Average Error: 3.6 → 2.3
Time: 1.2m
Precision: 64
Internal Precision: 128
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 7.021435509051398 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{x + e^{\log \left(e^{\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right)}\right) \cdot 2.0} \cdot y}\\ \mathbf{elif}\;t \le 1.20691627027635 \cdot 10^{-103}:\\ \;\;\;\;\frac{x}{x + e^{2.0 \cdot \frac{\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(t \cdot 3.0\right) \cdot z\right) - \left(\left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(t \cdot 3.0\right) - 2.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \frac{t \cdot \left(b - c\right)}{\sqrt{t + a}}}{\left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) \cdot \frac{t}{\sqrt{t + a}}}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + e^{\left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(\left(\frac{5.0}{6.0} + a\right) - {\left(\left(\frac{2.0}{t \cdot 3.0} \cdot \frac{2.0}{t \cdot 3.0}\right) \cdot \frac{2.0}{t \cdot 3.0}\right)}^{\frac{1}{3}}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if t < 7.021435509051398e-308

    1. Initial program 5.1

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied associate-/l*5.1

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\frac{t}{\sqrt{t + a}}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    4. Using strategy rm

    5. Applied add-log-exp5.1

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\log \left(e^{\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)}}}\]

    if 7.021435509051398e-308 < t < 1.20691627027635e-103

    1. Initial program 5.5

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied associate-/l*6.8

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\frac{t}{\sqrt{t + a}}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    4. Using strategy rm

    5. Applied flip-+10.6

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\color{blue}{\frac{a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}}{a - \frac{5.0}{6.0}}} - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

    6. Applied frac-sub10.6

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \color{blue}{\frac{\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]

    7. Applied associate-*r/10.6

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \color{blue}{\frac{\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]

    8. Applied frac-sub10.7

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\frac{z \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - \frac{t}{\sqrt{t + a}} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5.0}{6.0} \cdot \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}{\frac{t}{\sqrt{t + a}} \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}}\]

    9. Simplified4.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{blue}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(z \cdot \left(3.0 \cdot t\right)\right) - \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)\right) \cdot \frac{t \cdot \left(b - c\right)}{\sqrt{a + t}}}}{\frac{t}{\sqrt{t + a}} \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}\]

    if 1.20691627027635e-103 < t

    1. Initial program 2.2

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied associate-/l*0.2

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\frac{t}{\sqrt{t + a}}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    4. Using strategy rm

    5. Applied add-cbrt-cube0.2

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \color{blue}{\sqrt[3]{\left(\frac{2.0}{t \cdot 3.0} \cdot \frac{2.0}{t \cdot 3.0}\right) \cdot \frac{2.0}{t \cdot 3.0}}}\right)\right)}}\]
    6. Using strategy rm

    7. Applied pow1/30.2

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \color{blue}{{\left(\left(\frac{2.0}{t \cdot 3.0} \cdot \frac{2.0}{t \cdot 3.0}\right) \cdot \frac{2.0}{t \cdot 3.0}\right)}^{\frac{1}{3}}}\right)\right)}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 7.021435509051398 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{x + e^{\log \left(e^{\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right)}\right) \cdot 2.0} \cdot y}\\ \mathbf{elif}\;t \le 1.20691627027635 \cdot 10^{-103}:\\ \;\;\;\;\frac{x}{x + e^{2.0 \cdot \frac{\left(a - \frac{5.0}{6.0}\right) \cdot \left(\left(t \cdot 3.0\right) \cdot z\right) - \left(\left(\left(\frac{5.0}{6.0} + a\right) \cdot \left(t \cdot 3.0\right) - 2.0\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \frac{t \cdot \left(b - c\right)}{\sqrt{t + a}}}{\left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) \cdot \frac{t}{\sqrt{t + a}}}} \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + e^{\left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(\left(\frac{5.0}{6.0} + a\right) - {\left(\left(\frac{2.0}{t \cdot 3.0} \cdot \frac{2.0}{t \cdot 3.0}\right) \cdot \frac{2.0}{t \cdot 3.0}\right)}^{\frac{1}{3}}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019010 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

Details

Time bar (total: 1.2m)Debug log

sample293.0ms

Algorithm
intervals

simplify288.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
288.0ms
(/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.4b

localize65.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ (* z (sqrt (+ t a))) t)
3.2b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
0.3b
(/ 2.0 (* t 3.0))
0.2b
(* z (sqrt (+ t a)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
20×frac-sub
9×flip--
9×flip3--
8×associate-*r/
8×frac-times
6×add-log-exp
6×associate--r+
6×add-cube-cbrt
6×associate-*r*
6×*-un-lft-identity
6×add-sqr-sqrt
5×flip-+
5×flip3-+
4×add-exp-log
4×sqrt-div
4×add-cbrt-cube
4×pow1
3×sqrt-prod
3×distribute-lft-in
3×sub-neg
3×distribute-rgt-in
2×associate-/l/
2×div-inv
2×associate--l+
2×associate-*l/
2×frac-2neg
2×clear-num
1×associate-/l*
1×*-commutative
1×diff-log
1×associate-/r*
Counts
4 → 72
Calls
4 calls:
Slowest
9.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
4.0ms
(/ (* z (sqrt (+ t a))) t)
2.0ms
(* z (sqrt (+ t a)))
0.0ms
(/ 2.0 (* t 3.0))

series279.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
55.0ms
(/ (* z (sqrt (+ t a))) t)
42.0ms
(* z (sqrt (+ t a)))
13.0ms
(/ 2.0 (* t 3.0))

simplify7.9s

Counts
57 → 84
Calls
57 calls:
Slowest
824.0ms
(* t (* (+ b c) (* (- a (/ 5.0 6.0)) (* t 3.0))))
506.0ms
(- (* (* z (sqrt (+ t a))) (* (+ (* b b) (+ (* c c) (* b c))) (+ (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (+ (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (* (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))) (* t (* (- (pow b 3) (pow c 3)) (- (pow (+ a (/ 5.0 6.0)) 3) (pow (/ 2.0 (* t 3.0)) 3)))))
425.0ms
(- (* (* z (sqrt (+ t a))) (* (+ b c) (+ (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (+ (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (* (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))) (* t (* (- (* b b) (* c c)) (- (pow (+ a (/ 5.0 6.0)) 3) (pow (/ 2.0 (* t 3.0)) 3)))))
315.0ms
(- (* (* z (sqrt (+ t a))) (+ (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (+ (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (* (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))) (* t (* (- b c) (- (pow (+ a (/ 5.0 6.0)) 3) (pow (/ 2.0 (* t 3.0)) 3)))))
313.0ms
(- (* (* z (sqrt (+ t a))) (* (+ (* b b) (+ (* c c) (* b c))) (* (+ (* a a) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* a (/ 5.0 6.0)))) (* t 3.0)))) (* t (* (- (pow b 3) (pow c 3)) (- (* (+ (pow a 3) (pow (/ 5.0 6.0) 3)) (* t 3.0)) (* (+ (* a a) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* a (/ 5.0 6.0)))) 2.0)))))

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize40.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
2.0b
(/ z (/ t (sqrt (+ t a))))
0.4b
(/ t (sqrt (+ t a)))
0.3b
(/ 2.0 (* t 3.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
20×frac-sub
13×associate-/r*
9×flip--
9×flip3--
8×frac-times
7×add-cube-cbrt
7×*-un-lft-identity
7×add-sqr-sqrt
6×add-log-exp
6×associate--r+
5×flip-+
5×associate-/r/
5×flip3-+
4×div-inv
4×add-exp-log
4×associate-*r/
4×sqrt-div
4×add-cbrt-cube
4×pow1
3×sqrt-prod
3×distribute-lft-in
3×frac-2neg
3×sub-neg
3×clear-num
3×distribute-rgt-in
2×associate--l+
2×associate-*l/
1×diff-log
Counts
4 → 78
Calls
4 calls:
Slowest
16.0ms
(- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
1.0ms
(/ t (sqrt (+ t a)))
1.0ms
(/ z (/ t (sqrt (+ t a))))
1.0ms
(/ 2.0 (* t 3.0))

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
70.0ms
(/ z (/ t (sqrt (+ t a))))
57.0ms
(/ t (sqrt (+ t a)))
14.0ms
(/ 2.0 (* t 3.0))

simplify7.8s

Counts
62 → 90
Calls
62 calls:
Slowest
512.0ms
(- (* z (* (+ (* b b) (+ (* c c) (* b c))) (+ (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (+ (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (* (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))) (* (/ t (sqrt (+ t a))) (* (- (pow b 3) (pow c 3)) (- (pow (+ a (/ 5.0 6.0)) 3) (pow (/ 2.0 (* t 3.0)) 3)))))
442.0ms
(* (/ t (sqrt (+ t a))) (* (+ (* a a) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* a (/ 5.0 6.0)))) (* t 3.0)))
356.0ms
(* (/ t (sqrt (+ t a))) (* (+ (* b b) (+ (* c c) (* b c))) (+ (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (+ (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (* (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))
338.0ms
(- (* z (* (+ (* b b) (+ (* c c) (* b c))) (+ (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))) (* (/ t (sqrt (+ t a))) (* (- (pow b 3) (pow c 3)) (- (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0)))))))
328.0ms
(- (* z (* (+ b c) (+ (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (+ (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (* (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))) (* (/ t (sqrt (+ t a))) (* (- (* b b) (* c c)) (- (pow (+ a (/ 5.0 6.0)) 3) (pow (/ 2.0 (* t 3.0)) 3)))))

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize40.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
2.0b
(/ z (/ t (sqrt (+ t a))))
1.2b
(log (exp (- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))
0.4b
(/ t (sqrt (+ t a)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
20×frac-sub
12×associate-/r*
9×flip--
9×add-cube-cbrt
9×flip3--
9×*-un-lft-identity
9×add-sqr-sqrt
8×frac-times
6×add-log-exp
6×associate--r+
5×flip-+
5×associate-/r/
5×flip3-+
5×log-prod
5×pow1
4×log-pow
4×add-exp-log
4×associate-*r/
4×sqrt-div
4×add-cbrt-cube
4×sub-neg
3×div-inv
3×sqrt-prod
3×distribute-lft-in
3×exp-prod
3×distribute-rgt-in
2×associate--l+
2×associate-*l/
2×exp-sum
2×frac-2neg
2×clear-num
1×rem-log-exp
1×diff-log
1×exp-diff
1×log-div
Counts
4 → 85
Calls
4 calls:
Slowest
16.0ms
(- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
14.0ms
(log (exp (- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))
1.0ms
(/ t (sqrt (+ t a)))
1.0ms
(/ z (/ t (sqrt (+ t a))))

series451.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
167.0ms
(log (exp (- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))
59.0ms
(/ t (sqrt (+ t a)))
52.0ms
(/ z (/ t (sqrt (+ t a))))

simplify9.3s

Counts
72 → 97
Calls
72 calls:
Slowest
642.0ms
(* (/ t (sqrt (+ t a))) (* (+ (* b b) (+ (* c c) (* b c))) (+ (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
404.0ms
(* (/ t (sqrt (+ t a))) (* (+ (* a a) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* a (/ 5.0 6.0)))) (* t 3.0)))
375.0ms
(- (* z (* (+ (* b b) (+ (* c c) (* b c))) (+ (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (+ (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (* (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))) (* (/ t (sqrt (+ t a))) (* (- (pow b 3) (pow c 3)) (- (pow (+ a (/ 5.0 6.0)) 3) (pow (/ 2.0 (* t 3.0)) 3)))))
355.0ms
(* (/ t (sqrt (+ t a))) (+ (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
353.0ms
(- (* z (* (+ (* b b) (+ (* c c) (* b c))) (+ (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))) (* (/ t (sqrt (+ t a))) (* (- (pow b 3) (pow c 3)) (- (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0)))))))

prune2.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize49.0ms

Local error

Found 4 expressions with local error:

38.4b
(cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0))))
3.2b
(- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0)))))))
2.0b
(/ z (/ t (sqrt (+ t a))))
0.4b
(/ t (sqrt (+ t a)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
92×frac-sub
67×frac-times
49×cbrt-div
37×associate-*r/
37×associate-*l/
23×flip-+
23×flip3-+
21×flip--
21×flip3--
12×associate-/r*
7×add-cube-cbrt
7×*-un-lft-identity
7×add-sqr-sqrt
6×add-log-exp
6×associate--r+
5×associate-/r/
4×add-exp-log
4×sqrt-div
4×add-cbrt-cube
4×pow1
3×div-inv
3×sqrt-prod
3×distribute-lft-in
3×sub-neg
3×distribute-rgt-in
2×associate--l+
2×frac-2neg
2×clear-num
1×rem-cbrt-cube
1×pow3
1×diff-log
1×pow1/3
1×cbrt-prod
Counts
4 → 120
Calls
4 calls:
Slowest
41.0ms
(- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0)))))))
7.0ms
(cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0))))
1.0ms
(/ t (sqrt (+ t a)))
1.0ms
(/ z (/ t (sqrt (+ t a))))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
266.0ms
(- (/ z (/ t (sqrt (+ t a)))) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0)))))))
74.0ms
(cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0))))
56.0ms
(/ z (/ t (sqrt (+ t a))))
36.0ms
(/ t (sqrt (+ t a)))

simplify24.7s

Counts
142 → 132
Calls
142 calls:
Slowest
759.0ms
(* (/ t (sqrt (+ t a))) (* (+ b c) (* (- a (/ 5.0 6.0)) (cbrt (* (* t 3.0) (* t 3.0))))))
502.0ms
(* (/ t (sqrt (+ t a))) (* (+ b c) (* (- a (/ 5.0 6.0)) (cbrt (* (* t 3.0) (* t 3.0))))))
482.0ms
(- (* z (* (+ (* b b) (+ (* c c) (* b c))) (+ (* (+ a (/ 5.0 6.0)) (+ a (/ 5.0 6.0))) (+ (* (cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0)))) (cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0))))) (* (+ a (/ 5.0 6.0)) (cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0))))))))) (* (/ t (sqrt (+ t a))) (* (- (pow b 3) (pow c 3)) (- (pow (+ a (/ 5.0 6.0)) 3) (pow (cbrt (* (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0))) (/ 2.0 (* t 3.0)))) 3)))))
441.0ms
(* (/ t (sqrt (+ t a))) (* (+ b c) (* (- a (/ 5.0 6.0)) (cbrt (* t 3.0)))))
439.0ms
(* (/ t (sqrt (+ t a))) (* (+ (* a a) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* a (/ 5.0 6.0)))) (cbrt (* (* (* t 3.0) (* t 3.0)) (* t 3.0)))))

prune3.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes600.0ms

Accuracy

18.3% (2.2b remaining)

Error of 2.3b against oracle of 0.1b and baseline of 2.7b

bsearch1.5s

end0.0ms

sample6.1s

Algorithm
intervals