Average Error: 31.2 → 17.6
Time: 23.4s
Precision: 64
Internal Precision: 128
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
↓
\[\begin{array}{l} \mathbf{if}\;re \le -9.155692295214296 \cdot 10^{+68}:\\ \;\;\;\;\left(\frac{\log \left(\frac{-1}{re}\right) \cdot -2}{\sqrt{\log 10}} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \mathbf{elif}\;re \le -4.064052350582338 \cdot 10^{-291}:\\ \;\;\;\;\left(\frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt[3]{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{1}{\sqrt{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}}\right)\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \mathbf{elif}\;re \le 3.0369500767927204 \cdot 10^{-242}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(\frac{1}{\sqrt{\log 10}} \cdot \left(2 \cdot \log im\right)\right)\\ \mathbf{elif}\;re \le 8.937330246439569 \cdot 10^{+114}:\\ \;\;\;\;\left(\frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt[3]{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{1}{\sqrt{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}}\right)\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2 \cdot \log re}{\sqrt{\log 10}} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \end{array}\]

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 < -9.155692295214296e+68

    1. Initial program 45.7

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

    3. Applied add-sqr-sqrt45.7

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

    4. Applied pow1/245.7

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

    5. Applied log-pow45.7

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

    6. Applied times-frac45.7

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

    8. Applied add-sqr-sqrt45.7

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

    9. Applied associate-*l*45.7

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

    10. Taylor expanded around -inf 10.5

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

    11. Simplified10.5

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

    if -9.155692295214296e+68 < re < -4.064052350582338e-291 or 3.0369500767927204e-242 < re < 8.937330246439569e+114

    1. Initial program 20.8

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

    3. Applied add-sqr-sqrt20.8

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

    4. Applied pow1/220.8

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

    5. Applied log-pow20.8

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

    6. Applied times-frac20.7

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

    8. Applied add-sqr-sqrt20.7

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

    9. Applied associate-*l*20.7

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

    11. Applied add-cube-cbrt20.9

      \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\color{blue}{\left(\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}\right) \cdot \sqrt[3]{\log 10}}}}\right)\]

    12. Applied sqrt-prod20.9

      \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\color{blue}{\sqrt{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}} \cdot \sqrt{\sqrt[3]{\log 10}}}}\right)\]

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

      \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{\color{blue}{1 \cdot \log \left(re \cdot re + im \cdot im\right)}}{\sqrt{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}} \cdot \sqrt{\sqrt[3]{\log 10}}}\right)\]

    14. Applied times-frac20.7

      \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \color{blue}{\left(\frac{1}{\sqrt{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}} \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt[3]{\log 10}}}\right)}\right)\]

    15. Applied associate-*r*20.7

      \[\leadsto \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \color{blue}{\left(\left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{1}{\sqrt{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}}\right) \cdot \frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt[3]{\log 10}}}\right)}\]

    if -4.064052350582338e-291 < re < 3.0369500767927204e-242

    1. Initial program 32.7

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

    3. Applied add-sqr-sqrt32.7

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

    4. Applied pow1/232.7

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

    5. Applied log-pow32.8

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

    6. Applied times-frac32.8

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

    8. Applied div-inv32.6

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

    9. Taylor expanded around 0 33.5

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

    if 8.937330246439569e+114 < re

    1. Initial program 52.1

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

    3. Applied add-sqr-sqrt52.1

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

    4. Applied pow1/252.1

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

    5. Applied log-pow52.1

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

    6. Applied times-frac52.1

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

    8. Applied add-sqr-sqrt52.1

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

    9. Applied associate-*l*52.1

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

    10. Taylor expanded around inf 8.0

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

    11. Simplified8.0

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

  4. Final simplification17.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -9.155692295214296 \cdot 10^{+68}:\\ \;\;\;\;\left(\frac{\log \left(\frac{-1}{re}\right) \cdot -2}{\sqrt{\log 10}} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \mathbf{elif}\;re \le -4.064052350582338 \cdot 10^{-291}:\\ \;\;\;\;\left(\frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt[3]{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{1}{\sqrt{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}}\right)\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \mathbf{elif}\;re \le 3.0369500767927204 \cdot 10^{-242}:\\ \;\;\;\;\frac{\frac{1}{2}}{\sqrt{\log 10}} \cdot \left(\frac{1}{\sqrt{\log 10}} \cdot \left(2 \cdot \log im\right)\right)\\ \mathbf{elif}\;re \le 8.937330246439569 \cdot 10^{+114}:\\ \;\;\;\;\left(\frac{\log \left(re \cdot re + im \cdot im\right)}{\sqrt{\sqrt[3]{\log 10}}} \cdot \left(\sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}} \cdot \frac{1}{\sqrt{\sqrt[3]{\log 10} \cdot \sqrt[3]{\log 10}}}\right)\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2 \cdot \log re}{\sqrt{\log 10}} \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\right) \cdot \sqrt{\frac{\frac{1}{2}}{\sqrt{\log 10}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019010 
(FPCore (re im)
  :name "math.log10 on complex, real part"
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))

Details

Time bar (total: 21.8s)Debug log

sample60.0ms

Algorithm
intervals

simplify8.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
8.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize21.0ms

Local error

Found 3 expressions with local error:

29.5b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite26.0ms

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
16.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
4.0ms
(+ (* re re) (* im im))
4.0ms
(sqrt (+ (* re re) (* im im)))

series196.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
148.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
32.0ms
(sqrt (+ (* re re) (* im im)))
15.0ms
(+ (* re re) (* im im))

simplify948.0ms

Counts
55 → 71
Calls
55 calls:
Slowest
154.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
122.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
106.0ms
(* -1 (/ (log (/ 1 re)) (log 10)))
99.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))
87.0ms
(* -1 (/ (log (/ -1 re)) (log 10)))

prune791.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.8b

localize19.0ms

Local error

Found 4 expressions with local error:

30.6b
(log (+ (* re re) (* im im)))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.3b
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.0b
(+ (* re re) (* im im))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
38×add-cube-cbrt
38×*-un-lft-identity
38×add-sqr-sqrt
28×associate-*r*
27×sqrt-prod
20×pow1
14×log-pow
12×add-exp-log
11×add-cbrt-cube
6×add-log-exp
6×associate-/r*
4×associate-/l*
4×associate-*l*
4×log-div
3×div-inv
3×flip-+
3×flip3-+
3×log-prod
2×cbrt-unprod
2×prod-exp
2×div-exp
2×div-sub
2×cbrt-undiv
1×*-commutative
1×associate-*r/
1×associate-*l/
1×pow-prod-down
1×rem-log-exp
1×frac-2neg
1×sum-log
1×clear-num
1×+-commutative
1×frac-times
Counts
4 → 121
Calls
4 calls:
Slowest
14.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
13.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
4.0ms
(+ (* re re) (* im im))
3.0ms
(log (+ (* re re) (* im im)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
175.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
163.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
50.0ms
(log (+ (* re re) (* im im)))
15.0ms
(+ (* re re) (* im im))

simplify2.3s

Counts
118 → 133
Calls
118 calls:
Slowest
465.0ms
(* (* (* (/ 1/2 (sqrt (log 10))) (/ 1/2 (sqrt (log 10)))) (/ 1/2 (sqrt (log 10)))) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
138.0ms
(/ (log (- (* (* re re) (* re re)) (* (* im im) (* im im)))) (sqrt (log 10)))
134.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
113.0ms
(+ (log (/ 1/2 (sqrt (log 10)))) (- (log (log (+ (* re re) (* im im)))) (log (sqrt (log 10)))))
111.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.7b

localize10.0ms

Local error

Found 4 expressions with local error:

30.6b
(log (+ (* re re) (* im im)))
0.3b
(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10))))
0.3b
(* (/ 1/2 (sqrt (log 10))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10)))))
0.0b
(+ (* re re) (* im im))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
13×pow1
11×add-cbrt-cube
8×add-cube-cbrt
8×associate-*l*
8×*-un-lft-identity
8×add-sqr-sqrt
7×prod-exp
6×add-log-exp
5×associate-*r/
5×associate-*r*
4×cbrt-unprod
4×pow-prod-down
3×un-div-inv
3×log-prod
2×div-inv
2×flip-+
2×*-commutative
2×log-pow
2×flip3-+
2×rec-exp
2×log-div
2×frac-times
1×associate-*l/
1×rem-log-exp
1×sum-log
1×+-commutative
Counts
4 → 72
Calls
4 calls:
Slowest
16.0ms
(* (/ 1/2 (sqrt (log 10))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10)))))
5.0ms
(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10))))
4.0ms
(+ (* re re) (* im im))
2.0ms
(log (+ (* re re) (* im im)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
194.0ms
(* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10))))
154.0ms
(* (/ 1/2 (sqrt (log 10))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10)))))
62.0ms
(log (+ (* re re) (* im im)))
19.0ms
(+ (* re re) (* im im))

simplify2.7s

Counts
48 → 84
Calls
48 calls:
Slowest
483.0ms
(+ (log (/ 1/2 (sqrt (log 10)))) (+ (log (log (+ (* re re) (* im im)))) (log (/ 1 (sqrt (log 10))))))
405.0ms
(* (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (/ 1 (sqrt (log 10))) (/ 1 (sqrt (log 10)))) (/ 1 (sqrt (log 10)))))
370.0ms
(+ (log (/ 1/2 (sqrt (log 10)))) (log (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10))))))
154.0ms
(* (/ 1/2 (sqrt (log 10))) (* (log (+ (* re re) (* im im))) (/ 1 (sqrt (log 10)))))
146.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.6b

localize8.0ms

Local error

Found 4 expressions with local error:

30.6b
(log (+ (* re re) (* im im)))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
41×add-cube-cbrt
41×*-un-lft-identity
41×add-sqr-sqrt
35×sqrt-prod
29×associate-*r*
25×pow1
21×add-exp-log
20×add-cbrt-cube
14×log-pow
14×associate-*l*
10×sqrt-div
7×cbrt-unprod
7×prod-exp
6×associate-*r/
6×associate-/r*
6×frac-times
4×add-log-exp
4×associate-/l*
4×div-inv
4×associate-*l/
4×pow-prod-down
4×log-div
3×div-exp
3×log-prod
3×cbrt-undiv
2×flip-+
2×*-commutative
2×div-sub
2×flip3-+
1×rem-log-exp
1×frac-2neg
1×clear-num
Counts
4 → 144
Calls
4 calls:
Slowest
14.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
9.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
7.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
2.0ms
(log (+ (* re re) (* im im)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
583.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
239.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
168.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
54.0ms
(log (+ (* re re) (* im im)))

simplify4.8s

Counts
146 → 156
Calls
146 calls:
Slowest
557.0ms
(* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))))
335.0ms
(* -2 (/ (* (log (/ -1 re)) (pow (sqrt 1/2) 2)) (log 10)))
286.0ms
(* -2 (/ (* (log (/ 1 re)) (pow (sqrt 1/2) 2)) (log 10)))
269.0ms
(* (* (* (sqrt (/ 1/2 (sqrt (log 10)))) (sqrt (/ 1/2 (sqrt (log 10))))) (sqrt (/ 1/2 (sqrt (log 10))))) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
267.0ms
(* 2 (/ (* (log im) (pow (sqrt 1/2) 2)) (log 10)))

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.5b

regimes943.0ms

Accuracy

57% (10.2b remaining)

Error of 17.6b against oracle of 7.4b and baseline of 31.1b

bsearch308.0ms

end0.0ms

sample1.8s

Algorithm
intervals