Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify121.0ms

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

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: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.0b	(- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)
0.1b	(* x (+ 0.99229 (* x 0.04481)))
12.8b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

13.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
10.0ms	(- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)
6.0ms	(* x (+ 0.99229 (* x 0.04481)))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
84.0ms	(- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)
63.0ms	(* x (+ 0.99229 (* x 0.04481)))
60.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	524	1067
1	2237	989
2	5001	989

prune202.0ms

Filtered

107 candidates to 78 candidates (72.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Merged error: 0b

Counts

108 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 2.30753 (* x 0.27061)))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
2.8b	(/ (sqrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
4.2b	(* (sqrt (+ 2.30753 (* x 0.27061))) (/ (sqrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`times-frac`
37×	`add-cube-cbrt` `*-un-lft-identity`
32×	`sqrt-prod`
27×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `associate-l`
8×	`sqrt-div`
7×	`flip3-+` `flip-+` `unswap-sqr`
6×	`associate-/l*`
4×	`associate-/r/` `add-log-exp`
3×	`associate-r/` `prod-exp` `associate-/r` `cbrt-unprod`
2×	`cbrt-undiv` `frac-times` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `associate-/l/`
1×	`distribute-rgt-in` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 134

Calls

4 calls:

2.0ms	(sqrt (+ 2.30753 (* x 0.27061)))
5.0ms	(* x (+ 0.99229 (* x 0.04481)))
7.0ms	(/ (sqrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
15.0ms	(* (sqrt (+ 2.30753 (* x 0.27061))) (/ (sqrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (+ 2.30753 (* x 0.27061)))
61.0ms	(* x (+ 0.99229 (* x 0.04481)))
132.0ms	(/ (sqrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
60.0ms	(* (sqrt (+ 2.30753 (* x 0.27061))) (/ (sqrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))

simplify78.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	633	1747
1	2761	1559
2	5002	1521

prune312.0ms

Filtered

146 candidates to 100 candidates (68.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	146	4	150

Merged error: 0b

Counts

150 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x) 3)
0.1b	(* x (+ 0.99229 (* x 0.04481)))
12.8b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
16.9b	(cbrt (pow (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`cbrt-prod`
13×	`times-frac`
12×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`difference-of-squares`
7×	`pow1`
4×	`cube-div` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-r` `associate-l` `associate-/r` `flip-+` `associate-/l`
2×	`cube-mult` `cbrt-div` `flip3--` `unpow3` `associate-*r/` `associate-/r/` `flip--` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `pow-pow` `frac-2neg` `distribute-lft-in` `pow1/3` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

11.0ms	(pow (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x) 3)
5.0ms	(* x (+ 0.99229 (* x 0.04481)))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
11.0ms	(cbrt (pow (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x) 3))

series350.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(pow (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x) 3)
67.0ms	(* x (+ 0.99229 (* x 0.04481)))
60.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
94.0ms	(cbrt (pow (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x) 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	569	1467
1	2536	1392
2	5001	1386

prune247.0ms

Filtered

125 candidates to 78 candidates (62.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	125	4	129

Merged error: 0b

Counts

129 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (* 1.3436228731669864 (pow x 2)) 1.6316775383) (* 2.134856267379707 x))
0.2b	(* 1.3436228731669864 (pow x 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

6.0ms	(- (+ (* 1.3436228731669864 (pow x 2)) 1.6316775383) (* 2.134856267379707 x))
5.0ms	(* 1.3436228731669864 (pow x 2))

series47.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- (+ (* 1.3436228731669864 (pow x 2)) 1.6316775383) (* 2.134856267379707 x))
25.0ms	(* 1.3436228731669864 (pow x 2))

simplify144.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (140.0ms)

Iter	Nodes	Cost
0	193	233
1	766	207
2	4099	201
3	5003	200

prune64.0ms

Filtered

47 candidates to 30 candidates (63.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	47	4	51

Merged error: 0b

Counts

51 → 4

regimes52.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9

end0.0ms

sample355.0ms

Algorithm

intervals

Results

265.0ms

8000×

body

valid