (sqrt 2)) (* t (sqrt 2))) (* t (sqrt 2))) (* (* (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l)))) (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l))))) (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l))))))
629.0ms
(/ t (sqrt (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l))))))
607.0ms
(sqrt (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l)))))
600.0ms
(/ t (* (cbrt (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l))))) (cbrt (sqrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l)))))))
597.0ms
(/ (sqrt 2) (sqrt (cbrt (fma (fma (* 2 t) t (* l l)) (/ (+ 1 x) (+ -1 x)) (* l (- l))))))

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.8b

localize40.0ms

Local error

Found 4 expressions with local error:

32.4b
(sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
4.6b
(fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))
0.5b
(* t (sqrt 2))
0.1b
(* (* t 4) (/ t x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt
7×associate-*r*
7×*-un-lft-identity
6×add-exp-log
6×add-cbrt-cube
6×pow1
4×add-log-exp
4×log1p-expm1-u
4×expm1-log1p-u
3×sqrt-prod
2×*-commutative
1×div-inv
1×fma-udef
1×cbrt-unprod
1×associate-*r/
1×prod-exp
1×pow-prod-down
1×associate-*l*
1×pow1/2
1×rem-sqrt-square
Counts
4 → 56
Calls
4 calls:
Slowest
7.0ms
(* (* t 4) (/ t x))
2.0ms
(* t (sqrt 2))
2.0ms
(sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
0.0ms
(fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))

series372.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
64.0ms
(fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))
25.0ms
(* t (sqrt 2))
15.0ms
(* (* t 4) (/ t x))

simplify1.3s

Counts
26 → 68
Calls
26 calls:
Slowest
491.0ms
(* (* (* (* t 4) (* t 4)) (* t 4)) (* (* (/ t x) (/ t x)) (/ t x)))
144.0ms
(sqrt (sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))))
123.0ms
(sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
118.0ms
(sqrt (* (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))) (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))))
93.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))

prune907.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

32.4b
(sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
4.6b
(fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))
0.3b
(* (* t (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.2b
(* t (sqrt (sqrt 2)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*r*
10×add-sqr-sqrt
9×sqrt-prod
9×add-cube-cbrt
9×*-un-lft-identity
6×add-exp-log
6×add-cbrt-cube
6×pow1
4×add-log-exp
4×log1p-expm1-u
4×expm1-log1p-u
2×*-commutative
1×fma-udef
1×cbrt-unprod
1×prod-exp
1×pow-prod-down
1×associate-*l*
1×pow1/2
1×rem-sqrt-square
Counts
4 → 60
Calls
4 calls:
Slowest
7.0ms
(* (* t (sqrt (sqrt 2))) (sqrt (sqrt 2)))
2.0ms
(* t (sqrt (sqrt 2)))
1.0ms
(sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
0.0ms
(fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
249.0ms
(sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
71.0ms
(* t (sqrt (sqrt 2)))
41.0ms
(fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))
32.0ms
(* (* t (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify1.2s

Counts
31 → 72
Calls
31 calls:
Slowest
419.0ms
(* (* (* (* t (sqrt (sqrt 2))) (* t (sqrt (sqrt 2)))) (* t (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
140.0ms
(sqrt (* (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))) (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))))
121.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
121.0ms
(sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
94.0ms
(sqrt (sqrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))))

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.8b

localize15.0ms

Local error

Found 4 expressions with local error:

33.3b
(cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
33.3b
(cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
33.3b
(cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
32.4b
(sqrt (* (* (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))) (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))) (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-cube-cbrt
7×*-un-lft-identity
7×add-sqr-sqrt
4×add-log-exp
4×log1p-expm1-u
4×add-exp-log
4×add-cbrt-cube
4×pow1
4×expm1-log1p-u
3×pow1/3
1×sqrt-prod
1×pow1/2
Counts
4 → 50
Calls
4 calls:
Slowest
5.0ms
(sqrt (* (* (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))) (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))) (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))))
1.0ms
(cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
1.0ms
(cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
1.0ms
(cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))

series879.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
235.0ms
(sqrt (* (* (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x)))) (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))) (cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))))
232.0ms
(cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
210.0ms
(cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))
202.0ms
(cbrt (fma 2 (fma (/ l x) l (* t t)) (* (* t 4) (/ t x))))

simplify3.8s

Counts
22 → 62
Calls
22 calls:
Slowest
412.0ms
(exp (* 1/3 (- (+ (log -2) (log (/ -1 x))) (* 2 (log (/ -1 l))))))
395.0ms
(exp (* 1/3 (- (+ (log -2) (log (/ -1 x))) (* 2 (log (/ -1 l))))))
394.0ms
(exp (* 1/3 (- (+ (log 2) (log (/ 1 x))) (* 2 (log (/ 1 l))))))
385.0ms
(exp (* 1/3 (- (+ (log -2) (log (/ -1 x))) (* 2 (log (/ -1 l))))))
378.0ms
(exp (* 1/3 (- (+ (log 2) (log (/ 1 x))) (* 2 (log (/ 1 l))))))

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.8b

regimes479.0ms

Accuracy

73.7% (6.2b remaining)

Error of 10.1b against oracle of 4.0b and baseline of 27.4b

bsearch2.9s

end0.0ms

sample8.6s

Algorithm
intervals
Results
20033×(pre true 80)
10288×(body nan 80)
5061×(body real 80)
1065×(body real 640)
825×(body real 1280)
691×(body real 320)
623×(body nan 640)
602×(body nan 1280)
359×(body real 160)
339×(body nan 320)
180×(body nan 160)