Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample12.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune8.0ms

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))))

rewrite16.0ms

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))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series24.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (39.0ms)

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

prune127.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ (+ 1.0 (sqrt (+ x 1.0))) x)
0.2b	(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
99×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
19×	`associate-/r*`
18×	`distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `sqrt-prod`
3×	`flip3-+` `flip-+`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/` `inv-pow`

Counts

4 → 149

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) x)
9.0ms	(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series32.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
9.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) x)
15.0ms	(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify87.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	768	1530
1	3598	1400
2	5001	1316

prune186.0ms

Filtered

90 candidates to 161 candidates (-78.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	161	4	165

Merged error: 0b

Counts

165 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))))))
0.8b	(/ 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:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
31.0ms	(* (/ 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)))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
31.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
15.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
18.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1124	3013
1	5002	2717

prune461.0ms

Filtered

126 candidates to 217 candidates (-72.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	217	4	221

Merged error: 0b

Counts

221 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
0.2b	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
7.8b	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite35.0ms

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:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
10.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
6.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
7.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series43.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
15.0ms	(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
8.0ms	(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify89.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	775	1626
1	3592	1511
2	5001	1487

prune202.0ms

Filtered

84 candidates to 161 candidates (-91.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	161	4	165

Merged error: 0b

Counts

165 → 4

regimes30.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

end0.0ms

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample296.0ms

Algorithm

intervals

Results

212.0ms	7997×	body	80	valid
0.0ms	3×	body	1280	valid

Details

analyze2.0ms

sample12.0ms

simplify3.0ms

prune8.0ms

localize5.0ms

rewrite16.0ms

series24.0ms

simplify47.0ms

prune127.0ms

localize7.0ms

rewrite30.0ms

series32.0ms

simplify87.0ms

prune186.0ms

localize9.0ms

rewrite61.0ms

series75.0ms

simplify51.0ms

prune461.0ms

localize9.0ms

rewrite35.0ms

series43.0ms

simplify89.0ms

prune202.0ms

regimes30.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.0ms

sample296.0ms

Profiling