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

sample17.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify3.0ms

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: 0.1b

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)))
0.1b	(/ 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:

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

series23.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ 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

prune120.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

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

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
4.5b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.6b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`sum-cubes` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 183

Calls

4 calls:

13.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
12.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
19.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
9.0ms	(pow (sqrt (+ x 1.0)) 3)
5.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
15.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify49.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5113	2877

prune375.0ms

Filtered

101 candidates to 195 candidates (-93.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	195	4	199

Merged error: 0b

Counts

199 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
0.1b	(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
0.2b	(pow (sqrt (+ x 1.0)) 3)
5.7b	(cbrt (pow (sqrt (+ x 1.0)) 3))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
23×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`cbrt-prod`
16×	`sqrt-prod`
14×	`unpow-prod-down` `cube-prod`
12×	`times-frac`
9×	`distribute-lft-out`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`cube-div` `flip3-+` `sqrt-div` `associate-/r*` `flip-+`
3×	`pow-unpow` `pow-pow` `associate-/l*`
2×	`cube-mult` `cbrt-div` `unpow3` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log` `sqrt-pow2` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 112

Calls

4 calls:

10.0ms	(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
12.0ms	(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
5.0ms	(cbrt (pow (sqrt (+ x 1.0)) 3))

series35.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3)))
18.0ms	(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
9.0ms	(pow (sqrt (+ x 1.0)) 3)
4.0ms	(cbrt (pow (sqrt (+ x 1.0)) 3))

simplify33.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5541	1529

prune153.0ms

Filtered

73 candidates to 124 candidates (-69.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	124	4	128

Merged error: 0b

Counts

128 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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:

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

3.0ms	(sqrt (+ x 1.0))
27.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
18.0ms	(* (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

prune181.0ms

Filtered

92 candidates to 144 candidates (-56.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	144	4	148

Merged error: 0b

Counts

148 → 4

regimes80.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	56
1	56	56

end0.0ms

sample308.0ms

Algorithm

intervals

Results

215.0ms	7996×	body	80	valid
1.0ms	4×	body	1280	valid

Details

analyze3.0ms

sample17.0ms

simplify3.0ms

prune2.0ms

localize5.0ms

rewrite17.0ms

series23.0ms

simplify23.0ms

prune120.0ms

localize15.0ms

rewrite57.0ms

series31.0ms

simplify49.0ms

prune375.0ms

localize8.0ms

rewrite36.0ms

series35.0ms

simplify33.0ms

prune153.0ms

localize7.0ms

rewrite38.0ms

series52.0ms

simplify62.0ms

prune181.0ms

regimes80.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample308.0ms

Profiling