Average Error: 30.8 → 17.6
Time: 41.4s
Precision: 64
Internal Precision: 128
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -3.423353045456592 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{\sqrt{\log 10}}}{\frac{\sqrt{\log 10}}{\log \left(\frac{-1}{re}\right)} \cdot \frac{-1}{2}}\\ \mathbf{elif}\;re \le -2.722618750454037 \cdot 10^{-200}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \log \left(im \cdot im + re \cdot re\right)}{\sqrt{\log 10}}\\ \mathbf{elif}\;re \le -2.471056064955377 \cdot 10^{-233}:\\ \;\;\;\;\frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}} \cdot \left(\left(\log \left(\frac{-1}{im}\right) \cdot -2\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)\\ \mathbf{elif}\;re \le 1.2329804060890975 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \log \left(im \cdot im + re \cdot re\right)}{\sqrt{\log 10}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(2 \cdot \log re\right)\right) \cdot \frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}}\\ \end{array}\]

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if re < -3.423353045456592e+72

    1. Initial program 46.6

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    2. Using strategy rm

    3. Applied pow1/246.6

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\log 10}\]

    4. Applied log-pow46.6

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\log 10}\]

    5. Applied associate-/l*46.6

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{\log 10}{\log \left(re \cdot re + im \cdot im\right)}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity46.6

      \[\leadsto \frac{\frac{1}{2}}{\frac{\log 10}{\color{blue}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}}\]

    8. Applied add-sqr-sqrt46.6

      \[\leadsto \frac{\frac{1}{2}}{\frac{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}\]

    9. Applied times-frac46.7

      \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{\sqrt{\log 10}}{1} \cdot \frac{\sqrt{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    10. Applied associate-/r*46.6

      \[\leadsto \color{blue}{\frac{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}{\frac{\sqrt{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    11. Taylor expanded around -inf 10.8

      \[\leadsto \frac{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}{\color{blue}{\frac{-1}{2} \cdot \left(\frac{1}{\log \left(\frac{-1}{re}\right)} \cdot \sqrt{\log 10}\right)}}\]

    12. Simplified10.8

      \[\leadsto \frac{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}{\color{blue}{\frac{-1}{2} \cdot \frac{\sqrt{\log 10}}{\log \left(\frac{-1}{re}\right)}}}\]

    if -3.423353045456592e+72 < re < -2.722618750454037e-200 or -2.471056064955377e-233 < re < 1.2329804060890975e+141

    1. Initial program 20.9

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    2. Using strategy rm

    3. Applied pow1/220.9

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\log 10}\]

    4. Applied log-pow20.9

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\log 10}\]

    5. Applied associate-/l*20.9

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{\log 10}{\log \left(re \cdot re + im \cdot im\right)}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity20.9

      \[\leadsto \frac{\frac{1}{2}}{\frac{\log 10}{\color{blue}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}}\]

    8. Applied add-sqr-sqrt20.9

      \[\leadsto \frac{\frac{1}{2}}{\frac{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}\]

    9. Applied times-frac21.1

      \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{\sqrt{\log 10}}{1} \cdot \frac{\sqrt{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    10. Applied associate-/r*20.9

      \[\leadsto \color{blue}{\frac{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}{\frac{\sqrt{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]
    11. Using strategy rm

    12. Applied div-inv20.9

      \[\leadsto \frac{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}{\color{blue}{\sqrt{\log 10} \cdot \frac{1}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    13. Applied add-sqr-sqrt20.9

      \[\leadsto \frac{\color{blue}{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}} \cdot \sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}}{\sqrt{\log 10} \cdot \frac{1}{\log \left(re \cdot re + im \cdot im\right)}}\]

    14. Applied times-frac20.8

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}{\sqrt{\log 10}} \cdot \frac{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}{\frac{1}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    15. Simplified20.8

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}}} \cdot \frac{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}{\frac{1}{\log \left(re \cdot re + im \cdot im\right)}}\]

    16. Simplified20.7

      \[\leadsto \frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}} \cdot \color{blue}{\left(\log \left(im \cdot im + re \cdot re\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)}\]
    17. Using strategy rm

    18. Applied associate-*l/20.8

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\log \left(im \cdot im + re \cdot re\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)}{\sqrt{\log 10}}}\]

    19. Simplified20.9

      \[\leadsto \frac{\color{blue}{\log \left(re \cdot re + im \cdot im\right) \cdot \frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}}\]

    if -2.722618750454037e-200 < re < -2.471056064955377e-233

    1. Initial program 29.8

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    2. Using strategy rm

    3. Applied pow1/229.8

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\log 10}\]

    4. Applied log-pow29.8

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\log 10}\]

    5. Applied associate-/l*29.8

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{\log 10}{\log \left(re \cdot re + im \cdot im\right)}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity29.8

      \[\leadsto \frac{\frac{1}{2}}{\frac{\log 10}{\color{blue}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}}\]

    8. Applied add-sqr-sqrt29.8

      \[\leadsto \frac{\frac{1}{2}}{\frac{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}\]

    9. Applied times-frac30.0

      \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{\sqrt{\log 10}}{1} \cdot \frac{\sqrt{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    10. Applied associate-/r*29.8

      \[\leadsto \color{blue}{\frac{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}{\frac{\sqrt{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]
    11. Using strategy rm

    12. Applied div-inv29.8

      \[\leadsto \frac{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}{\color{blue}{\sqrt{\log 10} \cdot \frac{1}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    13. Applied add-sqr-sqrt29.8

      \[\leadsto \frac{\color{blue}{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}} \cdot \sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}}{\sqrt{\log 10} \cdot \frac{1}{\log \left(re \cdot re + im \cdot im\right)}}\]

    14. Applied times-frac29.7

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}{\sqrt{\log 10}} \cdot \frac{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}{\frac{1}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    15. Simplified29.7

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}}} \cdot \frac{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}{\frac{1}{\log \left(re \cdot re + im \cdot im\right)}}\]

    16. Simplified29.7

      \[\leadsto \frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}} \cdot \color{blue}{\left(\log \left(im \cdot im + re \cdot re\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)}\]

    17. Taylor expanded around -inf 36.5

      \[\leadsto \frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}} \cdot \left(\color{blue}{\left(-2 \cdot \log \left(\frac{-1}{im}\right)\right)} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)\]

    18. Simplified36.5

      \[\leadsto \frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}} \cdot \left(\color{blue}{\left(\log \left(\frac{-1}{im}\right) \cdot -2\right)} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)\]

    if 1.2329804060890975e+141 < re

    1. Initial program 58.5

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
    2. Using strategy rm

    3. Applied pow1/258.5

      \[\leadsto \frac{\log \color{blue}{\left({\left(re \cdot re + im \cdot im\right)}^{\frac{1}{2}}\right)}}{\log 10}\]

    4. Applied log-pow58.5

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \log \left(re \cdot re + im \cdot im\right)}}{\log 10}\]

    5. Applied associate-/l*58.5

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{\frac{\log 10}{\log \left(re \cdot re + im \cdot im\right)}}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity58.5

      \[\leadsto \frac{\frac{1}{2}}{\frac{\log 10}{\color{blue}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}}\]

    8. Applied add-sqr-sqrt58.5

      \[\leadsto \frac{\frac{1}{2}}{\frac{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}\]

    9. Applied times-frac58.5

      \[\leadsto \frac{\frac{1}{2}}{\color{blue}{\frac{\sqrt{\log 10}}{1} \cdot \frac{\sqrt{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    10. Applied associate-/r*58.5

      \[\leadsto \color{blue}{\frac{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}{\frac{\sqrt{\log 10}}{\log \left(re \cdot re + im \cdot im\right)}}}\]
    11. Using strategy rm

    12. Applied div-inv58.5

      \[\leadsto \frac{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}{\color{blue}{\sqrt{\log 10} \cdot \frac{1}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    13. Applied add-sqr-sqrt58.5

      \[\leadsto \frac{\color{blue}{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}} \cdot \sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}}{\sqrt{\log 10} \cdot \frac{1}{\log \left(re \cdot re + im \cdot im\right)}}\]

    14. Applied times-frac58.5

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}{\sqrt{\log 10}} \cdot \frac{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}{\frac{1}{\log \left(re \cdot re + im \cdot im\right)}}}\]

    15. Simplified58.5

      \[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}}} \cdot \frac{\sqrt{\frac{\frac{1}{2}}{\frac{\sqrt{\log 10}}{1}}}}{\frac{1}{\log \left(re \cdot re + im \cdot im\right)}}\]

    16. Simplified58.5

      \[\leadsto \frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}} \cdot \color{blue}{\left(\log \left(im \cdot im + re \cdot re\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)}\]

    17. Taylor expanded around 0 6.8

      \[\leadsto \frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}} \cdot \left(\color{blue}{\left(2 \cdot \log re\right)} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification17.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -3.423353045456592 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{\sqrt{\log 10}}}{\frac{\sqrt{\log 10}}{\log \left(\frac{-1}{re}\right)} \cdot \frac{-1}{2}}\\ \mathbf{elif}\;re \le -2.722618750454037 \cdot 10^{-200}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \log \left(im \cdot im + re \cdot re\right)}{\sqrt{\log 10}}\\ \mathbf{elif}\;re \le -2.471056064955377 \cdot 10^{-233}:\\ \;\;\;\;\frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}} \cdot \left(\left(\log \left(\frac{-1}{im}\right) \cdot -2\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right)\\ \mathbf{elif}\;re \le 1.2329804060890975 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \log \left(im \cdot im + re \cdot re\right)}{\sqrt{\log 10}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(2 \cdot \log re\right)\right) \cdot \frac{\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}}{\sqrt{\log 10}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019018 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))

Details

Time bar (total: 39.7s)Debug log

sample56.0ms

Algorithm
intervals
Results
44.0ms256×body80valid

simplify19.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
19.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize32.0ms

Local error

Found 3 expressions with local error:

26.2b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
15×times-frac
15×add-sqr-sqrt
14×add-cube-cbrt
14×*-un-lft-identity
8×log-pow
7×pow1
5×add-log-exp
5×associate-/l*
5×add-exp-log
5×pow1/2
5×add-cbrt-cube
4×sqrt-div
3×flip-+
3×sqrt-prod
3×flip3-+
3×associate-/r*
2×div-sub
2×log-div
1×div-inv
1×div-exp
1×frac-2neg
1×sum-log
1×clear-num
1×rem-sqrt-square
1×+-commutative
1×cbrt-undiv
Counts
3 → 62
Calls
3 calls:
Slowest
9.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
3.0ms
(sqrt (+ (* re re) (* im im)))
2.0ms
(+ (* re re) (* im im))

series181.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
132.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
29.0ms
(sqrt (+ (* re re) (* im im)))
20.0ms
(+ (* re re) (* im im))

simplify1.0s

Counts
55 → 71
Calls
55 calls:
Slowest
158.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
149.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
143.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
84.0ms
(* -1 (/ (log (/ 1 re)) (log 10)))
75.0ms
(* -1 (/ (log (/ -1 re)) (log 10)))

prune842.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.8b

localize18.0ms

Local error

Found 4 expressions with local error:

27.2b
(log (+ (* re re) (* im im)))
0.5b
(/ (log 10) (log (+ (* re re) (* im im))))
0.3b
(/ 1/2 (/ (log 10) (log (+ (* re re) (* im im)))))
0.0b
(+ (* re re) (* im im))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×add-cube-cbrt
22×*-un-lft-identity
22×add-sqr-sqrt
20×associate-/r*
12×pow1
8×log-pow
7×add-exp-log
6×add-log-exp
6×add-cbrt-cube
3×associate-/l*
3×div-inv
3×log-prod
2×flip-+
2×flip3-+
2×frac-2neg
2×clear-num
2×log-div
1×associate-/r/
1×rem-log-exp
1×div-exp
1×sum-log
1×+-commutative
1×cbrt-undiv
Counts
4 → 83
Calls
4 calls:
Slowest
7.0ms
(/ (log 10) (log (+ (* re re) (* im im))))
3.0ms
(log (+ (* re re) (* im im)))
2.0ms
(+ (* re re) (* im im))
1.0ms
(/ 1/2 (/ (log 10) (log (+ (* re re) (* im im)))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (log 10) (log (+ (* re re) (* im im))))
134.0ms
(/ 1/2 (/ (log 10) (log (+ (* re re) (* im im)))))
49.0ms
(log (+ (* re re) (* im im)))
15.0ms
(+ (* re re) (* im im))

simplify996.0ms

Counts
68 → 95
Calls
68 calls:
Slowest
120.0ms
(/ (* (* (log 10) (log 10)) (log 10)) (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))))
119.0ms
(* -1 (/ (log (/ 1 re)) (log 10)))
115.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))
91.0ms
(* -1 (/ (log (/ -1 re)) (log 10)))
50.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.7b

localize25.0ms

Local error

Found 4 expressions with local error:

27.2b
(log (+ (* re re) (* im im)))
0.4b
(/ (sqrt (log 10)) (log (+ (* re re) (* im im))))
0.3b
(/ (/ 1/2 (/ (sqrt (log 10)) 1)) (/ (sqrt (log 10)) (log (+ (* re re) (* im im)))))
0.0b
(+ (* re re) (* im im))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
308×times-frac
141×add-cube-cbrt
141×*-un-lft-identity
141×add-sqr-sqrt
87×sqrt-prod
48×pow1
44×log-pow
37×div-inv
32×associate-/r*
30×associate-/r/
12×add-exp-log
11×associate-/l*
11×add-cbrt-cube
6×add-log-exp
4×div-exp
4×cbrt-undiv
3×log-prod
2×flip-+
2×flip3-+
2×frac-2neg
2×clear-num
2×log-div
1×associate-/l/
1×rem-log-exp
1×sum-log
1×+-commutative
Counts
4 → 260
Calls
4 calls:
Slowest
9.0ms
(/ (/ 1/2 (/ (sqrt (log 10)) 1)) (/ (sqrt (log 10)) (log (+ (* re re) (* im im)))))
7.0ms
(/ (sqrt (log 10)) (log (+ (* re re) (* im im))))
4.0ms
(+ (* re re) (* im im))
3.0ms
(log (+ (* re re) (* im im)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(/ (/ 1/2 (/ (sqrt (log 10)) 1)) (/ (sqrt (log 10)) (log (+ (* re re) (* im im)))))
192.0ms
(/ (sqrt (log 10)) (log (+ (* re re) (* im im))))
64.0ms
(log (+ (* re re) (* im im)))
25.0ms
(+ (* re re) (* im im))

simplify21.9s

Counts
394 → 272
Calls
394 calls:
Slowest
680.0ms
(/ (/ 1/2 (sqrt (log 10))) (/ (sqrt 1) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))))
437.0ms
(/ (/ 1/2 (sqrt (log 10))) (/ (* (cbrt (sqrt (log 10))) (cbrt (sqrt (log 10)))) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))))
401.0ms
(/ (* (cbrt (/ 1/2 (/ (sqrt (log 10)) 1))) (cbrt (/ 1/2 (/ (sqrt (log 10)) 1)))) (/ (sqrt 1) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))))
392.0ms
(/ (/ 1/2 (sqrt (log 10))) (/ 1 (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))))
349.0ms
(/ (* (cbrt (/ 1/2 (/ (sqrt (log 10)) 1))) (cbrt (/ 1/2 (/ (sqrt (log 10)) 1)))) (/ (* (cbrt (sqrt (log 10))) (cbrt (sqrt (log 10)))) (* (cbrt (log (+ (* re re) (* im im)))) (cbrt (log (+ (* re re) (* im im)))))))

prune3.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.7b

localize18.0ms

Local error

Found 4 expressions with local error:

27.2b
(log (+ (* im im) (* re re)))
0.4b
(* (log (+ (* im im) (* re re))) (sqrt (/ 1/2 (sqrt (log 10)))))
0.4b
(* (/ (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (log 10))) (* (log (+ (* im im) (* re re))) (sqrt (/ 1/2 (sqrt (log 10))))))
0.0b
(+ (* im im) (* re re))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
50×associate-*l*
49×sqrt-prod
42×times-frac
35×add-cube-cbrt
35×*-un-lft-identity
35×add-sqr-sqrt
19×add-exp-log
18×add-cbrt-cube
13×pow1
8×div-inv
8×associate-*r*
7×cbrt-unprod
7×prod-exp
6×add-log-exp
4×associate-*r/
4×pow-prod-down
3×sqrt-div
3×log-prod
2×flip-+
2×*-commutative
2×log-pow
2×div-exp
2×flip3-+
2×log-div
2×cbrt-undiv
1×associate-*l/
1×rem-log-exp
1×sum-log
1×+-commutative
1×frac-times
Counts
4 → 116
Calls
4 calls:
Slowest
24.0ms
(* (/ (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (log 10))) (* (log (+ (* im im) (* re re))) (sqrt (/ 1/2 (sqrt (log 10))))))
5.0ms
(* (log (+ (* im im) (* re re))) (sqrt (/ 1/2 (sqrt (log 10)))))
4.0ms
(+ (* im im) (* re re))
2.0ms
(log (+ (* im im) (* re re)))

series635.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
376.0ms
(* (log (+ (* im im) (* re re))) (sqrt (/ 1/2 (sqrt (log 10)))))
177.0ms
(* (/ (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (log 10))) (* (log (+ (* im im) (* re re))) (sqrt (/ 1/2 (sqrt (log 10))))))
67.0ms
(log (+ (* im im) (* re re)))
15.0ms
(+ (* im im) (* re re))

simplify3.9s

Counts
92 → 128
Calls
92 calls:
Slowest
622.0ms
(* (* (* (/ (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (log 10))) (/ (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (log 10)))) (/ (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (log 10)))) (* (* (* (log (+ (* im im) (* re re))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (log (+ (* im im) (* re re))) (sqrt (/ 1/2 (sqrt (log 10)))))) (* (log (+ (* im im) (* re re))) (sqrt (/ 1/2 (sqrt (log 10)))))))
376.0ms
(* -2 (/ (* (log (/ -1 im)) (pow (sqrt 1/2) 2)) (log 10)))
286.0ms
(* -2 (* (pow (/ 1 (log 10)) 1/4) (* (log (/ 1 im)) (sqrt 1/2))))
272.0ms
(* 2 (/ (* (log re) (pow (sqrt 1/2) 2)) (log 10)))
240.0ms
(* (* (* (log (+ (* im im) (* re re))) (log (+ (* im im) (* re re)))) (log (+ (* im im) (* re re)))) (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))))

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.5b

regimes917.0ms

Accuracy

43% (17.3b remaining)

Error of 17.6b against oracle of 0.3b and baseline of 30.7b

bsearch316.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.3s8000×body80valid