Herbie results

Average Percentage Accurate: 70.4% → 96.7%

Time: 6.9min

Bad Runs: 0/45

Speedup: 4×

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 Speed

A joint speed-accuracy pareto curve. Accuracy is on the vertical axis, speed is on the horizontal axis. Up and to the right is better. The initial program is shown by the red square.

Test	Start	Result ?	Target ?	Time
arccos	100.0%	100.0%		8.0s	»
Rump's expression from Stadtherr's award speech	9.2%	9.2%		0.9s	»
Rosa's TurbineBenchmark	84.6%	99.7%		15.2s	»
Rosa's FloatVsDoubleBenchmark	70.6%	99.4%		53.4s	»
Rosa's DopplerBench	72.3%	97.6%		10.4s	»
Rosa's Benchmark	99.8%	99.8%		6.9s	»
Radioactive exchange between two surfaces	86.6%	99.8%		4.7s	»
NMSE Section 6.1 mentioned, B	79.1%	99.6%		12.2s	»
NMSE Section 6.1 mentioned, A	73.8%	99.9%		17.2s	»
Kahan's Unum-Targeted Monster				4.3s	»
Kahan's Monster				2.7s	»
Kahan p13 Example 3	100.0%	100.0%		7.4s	»
Kahan p13 Example 2	100.0%	100.0%		12.2s	»
Kahan p13 Example 1	99.9%	100.0%		14.5s	»
From Warwick Tucker's Validated Numerics	9.2%	100.0%		2.0s	»
From Rump in a 1983 paper, rewritten	3.1%	100.0%		2.4s	»
From Rump in a 1983 paper	18.8%	100.0%		2.8s	»
ENA, Section 1.4, Mentioned, B	87.7%	99.6%		8.5s	»
ENA, Section 1.4, Exercise 4b, n=5	88.9%	99.2%		11.1s	»
ENA, Section 1.4, Exercise 4b, n=2	75.9%	100.0%		4.4s	»
ENA, Section 1.4, Exercise 1	94.5%	99.4%		10.1s	»
x / (x^2 + 1)	76.6%	100.0%	99.8%	2.1s	»
simple fma test	29.0%	100.0%	100.0%	2.4s	»
ln(1 + x)	39.0%	100.0%	99.7%	3.0s	»
fma_test2	34.1%	99.6%	99.6%	10.0s	»
fma_test1	3.4%	99.7%	21.0%	4.7s	»
The quadratic formula (r2)	51.6%	85.5%	70.2%	19.5s	»
The quadratic formula (r1)	52.1%	85.4%	70.2%	19.2s	»
Rectangular parallelepiped of dimension a×b×c	100.0%	100.0%	100.0%	1.1s	»
Kahan's exp quotient	52.9%	100.0%	52.2%	2.8s	»
Kahan p9 Example	68.3%	100.0%	99.9%	12.5s	»
Expression, p6	94.3%	100.0%	94.0%	4.5s	»
Expression, p14	99.9%	100.0%	99.9%	6.5s	»
Expression 4, p15	100.0%	100.0%	100.0%	3.9s	»
Expression 3, p15	100.0%	100.0%	100.0%	3.3s	»
Expression 2, p15	100.0%	100.0%	100.0%	1.4s	»
Expression 1, p15	99.4%	99.6%	99.6%	9.2s	»
ENA, Section 1.4, Mentioned, A	53.6%	100.0%	100.0%	8.4s	»
ENA, Section 1.4, Exercise 4d	61.7%	99.0%	99.5%	8.1s	»
ENA, Section 1.4, Exercise 4a	53.5%	99.6%	98.6%	21.8s	»
Difference of squares	93.7%	100.0%	100.0%	1.9s	»
Compound Interest	28.6%	95.8%	34.2%	23.0s	»
Complex division, real part	61.1%	84.9%	99.4%	12.1s	»
Complex division, imag part	61.5%	97.3%	99.5%	19.2s	»
Area of a triangle				0.2s	»

Test

Start

Result ?

Target ?

Time

arccos

100.0%

8.0s

Rump's expression from Stadtherr's award speech

9.2%

0.9s

Rosa's TurbineBenchmark

84.6%

99.7%

15.2s

Rosa's FloatVsDoubleBenchmark

70.6%

99.4%

53.4s

Rosa's DopplerBench

72.3%

97.6%

10.4s

Rosa's Benchmark

99.8%

6.9s

Radioactive exchange between two surfaces

86.6%

99.8%

4.7s

NMSE Section 6.1 mentioned, B

79.1%

99.6%

12.2s

NMSE Section 6.1 mentioned, A

73.8%

99.9%

17.2s

Kahan's Unum-Targeted Monster

4.3s

Kahan's Monster

2.7s

Kahan p13 Example 3

100.0%

7.4s

Kahan p13 Example 2

100.0%

12.2s

Kahan p13 Example 1

99.9%

100.0%

14.5s

From Warwick Tucker's Validated Numerics

9.2%

100.0%

2.0s

From Rump in a 1983 paper, rewritten

3.1%

100.0%

2.4s

From Rump in a 1983 paper

18.8%

100.0%

2.8s

ENA, Section 1.4, Mentioned, B

87.7%

99.6%

8.5s

ENA, Section 1.4, Exercise 4b, n=5

88.9%

99.2%

11.1s

ENA, Section 1.4, Exercise 4b, n=2

75.9%

100.0%

4.4s

ENA, Section 1.4, Exercise 1

94.5%

99.4%

10.1s

x / (x^2 + 1)

76.6%

100.0%

99.8%

2.1s

simple fma test

29.0%

100.0%

2.4s

ln(1 + x)

39.0%

100.0%

99.7%

3.0s

fma_test2

34.1%

99.6%

10.0s

fma_test1

3.4%

99.7%

21.0%

4.7s

The quadratic formula (r2)

51.6%

85.5%

70.2%

19.5s

The quadratic formula (r1)

52.1%

85.4%

70.2%

19.2s

Rectangular parallelepiped of dimension a×b×c

100.0%

1.1s

Kahan's exp quotient

52.9%

100.0%

52.2%

2.8s

Kahan p9 Example

68.3%

100.0%

99.9%

12.5s

Expression, p6

94.3%

100.0%

94.0%

4.5s

Expression, p14

99.9%

100.0%

99.9%

6.5s

Expression 4, p15

100.0%

3.9s

Expression 3, p15

100.0%

3.3s

Expression 2, p15

100.0%

1.4s

Expression 1, p15

99.4%

99.6%

9.2s

ENA, Section 1.4, Mentioned, A

53.6%

100.0%

8.4s

ENA, Section 1.4, Exercise 4d

61.7%

99.0%

99.5%

8.1s

ENA, Section 1.4, Exercise 4a

53.5%

99.6%

98.6%

21.8s

Difference of squares

93.7%

100.0%

1.9s

Compound Interest

28.6%

95.8%

34.2%

23.0s

Complex division, real part

61.1%

84.9%

99.4%

12.1s

Complex division, imag part

61.5%

97.3%

99.5%

19.2s

Area of a triangle

0.2s