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	29.4	0.8		23.8s	»
raw-angle from scale-rotated-ellipse				2.5min	»
b parameter of renormalized beta distribution	0.1	0.1		9.1s	»
b from scale-rotated-ellipse				2.5min	»
ab-angle->ABCF D	16.2	0.3		4.9s	»
ab-angle->ABCF C	20.5	20.5		20.4s	»
ab-angle->ABCF B	31.3	21.5		29.9s	»
ab-angle->ABCF A	20.6	20.6		27.3s	»
a parameter of renormalized beta distribution	0.2	0.2		7.7s	»
a from scale-rotated-ellipse				2.5min	»
Trigonometry B	0.3	0.3		14.6s	»
Trigonometry A	0.1	0.1		15.5s	»
Spherical law of cosines	16.9	3.8		56.4s	»
Simplification of discriminant from scale-rotated-ellipse	40.6	5.8		1.7min	»
Quadratic roots, wide range	52.6	1.6		20.8s	»
Quadratic roots, narrow range	28.8	0.5		25.9s	»
Quadratic roots, medium range	44.1	0.9		28.9s	»
Quadratic roots, full range	34.1	11.2		24.3s	»
Midpoint on a great circle	0.9	0.2		29.3s	»
Logistic function from Lakshay Garg	29.8	0.3		11.0s	»
Hyperbolic tangent	58.0	0.0		4.7s	»
Hyperbolic sine	58.0	0.0		7.9s	»
Hyperbolic secant	0.0	0.0		1.1s	»
Hyperbolic arc-cosine	32.5	0.3		3.8s	»
Hyperbolic arc-(co)tangent	58.5	0.0		5.8s	»
Hyperbolic arc-(co)secant	0.0	0.0		7.0s	»
Example from Robby	0.1	0.1		27.8s	»
Example 2 from Robby	0.1	0.1		20.0s	»
Equirectangular approximation to distance on a great circle	38.7	3.9		24.9s	»
Eccentricity of an ellipse	14.5	0.0		4.2s	»
Distance on a great circle	24.1	14.0		1.9min	»
Destination given bearing on a great circle	0.2	0.1		41.6s	»
Cubic critical, wide range	52.6	0.6		19.1s	»
Cubic critical, narrow range	28.9	0.3		21.8s	»
Cubic critical, medium range	44.1	0.2		23.3s	»
Cubic critical	34.1	11.2		35.9s	»
Bearing on a great circle	12.9	0.2		1.2min	»
Asymptote C	29.3	0.0		13.8s	»
Asymptote B	0.0	0.0		4.2s	»
Asymptote A	14.3	0.1		8.4s	»
ABCF->ab-angle b	52.6	38.6		47.6s	»
ABCF->ab-angle angle	29.5	7.4		32.1s	»
ABCF->ab-angle a	52.4	39.0		1.2min	»
2-ancestry mixing, zero discriminant	15.4	0.9		8.5s	»
2-ancestry mixing, positive discriminant	35.6	1.4		22.5s	»
2-ancestry mixing, negative discriminant	1.0	1.3		9.8s	»
Quotient of sum of exps	0.5	0.8	0.0	13.0s	»
Quotient of products	11.2	2.3	11.3	6.1s	»
Logistic regression 2	0.5	0.5	0.1	12.9s	»
Hyperbolic arcsine	52.5	0.1	45.0	15.7s	»
Harley's example				2.5min	»
Exp of sum of logs	5.7	0	0	2.0s	»
(- (/ x0 (- 1 x1)) x0)				0.0s	»

Test

Start

Result ?

Target ?

Time

symmetry log of sum of exp

29.4

0.8

23.8s

raw-angle from scale-rotated-ellipse

2.5min

b parameter of renormalized beta distribution

0.1

9.1s

b from scale-rotated-ellipse

2.5min

ab-angle->ABCF D

16.2

0.3

4.9s

ab-angle->ABCF C

20.5

20.4s

ab-angle->ABCF B

31.3

21.5

29.9s

ab-angle->ABCF A

20.6

27.3s

a parameter of renormalized beta distribution

0.2

7.7s

a from scale-rotated-ellipse

2.5min

Trigonometry B

0.3

14.6s

Trigonometry A

0.1

15.5s

Spherical law of cosines

16.9

3.8

56.4s

Simplification of discriminant from scale-rotated-ellipse

40.6

5.8

1.7min

Quadratic roots, wide range

52.6

1.6

20.8s

Quadratic roots, narrow range

28.8

0.5

25.9s

Quadratic roots, medium range

44.1

0.9

28.9s

Quadratic roots, full range

34.1

11.2

24.3s

Midpoint on a great circle

0.9

0.2

29.3s

Logistic function from Lakshay Garg

29.8

0.3

11.0s

Hyperbolic tangent

58.0

0.0

4.7s

Hyperbolic sine

58.0

0.0

7.9s

Hyperbolic secant

0.0

1.1s

Hyperbolic arc-cosine

32.5

0.3

3.8s

Hyperbolic arc-(co)tangent

58.5

0.0

5.8s

Hyperbolic arc-(co)secant

0.0

7.0s

Example from Robby

0.1

27.8s

Example 2 from Robby

0.1

20.0s

Equirectangular approximation to distance on a great circle

38.7

3.9

24.9s

Eccentricity of an ellipse

14.5

0.0

4.2s

Distance on a great circle

24.1

14.0

1.9min

Destination given bearing on a great circle

0.2

0.1

41.6s

Cubic critical, wide range

52.6

0.6

19.1s

Cubic critical, narrow range

28.9

0.3

21.8s

Cubic critical, medium range

44.1

0.2

23.3s

Cubic critical

34.1

11.2

35.9s

Bearing on a great circle

12.9

0.2

1.2min

Asymptote C

29.3

0.0

13.8s

Asymptote B

0.0

4.2s

Asymptote A

14.3

0.1

8.4s

ABCF->ab-angle b

52.6

38.6

47.6s

ABCF->ab-angle angle

29.5

7.4

32.1s

ABCF->ab-angle a

52.4

39.0

1.2min

2-ancestry mixing, zero discriminant

15.4

0.9

8.5s

2-ancestry mixing, positive discriminant

35.6

1.4

22.5s

2-ancestry mixing, negative discriminant

1.0

1.3

9.8s

Quotient of sum of exps

0.5

0.8

0.0

13.0s

Quotient of products

11.2

2.3

11.3

6.1s

Logistic regression 2

0.5

0.1

12.9s

Hyperbolic arcsine

52.5

0.1

45.0

15.7s

Harley's example

2.5min

Exp of sum of logs

5.7

2.0s

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

0.0s