Details

sample45.0ms

Algorithm

intervals

Results

24.0ms	99×	body	1280	valid
7.0ms	128×	body	80	valid
3.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify11.0ms

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: 14.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.7b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

9.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series803.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
258.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
97.0ms	(/ 1.0 (hypot 1.0 x))
345.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	533	1129
1	2036	878
2	5001	876

prune305.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.2b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

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

series674.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
106.0ms	(/ 1.0 (hypot 1.0 x))
101.0ms	(/ 1.0 (hypot 1.0 x))
151.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	430	681
1	1662	625
2	5001	623

prune384.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.2b	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
2.6b	(log (exp (/ 1.0 (hypot 1.0 x))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
14×	`log-pow`
13×	`exp-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`rem-log-exp` `fma-udef`

Counts

4 → 95

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
0.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
4.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 1.0 (hypot 1.0 x))
102.0ms	(/ 1.0 (hypot 1.0 x))
152.0ms	(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))
102.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

simplify154.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (146.0ms)

Iter	Nodes	Cost
0	290	615
1	924	563
2	4602	556
3	5001	549

prune467.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.2b	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

168×	`prod-diff`
128×	`add-sqr-sqrt`
114×	`*-un-lft-identity`
109×	`unpow-prod-down` `cube-prod`
104×	`add-cube-cbrt`
36×	`sqr-pow`
28×	`cube-mult` `unpow3`
26×	`sqrt-prod`
18×	`times-frac`
16×	`difference-of-squares`
12×	`fma-neg`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cbrt-undiv` `cube-div` `frac-2neg` `sqrt-pow1` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `div-inv`
1×	`difference-cubes` `pow-to-exp` `sub-neg` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `pow-exp` `sqrt-pow2` `flip--` `flip-+` `rem-cube-cbrt`

Counts

4 → 307

Calls

4 calls:

2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
8.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
25.0ms	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

series2.1s

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1.0 (hypot 1.0 x))
100.0ms	(/ 1.0 (hypot 1.0 x))
678.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.2s	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

simplify198.0ms

Algorithm

egg-herbie

Counts

319 → 319

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1094	6420
1	4704	4472
2	5001	4472

prune647.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes212.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 15.0b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	39
1	46	39

end0.0ms

sample1.3s

Algorithm

intervals

Results

702.0ms	2856×	body	1280	valid
238.0ms	4029×	body	80	valid
124.0ms	612×	body	640	valid
47.0ms	321×	body	320	valid
18.0ms	182×	body	160	valid