Details

analyze8.0ms

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 99.993896%

sample18.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify114.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	9
1	51	9
2	69	9
3	86	9
4	94	9
5	105	9
6	139	9
7	177	9
8	202	9
9	246	9
10	416	9
11	615	9
12	992	9
13	1948	9
14	2240	9
15	3154	9
16	5001	9

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: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.99229 (* x 0.04481))
0.0b	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
14.1b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

3.0ms	(+ 0.99229 (* x 0.04481))
13.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
5.0ms	(* x (+ 0.99229 (* x 0.04481)))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series24.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ 0.99229 (* x 0.04481))
8.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
6.0ms	(* x (+ 0.99229 (* x 0.04481)))
5.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	512	893
1	2220	827
2	5002	827

prune159.0ms

Filtered

75 candidates to 103 candidates (-37.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	3	104

Merged error: 0b

Counts

104 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.99229 (* x 0.04481))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
0.1b	(* 0.70711 (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
14.1b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

3.0ms	(+ 0.99229 (* x 0.04481))
5.0ms	(* x (+ 0.99229 (* x 0.04481)))
9.0ms	(* 0.70711 (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series21.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ 0.99229 (* x 0.04481))
5.0ms	(* x (+ 0.99229 (* x 0.04481)))
5.0ms	(* 0.70711 (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
7.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	521	973
1	2427	877
2	5001	877

prune171.0ms

Filtered

83 candidates to 110 candidates (-32.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	110	3	113

Merged error: 0b

Counts

113 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ 0.99229 (* x 0.04481)))
0.2b	(* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))
2.6b	(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
19.8b	(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481)))))) (- 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
31×	`add-sqr-sqrt`
25×	`add-exp-log` `times-frac` `add-cbrt-cube`
24×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l`
19×	`pow-prod-down`
18×	`associate-*r/`
11×	`prod-exp` `cbrt-unprod`
8×	`flip3-+` `flip-+`
7×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `difference-of-squares`
6×	`frac-times`
4×	`flip3--` `associate-/r*` `associate-/r/` `pow-sqr` `pow-prod-up` `flip--` `add-log-exp`
3×	`associate-l/` `-commutative` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `pow-plus` `div-exp` `div-inv` `associate-/l/`
1×	`pow2` `frac-2neg` `swap-sqr` `clear-num`

Counts

4 → 148

Calls

4 calls:

5.0ms	(* x (+ 0.99229 (* x 0.04481)))
10.0ms	(* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))
9.0ms	(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
12.0ms	(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481)))))) (- 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* x (+ 0.99229 (* x 0.04481)))
4.0ms	(* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481))))))
9.0ms	(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* x (+ 0.99229 (* x 0.04481))) (* x (+ 0.99229 (* x 0.04481)))))) (- 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	785	2202
1	4228	1980
2	5001	1980

prune332.0ms

Filtered

103 candidates to 160 candidates (-55.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	160	3	163

Merged error: 0b

Counts

163 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1.3436228731669864 (pow x 2)) 1.6316775383)
0.0b	(- (+ (* 1.3436228731669864 (pow x 2)) 1.6316775383) (* 2.134856267379707 x))
0.1b	(* 1.3436228731669864 (pow x 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-log-exp`
8×	`add-exp-log` `associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `associate-l` `prod-exp`
2×	`diff-log` `sum-log` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `flip3-+` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `flip-+`

Counts

3 → 52

Calls

3 calls:

4.0ms	(+ (* 1.3436228731669864 (pow x 2)) 1.6316775383)
6.0ms	(- (+ (* 1.3436228731669864 (pow x 2)) 1.6316775383) (* 2.134856267379707 x))
6.0ms	(* 1.3436228731669864 (pow x 2))

series11.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* 1.3436228731669864 (pow x 2)) 1.6316775383)
3.0ms	(- (+ (* 1.3436228731669864 (pow x 2)) 1.6316775383) (* 2.134856267379707 x))
3.0ms	(* 1.3436228731669864 (pow x 2))

simplify175.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	237	299
1	891	276
2	4637	269
3	5001	269

prune69.0ms

Filtered

40 candidates to 61 candidates (-52.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	61	3	64

Merged error: 0b

Counts

64 → 3

regimes28.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	11
1	33	11
2	34	11
3	34	11

end0.0ms

analyze4.0ms

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 99.993896%

sample445.0ms

Algorithm

intervals

Results

346.0ms

8000×

body

valid

Details

analyze8.0ms

sample18.0ms

simplify114.0ms

prune2.0ms

localize11.0ms

rewrite29.0ms

series24.0ms

simplify61.0ms

prune159.0ms

localize12.0ms

rewrite26.0ms

series21.0ms

simplify64.0ms

prune171.0ms

localize16.0ms

rewrite42.0ms

series25.0ms

simplify117.0ms

prune332.0ms

localize7.0ms

rewrite17.0ms

series11.0ms

simplify175.0ms

prune69.0ms

regimes28.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze4.0ms

sample445.0ms

Profiling