Herbie results

Output vs Input Accuracy

Each point represents a Herbie run below. Its horizontal position shows initial accuracy, and vertical position shows final accuracy. Points above the line are improved by Herbie.

Accuracy vs Cost

A joint cost-accuracy pareto curve for the Herbie runs below. Accuracy is on the vertical axis, and cost is on the vertical axis. Down and to the left is better. The initial programs are shown by the red square.

Test	Start	Result ?	Target ?	Time
powComplex, real part	51.32%	5.33%		18.4s	»
powComplex, imaginary part	51.47%	5.57%		25.0s	»
normal distribution	0.6%	0.36%		11.5s	»
math.square on complex, real part	0.01%	0%		1.3s	»
math.square on complex, imaginary part	0.01%	0.05%		1.2s	»
math.sqrt on complex, imaginary part, im greater than 0 branch	60.34%	11.79%		10.7s	»
math.sin on complex, real part	0.08%	0.07%		11.2s	»
math.log10 on complex, real part	50.59%	0.92%		11.0s	»
math.log10 on complex, imaginary part	1.32%	0.22%		6.4s	»
math.log/2 on complex, real part	50.47%	0.57%		13.4s	»
math.log/2 on complex, imaginary part	50.16%	0.48%		9.6s	»
math.log/1 on complex, real part	50.13%	0%		1.3s	»
math.log/1 on complex, imaginary part	0%	0%		0.6s	»
math.exp on complex, real part	0.02%	0.02%		7.7s	»
math.exp on complex, imaginary part	0.03%	0.03%		7.5s	»
math.cos on complex, real part	0.02%	0.02%		10.1s	»
math.arg on complex	0%	0%		0.7s	»
math.abs on complex (squared)	0.01%	0%		1.2s	»
math.abs on complex	49.86%	0%		1.0s	»
_multiplyComplex, real part	0.02%	0.02%		4.3s	»
_multiplyComplex, imaginary part	0.02%	0.01%		2.9s	»
_divideComplex, real part	40.99%	7.48%		15.6s	»
_divideComplex, imaginary part	41.11%	19.16%		19.2s	»
Rust f64::atanh	0.03%	0.03%		2.0s	»
Rust f32::atanh	0.2%	0.2%		5.4s	»
Octave 3.8, oct_fill_randg	0.23%	0.2%		10.6s	»
Octave 3.8, jcobi/4, as called	73.41%	0.46%		2.3s	»
Octave 3.8, jcobi/4	84.57%	14.05%		24.5s	»
Octave 3.8, jcobi/3	5.9%	0.53%		18.8s	»
Octave 3.8, jcobi/2	37.86%	2.38%		21.6s	»
Octave 3.8, jcobi/1	25.27%	0.45%		6.9s	»
Jmat.Real.lambertw, estimator	0.41%	0.01%		3.5s	»
Jmat.Real.gamma, branch z less than 0.5	2.67%	0.8%		1.4min	»
Jmat.Real.gamma, branch z greater than 0.5	6.46%	3.19%		31.9s	»
Jmat.Real.erfi, branch x less than or equal to 0.5	0.28%	0.27%		10.4s	»
Jmat.Real.erfi, branch x greater than or equal to 5	4.47%	1.98%		16.7s	»
Jmat.Real.erf	20.61%	0.44%		15.8s	»
Jmat.Real.dawson	44.67%	0.05%		5.0s	»
math.sqrt on complex, real part	61.09%	17.41%	53.21%	8.3s	»
math.sin on complex, imaginary part	90.52%	1.12%	0.42%	13.9s	»
math.cube on real	0.2%	0%	0%	1.6s	»
math.cube on complex, real part	12.2%	0.26%	0.38%	10.4s	»
math.cube on complex, imaginary part	12.29%	0.28%	0.38%	8.0s	»
math.cos on complex, imaginary part	67.86%	1.16%	0.48%	12.0s	»
Rust f64::asinh	71.26%	0.3%	0.09%	4.2s	»
Rust f64::acosh	50.05%	0.47%	0.07%	2.0s	»
Rust f32::asinh	64.18%	0.7%	0.47%	9.0s	»
Rust f32::acosh	50.71%	1.89%	0.81%	10.4s	»
Jmat.Real.lambertw, newton loop step	22.02%	0.48%	20.94%	11.9s	»
Ian Simplification	93.18%	91.72%	0%	17.9s	»
FastMath test5	0.2%	0%	0%	2.2s	»
FastMath test3	0.11%	0.07%	0.09%	7.5s	»
FastMath test2	0.29%	0.04%	0.04%	3.0s	»
FastMath test1	0.41%	0%	0%	1.0s	»
FastMath repmul	0.22%	0%	0%	1.8s	»
FastMath dist4	0.04%	0.04%	0.04%	8.8s	»
FastMath dist3	0.07%	0.04%	0.03%	4.8s	»
FastMath dist	0.02%	0.01%	0.02%	2.2s	»

Test

Start

Result ?

Target ?

Time

powComplex, real part

51.32%

5.33%

18.4s

powComplex, imaginary part

51.47%

5.57%

25.0s

normal distribution

0.6%

0.36%

11.5s

math.square on complex, real part

0.01%

1.3s

math.square on complex, imaginary part

0.01%

0.05%

1.2s

math.sqrt on complex, imaginary part, im greater than 0 branch

60.34%

11.79%

10.7s

math.sin on complex, real part

0.08%

0.07%

11.2s

math.log10 on complex, real part

50.59%

0.92%

11.0s

math.log10 on complex, imaginary part

1.32%

0.22%

6.4s

math.log/2 on complex, real part

50.47%

0.57%

13.4s

math.log/2 on complex, imaginary part

50.16%

0.48%

9.6s

math.log/1 on complex, real part

50.13%

1.3s

math.log/1 on complex, imaginary part

0.6s

math.exp on complex, real part

0.02%

7.7s

math.exp on complex, imaginary part

0.03%

7.5s

math.cos on complex, real part

0.02%

10.1s

math.arg on complex

0.7s

math.abs on complex (squared)

0.01%

1.2s

math.abs on complex

49.86%

1.0s

_multiplyComplex, real part

0.02%

4.3s

_multiplyComplex, imaginary part

0.02%

0.01%

2.9s

_divideComplex, real part

40.99%

7.48%

15.6s

_divideComplex, imaginary part

41.11%

19.16%

19.2s

Rust f64::atanh

0.03%

2.0s

Rust f32::atanh

0.2%

5.4s

Octave 3.8, oct_fill_randg

0.23%

0.2%

10.6s

Octave 3.8, jcobi/4, as called

73.41%

0.46%

2.3s

Octave 3.8, jcobi/4

84.57%

14.05%

24.5s

Octave 3.8, jcobi/3

5.9%

0.53%

18.8s

Octave 3.8, jcobi/2

37.86%

2.38%

21.6s

Octave 3.8, jcobi/1

25.27%

0.45%

6.9s

Jmat.Real.lambertw, estimator

0.41%

0.01%

3.5s

Jmat.Real.gamma, branch z less than 0.5

2.67%

0.8%

1.4min

Jmat.Real.gamma, branch z greater than 0.5

6.46%

3.19%

31.9s

Jmat.Real.erfi, branch x less than or equal to 0.5

0.28%

0.27%

10.4s

Jmat.Real.erfi, branch x greater than or equal to 5

4.47%

1.98%

16.7s

Jmat.Real.erf

20.61%

0.44%

15.8s

Jmat.Real.dawson

44.67%

0.05%

5.0s

math.sqrt on complex, real part

61.09%

17.41%

53.21%

8.3s

math.sin on complex, imaginary part

90.52%

1.12%

0.42%

13.9s

math.cube on real

0.2%

1.6s

math.cube on complex, real part

12.2%

0.26%

0.38%

10.4s

math.cube on complex, imaginary part

12.29%

0.28%

0.38%

8.0s

math.cos on complex, imaginary part

67.86%

1.16%

0.48%

12.0s

Rust f64::asinh

71.26%

0.3%

0.09%

4.2s

Rust f64::acosh

50.05%

0.47%

0.07%

2.0s

Rust f32::asinh

64.18%

0.7%

0.47%

9.0s

Rust f32::acosh

50.71%

1.89%

0.81%

10.4s

Jmat.Real.lambertw, newton loop step

22.02%

0.48%

20.94%

11.9s

Ian Simplification

93.18%

91.72%

17.9s

FastMath test5

0.2%

2.2s

FastMath test3

0.11%

0.07%

0.09%

7.5s

FastMath test2

0.29%

0.04%

3.0s

FastMath test1

0.41%

1.0s

FastMath repmul

0.22%

1.8s

FastMath dist4

0.04%

8.8s

FastMath dist3

0.07%

0.04%

0.03%

4.8s

FastMath dist

0.02%

0.01%

0.02%

2.2s