Details

sample18.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	86×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(sqrt (+ x 1.0))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

10.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series568.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(+ 1.0 (sqrt (+ x 1.0)))
69.0ms	(sqrt (+ x 1.0))
411.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	460	585
1	1938	554
2	5002	551

prune312.0ms

Filtered

70 candidates to 55 candidates (21.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Merged error: 0b

Counts

71 → 3

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `flip-+`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 106

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
10.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
12.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series865.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (+ x 1.0))
86.0ms	(+ 1.0 (sqrt (+ x 1.0)))
303.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
410.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify78.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	681	1007
1	3263	915
2	5002	876

prune588.0ms

Filtered

118 candidates to 76 candidates (35.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	118	3	121

Merged error: 0b

Counts

121 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
106×	`times-frac`
101×	`*-un-lft-identity`
71×	`sqrt-prod`
65×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`distribute-lft-out` `unswap-sqr`
14×	`associate-/r*`
11×	`div-exp`
10×	`sqrt-div`
9×	`pow1`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`frac-times` `rem-sqrt-square` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 205

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
29.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
8.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series2.6s

Counts

4 → 12

Calls

4 calls:

322.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
1.0s	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
431.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
789.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1124	3019
1	5001	2717

prune1.3s

Filtered

217 candidates to 126 candidates (41.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	217	3	220

Merged error: 0b

Counts

220 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
6.2b	(- (- (* 1.0 1.0) x) 1.0)
6.3b	(- 1.0 (sqrt (+ x 1.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`associate-l`
16×	`times-frac`
15×	`add-cube-cbrt`
11×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`difference-of-squares`
7×	`pow1`
6×	`associate-r` `sqrt-prod` `distribute-lft-out--`
5×	`sub-neg` `flip3--` `flip--`
4×	`diff-log`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `associate-*r/` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate--l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
19.0ms	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
6.0ms	(- (- (* 1.0 1.0) x) 1.0)
6.0ms	(- 1.0 (sqrt (+ x 1.0)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (+ x 1.0))
154.0ms	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
15.0ms	(- (- (* 1.0 1.0) x) 1.0)
111.0ms	(- 1.0 (sqrt (+ x 1.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	503	940
1	2155	875
2	5001	866

prune484.0ms

Filtered

112 candidates to 82 candidates (26.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	112	3	115

Merged error: 0b

Counts

115 → 3

regimes28.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5

end0.0ms

sample414.0ms

Algorithm

intervals

Results

198.0ms	7998×	body	80	valid
58.0ms	2636×	body	80	nan
0.0ms	2×	body	1280	valid

Details

sample18.0ms

simplify3.0ms

prune3.0ms

localize5.0ms

rewrite21.0ms

series568.0ms

simplify48.0ms

prune312.0ms

localize6.0ms

rewrite34.0ms

series865.0ms

simplify78.0ms

prune588.0ms

localize9.0ms

rewrite61.0ms

series2.6s

simplify52.0ms

prune1.3s

localize9.0ms

rewrite37.0ms

series350.0ms

simplify55.0ms

prune484.0ms

regimes28.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample414.0ms

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