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
symmetry log of sum of exp	45.97%	1.56%		16.9s	»
raw-angle from scale-rotated-ellipse				2.5min	»
b parameter of renormalized beta distribution	0.12%	0.12%		7.6s	»
b from scale-rotated-ellipse				2.5min	»
ab-angle->ABCF D	25.35%	0.47%		3.9s	»
ab-angle->ABCF C	31.77%	31.75%		18.6s	»
ab-angle->ABCF B	49.92%	34.75%		24.2s	»
ab-angle->ABCF A	31.66%	31.73%		21.5s	»
a parameter of renormalized beta distribution	0.27%	0.42%		7.1s	»
a from scale-rotated-ellipse	99.22%	64.27%		1.4min	»
Trigonometry B	0.51%	0.49%		11.0s	»
Trigonometry A	0.22%	0.22%		9.6s	»
Spherical law of cosines	26.93%	6.46%		40.2s	»
Simplification of discriminant from scale-rotated-ellipse	64.8%	9.57%		1.1min	»
Quadratic roots, wide range	82.22%	0.13%		13.2s	»
Quadratic roots, narrow range	44.25%	0.45%		17.9s	»
Quadratic roots, medium range	68.48%	0.61%		15.2s	»
Quadratic roots, full range	53.2%	12.34%		21.0s	»
Midpoint on a great circle	1.57%	0.37%		24.8s	»
Logistic function from Lakshay Garg	46.43%	0.66%		13.6s	»
Hyperbolic tangent	90.68%	0.02%		4.7s	»
Hyperbolic sine	90.88%	0.01%		3.1s	»
Hyperbolic secant	0.02%	0.02%		1.1s	»
Hyperbolic arc-cosine	50.73%	0.6%		4.0s	»
Hyperbolic arc-(co)tangent	91.7%	0.01%		6.0s	»
Hyperbolic arc-(co)secant	0.08%	0%		5.8s	»
Example from Robby	0.2%	0.2%		20.3s	»
Example 2 from Robby	0.19%	0.2%		17.4s	»
Equirectangular approximation to distance on a great circle	60.62%	5.84%		18.2s	»
Eccentricity of an ellipse	23.45%	0%		5.6s	»
Distance on a great circle	38.32%	20.95%		1.7min	»
Destination given bearing on a great circle	0.26%	0.26%		31.1s	»
Cubic critical, wide range	82.21%	0.13%		13.7s	»
Cubic critical, narrow range	44.51%	0.86%		20.7s	»
Cubic critical, medium range	68.48%	0.63%		20.1s	»
Cubic critical	53.26%	15.41%		23.5s	»
Bearing on a great circle	20.69%	0.28%		42.0s	»
Asymptote C	45.34%	0.23%		9.6s	»
Asymptote B	0.02%	0.02%		3.3s	»
Asymptote A	22.83%	0.11%		6.7s	»
ABCF->ab-angle b	80.92%	60.82%		52.0s	»
ABCF->ab-angle angle	46.12%	17.33%		21.7s	»
ABCF->ab-angle a	81.62%	68.68%		45.6s	»
2-ancestry mixing, zero discriminant	23.61%	1.27%		6.1s	»
2-ancestry mixing, positive discriminant	55.35%	3.14%		12.2s	»
2-ancestry mixing, negative discriminant	1.54%	1.53%		3.7s	»
Quotient of sum of exps	0.88%	0.02%	0.02%	7.1s	»
Quotient of products	17.87%	5.69%	17.91%	5.7s	»
Logistic regression 2	1.04%	0.98%	0.08%	7.3s	»
Hyperbolic arcsine	82.68%	0.33%	70.74%	5.1s	»
Harley's example				2.5min	»
Exp of sum of logs	8.91%	0%	0%	1.7s	»
(- (/ x0 (- 1 x1)) x0)				0.0s	»

Test

Start

Result ?

Target ?

Time

symmetry log of sum of exp

45.97%

1.56%

16.9s

raw-angle from scale-rotated-ellipse

2.5min

b parameter of renormalized beta distribution

0.12%

7.6s

b from scale-rotated-ellipse

2.5min

ab-angle->ABCF D

25.35%

0.47%

3.9s

ab-angle->ABCF C

31.77%

31.75%

18.6s

ab-angle->ABCF B

49.92%

34.75%

24.2s

ab-angle->ABCF A

31.66%

31.73%

21.5s

a parameter of renormalized beta distribution

0.27%

0.42%

7.1s

a from scale-rotated-ellipse

99.22%

64.27%

1.4min

Trigonometry B

0.51%

0.49%

11.0s

Trigonometry A

0.22%

9.6s

Spherical law of cosines

26.93%

6.46%

40.2s

Simplification of discriminant from scale-rotated-ellipse

64.8%

9.57%

1.1min

Quadratic roots, wide range

82.22%

0.13%

13.2s

Quadratic roots, narrow range

44.25%

0.45%

17.9s

Quadratic roots, medium range

68.48%

0.61%

15.2s

Quadratic roots, full range

53.2%

12.34%

21.0s

Midpoint on a great circle

1.57%

0.37%

24.8s

Logistic function from Lakshay Garg

46.43%

0.66%

13.6s

Hyperbolic tangent

90.68%

0.02%

4.7s

Hyperbolic sine

90.88%

0.01%

3.1s

Hyperbolic secant

0.02%

1.1s

Hyperbolic arc-cosine

50.73%

0.6%

4.0s

Hyperbolic arc-(co)tangent

91.7%

0.01%

6.0s

Hyperbolic arc-(co)secant

0.08%

5.8s

Example from Robby

0.2%

20.3s

Example 2 from Robby

0.19%

0.2%

17.4s

Equirectangular approximation to distance on a great circle

60.62%

5.84%

18.2s

Eccentricity of an ellipse

23.45%

5.6s

Distance on a great circle

38.32%

20.95%

1.7min

Destination given bearing on a great circle

0.26%

31.1s

Cubic critical, wide range

82.21%

0.13%

13.7s

Cubic critical, narrow range

44.51%

0.86%

20.7s

Cubic critical, medium range

68.48%

0.63%

20.1s

Cubic critical

53.26%

15.41%

23.5s

Bearing on a great circle

20.69%

0.28%

42.0s

Asymptote C

45.34%

0.23%

9.6s

Asymptote B

0.02%

3.3s

Asymptote A

22.83%

0.11%

6.7s

ABCF->ab-angle b

80.92%

60.82%

52.0s

ABCF->ab-angle angle

46.12%

17.33%

21.7s

ABCF->ab-angle a

81.62%

68.68%

45.6s

2-ancestry mixing, zero discriminant

23.61%

1.27%

6.1s

2-ancestry mixing, positive discriminant

55.35%

3.14%

12.2s

2-ancestry mixing, negative discriminant

1.54%

1.53%

3.7s

Quotient of sum of exps

0.88%

0.02%

7.1s

Quotient of products

17.87%

5.69%

17.91%

5.7s

Logistic regression 2

1.04%

0.98%

0.08%

7.3s

Hyperbolic arcsine

82.68%

0.33%

70.74%

5.1s

Harley's example

2.5min

Exp of sum of logs

8.91%

1.7s

(- (/ x0 (- 1 x1)) x0)

0.0s