Details

sample17.0ms

Algorithm

intervals

Results

8.0ms

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

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))
0.1b	(* x (+ 0.99229 (* x 0.04481)))
14.9b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite28.0ms

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:

12.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
3.0ms	(+ 2.30753 (* x 0.27061))
5.0ms	(* x (+ 0.99229 (* x 0.04481)))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
31.0ms	(+ 2.30753 (* x 0.27061))
66.0ms	(* x (+ 0.99229 (* x 0.04481)))
61.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	516	893
1	2218	827
2	5002	827

prune198.0ms

Filtered

103 candidates to 74 candidates (71.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	4	104

Merged error: 0b

Counts

104 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
0.1b	(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
14.8b	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
14.8b	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

7.0ms	(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
14.0ms	(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
4.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
3.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
56.0ms	(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
80.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
82.0ms	(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	929	6227
1	3540	5694
2	5001	5608

prune496.0ms

Filtered

276 candidates to 149 candidates (54.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	276	4	280

Merged error: 0b

Counts

280 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 2.30753 (* x 0.27061)))
0.7b	(* (cbrt (+ 2.30753 (* x 0.27061))) (cbrt (+ 2.30753 (* x 0.27061))))
2.5b	(/ (cbrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
12.3b	(* (* (cbrt (+ 2.30753 (* x 0.27061))) (cbrt (+ 2.30753 (* x 0.27061)))) (/ (cbrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
41×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
40×	`cbrt-div`
38×	`times-frac`
30×	`associate-r`
22×	`flip3-+` `flip-+`
20×	`add-exp-log` `frac-times`
16×	`pow1`
14×	`associate-*l/`
11×	`add-cbrt-cube`
7×	`pow1/3` `associate-r/` `associate-l*` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`swap-sqr` `associate-/l*`
5×	`pow-prod-down`
4×	`associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/r*`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv` `associate-/l/`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num`

Counts

4 → 167

Calls

4 calls:

2.0ms	(cbrt (+ 2.30753 (* x 0.27061)))
8.0ms	(* (cbrt (+ 2.30753 (* x 0.27061))) (cbrt (+ 2.30753 (* x 0.27061))))
6.0ms	(/ (cbrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
17.0ms	(* (* (cbrt (+ 2.30753 (* x 0.27061))) (cbrt (+ 2.30753 (* x 0.27061)))) (/ (cbrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (+ 2.30753 (* x 0.27061)))
156.0ms	(* (cbrt (+ 2.30753 (* x 0.27061))) (cbrt (+ 2.30753 (* x 0.27061))))
207.0ms	(/ (cbrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
85.0ms	(* (* (cbrt (+ 2.30753 (* x 0.27061))) (cbrt (+ 2.30753 (* x 0.27061)))) (/ (cbrt (+ 2.30753 (* x 0.27061))) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1002	2836
1	4623	2622
2	5001	2519

prune543.0ms

Filtered

179 candidates to 132 candidates (73.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	179	4	183

Merged error: 0b

Counts

183 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

14.8b	(/ (* 0.70711 (- (* (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (* x x))) (+ (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
14.9b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
14.9b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
14.9b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
31×	`times-frac`
30×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
10×	`associate-/l*`
8×	`associate-/r/` `associate-/l/`
7×	`flip3-+` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-2neg` `clear-num` `div-inv` `add-log-exp`
2×	`associate-*r/` `distribute-lft-out`
1×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

23.0ms	(/ (* 0.70711 (- (* (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (* x x))) (+ (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
6.0ms	(/ (+ 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)))))
10.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(/ (* 0.70711 (- (* (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (* x x))) (+ (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
62.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
57.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
62.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	472	2145
1	2090	1899
2	5001	1882

prune339.0ms

Filtered

132 candidates to 106 candidates (80.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	132	4	136

Merged error: 0b

Counts

136 → 4

regimes60.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms

sample363.0ms

Algorithm

intervals

Results

272.0ms

8000×

body

valid