Details

analyze3.0ms

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

6.0ms

256×

body

valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

prune2.0ms

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

rewrite17.0ms

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:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series28.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
20.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify23.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	4963	1021
1	4963	1021

prune115.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	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	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(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:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
8.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
13.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
12.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
15.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify32.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5182	1663

prune165.0ms

Filtered

75 candidates to 118 candidates (-57.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	118	4	122

Merged error: 0b

Counts

122 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

11.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series60.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
37.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4766	1713
1	4766	1713

prune235.0ms

Filtered

79 candidates to 98 candidates (-24.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	98	4	102

Merged error: 0b

Counts

102 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 132

Calls

4 calls:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
17.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
29.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
15.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4970	2333
1	4970	2333

prune188.0ms

Filtered

92 candidates to 144 candidates (-56.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	144	4	148

Merged error: 0b

Counts

148 → 4

regimes67.0ms

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	8
1	8	8

end0.0ms

sample293.0ms

Algorithm

intervals

Results

206.0ms	7994×	body	80	valid
1.0ms	6×	body	1280	valid

Details

analyze3.0ms

sample12.0ms

simplify2.0ms

prune2.0ms

localize5.0ms

rewrite17.0ms

series28.0ms

simplify23.0ms

prune115.0ms

localize7.0ms

rewrite34.0ms

series35.0ms

simplify32.0ms

prune165.0ms

localize9.0ms

rewrite24.0ms

series60.0ms

simplify61.0ms

prune235.0ms

localize7.0ms

rewrite39.0ms

series52.0ms

simplify62.0ms

prune188.0ms

regimes67.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample293.0ms

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