Details

sample30.0ms

Algorithm

intervals

Results

15.0ms	98×	body	1280	valid
3.0ms	123×	body	80	valid
3.0ms	21×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	26	6
2	33	6
3	35	6
4	41	6
5	44	6
6	44	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.4b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
12×	`prod-diff`
9×	`times-frac`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-prod`
3×	`expm1-log1p-u` `fma-neg` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 75

Calls

3 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series708.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(/ 1.0 (hypot 1.0 x))
257.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
351.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	488	1022
1	1852	782
2	5003	780

prune216.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.0b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`+-commutative` `sum-log` `fma-udef`

Counts

4 → 91

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ 1.0 (hypot 1.0 x))
1.4s	(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
320.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
154.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify94.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	867	1615
1	3960	1498
2	5001	1488

prune390.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.0b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.0b	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
28×	`times-frac`
25×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`log-pow`
18×	`exp-prod`
10×	`pow1`
9×	`distribute-lft-out`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `associate-/r*` `log1p-expm1-u`
3×	`fma-def`
2×	`flip3-+` `associate-/r/` `flip-+` `fma-udef`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `rem-log-exp` `exp-sum` `clear-num` `sum-log` `div-inv`

Counts

4 → 100

Calls

4 calls:

9.0ms	(/ (log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
1.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

series1.9s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
331.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
161.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
156.0ms	(log (exp (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))))

simplify96.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	812	2187
1	3539	2005
2	5003	1993

prune401.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.5 (/ (sqrt 0.5) (* x (sqrt 1.0))) (- (fma (sqrt 1.0) (sqrt 0.5) 1.0) (* 0.125 (/ (sqrt 0.5) (* (pow x 2) (pow (sqrt 1.0) 3))))))
0.5b	(/ (sqrt 0.5) (* x (sqrt 1.0)))
0.6b	(/ (sqrt 0.5) (* (pow x 2) (pow (sqrt 1.0) 3)))
1.0b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `div-exp` `sqrt-prod` `associate-/l`
10×	`prod-exp`
6×	`pow-to-exp` `pow-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma 0.5 (/ (sqrt 0.5) (* x (sqrt 1.0))) (- (fma (sqrt 1.0) (sqrt 0.5) 1.0) (* 0.125 (/ (sqrt 0.5) (* (pow x 2) (pow (sqrt 1.0) 3))))))
4.0ms	(/ (sqrt 0.5) (* x (sqrt 1.0)))
7.0ms	(/ (sqrt 0.5) (* (pow x 2) (pow (sqrt 1.0) 3)))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series621.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(fma 0.5 (/ (sqrt 0.5) (* x (sqrt 1.0))) (- (fma (sqrt 1.0) (sqrt 0.5) 1.0) (* 0.125 (/ (sqrt 0.5) (* (pow x 2) (pow (sqrt 1.0) 3))))))
95.0ms	(/ (sqrt 0.5) (* x (sqrt 1.0)))
147.0ms	(/ (sqrt 0.5) (* (pow x 2) (pow (sqrt 1.0) 3)))
158.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	388	872
1	1622	777
2	5001	777

prune404.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

regimes112.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 14.7b

bsearch177.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	0.5216864221254912
10	-64880754058.88788	-2.651420353119469e-05	-0.0030391710919177024

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	59
1	61	59

end0.0ms

sample800.0ms

Algorithm

intervals

Results

462.0ms	2909×	body	1280	valid
110.0ms	4022×	body	80	valid
89.0ms	621×	body	640	valid
25.0ms	293×	body	320	valid
8.0ms	155×	body	160	valid