Details

sample17.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	94×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

rewrite19.0ms

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:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series219.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
47.0ms	(+ 1.0 (sqrt (+ x 1.0)))
141.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	317	483
1	1159	435
2	5002	427

prune133.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Merged error: 0b

Counts

71 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.3b	(/ 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)))))

rewrite69.0ms

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:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
9.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
36.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
9.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series914.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
432.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
149.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
207.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify98.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	794	2673
1	3958	2343
2	5003	2180

prune330.0ms

Filtered

217 candidates to 117 candidates (53.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	217	5	222

Merged error: 0b

Counts

222 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
0.2b	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
9.5b	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

70×	`cbrt-prod` `*-un-lft-identity`
51×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `flip-+`
3×	`pow-unpow` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 149

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
11.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
7.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series360.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ 1.0 (sqrt (+ x 1.0)))
116.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
147.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
48.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	498	1438
1	2174	1302
2	5001	1278

prune213.0ms

Filtered

161 candidates to 80 candidates (49.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	161	5	166

Merged error: 0b

Counts

166 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(/ x (/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) (+ x (- 1.0 (* 1.0 (- (sqrt (+ x 1.0)) 1.0))))))
4.0b	(- (sqrt (+ x 1.0)) 1.0)
9.5b	(/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) (+ x (- 1.0 (* 1.0 (- (sqrt (+ x 1.0)) 1.0)))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

431×	`*-un-lft-identity`
306×	`times-frac`
153×	`distribute-lft-out`
127×	`add-sqr-sqrt`
123×	`add-cube-cbrt`
91×	`unpow-prod-down` `cube-prod`
46×	`associate-/r*`
21×	`sum-cubes`
12×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
11×	`associate-/r/`
9×	`sqrt-prod`
7×	`flip3-+` `flip-+`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow-unpow` `pow-pow`
2×	`cube-div` `frac-2neg` `sqrt-div` `clear-num` `associate-/l/` `difference-of-squares`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `unpow3` `pow-exp` `sqrt-pow2` `flip--` `distribute-lft-out--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 302

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) 3)
32.0ms	(/ x (/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) (+ x (- 1.0 (* 1.0 (- (sqrt (+ x 1.0)) 1.0))))))
7.0ms	(- (sqrt (+ x 1.0)) 1.0)
24.0ms	(/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) (+ x (- 1.0 (* 1.0 (- (sqrt (+ x 1.0)) 1.0)))))

series855.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (sqrt (+ x 1.0)) 3)
398.0ms	(/ x (/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) (+ x (- 1.0 (* 1.0 (- (sqrt (+ x 1.0)) 1.0))))))
49.0ms	(- (sqrt (+ x 1.0)) 1.0)
346.0ms	(/ (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)) (+ x (- 1.0 (* 1.0 (- (sqrt (+ x 1.0)) 1.0)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1167	5700
1	5001	5500

prune494.0ms

Filtered

314 candidates to 146 candidates (46.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	314	5	319

Merged error: 0b

Counts

319 → 5

regimes44.0ms

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	8	4
1	8	4

end0.0ms

sample407.0ms

Algorithm

intervals

Results

217.0ms	7995×	body	80	valid
66.0ms	2751×	body	80	nan
1.0ms	5×	body	1280	valid

Details

sample17.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite19.0ms

series219.0ms

simplify38.0ms

prune133.0ms

localize9.0ms

rewrite69.0ms

series914.0ms

simplify98.0ms

prune330.0ms

localize9.0ms

rewrite37.0ms

series360.0ms

simplify67.0ms

prune213.0ms

localize14.0ms

rewrite90.0ms

series855.0ms

simplify84.0ms

prune494.0ms

regimes44.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample407.0ms

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