Details

sample15.0ms

Algorithm

intervals

Results

5.0ms	66×	body	640	valid
3.0ms	133×	body	80	valid
2.0ms	33×	body	320	valid
1.0ms	24×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	12	4
2	12	4

prune1.0ms

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: 15.9b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
2.3b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

418×	`*-un-lft-identity`
358×	`times-frac`
303×	`add-sqr-sqrt`
291×	`add-cube-cbrt`
234×	`prod-diff`
90×	`frac-sub`
70×	`associate-/r*`
60×	`associate-/l*`
58×	`distribute-lft-out`
35×	`div-inv`
30×	`associate-/r/`
20×	`frac-2neg` `clear-num`
18×	`fma-neg`
15×	`flip3-+` `flip-+`
8×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `flip--`

Counts

2 → 403

Calls

2 calls:

5.0ms	(/ 1.0 (+ x 1.0))
32.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

series92.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ 1.0 (+ x 1.0))
65.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

simplify105.0ms

Algorithm

egg-herbie

Counts

409 → 409

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1613	7907
1	5001	6283

prune415.0ms

Filtered

409 candidates to 178 candidates (43.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	406	3	409
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	407	3	410

Merged error: 0.7b

Counts

410 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (+ x 1.0) (sqrt 1.0)) (/ x 1.0))
0.0b	(/ (- (* 1 (/ x (sqrt 1.0))) (* (/ (+ x 1.0) 1.0) (sqrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (/ x 1.0)))
1.7b	(- (* 1 (/ x (sqrt 1.0))) (* (/ (+ x 1.0) 1.0) (sqrt 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

11835×	`add-sqr-sqrt`
7172×	`times-frac`
4581×	`*-un-lft-identity`
3744×	`unswap-sqr`
2606×	`sqrt-prod`
2241×	`add-cube-cbrt`
2230×	`associate-l`
1890×	`difference-of-squares`
1518×	`associate-r`
1116×	`prod-diff`
506×	`associate-/r*`
432×	`distribute-lft-out`
430×	`associate-/l*`
372×	`associate-*l/`
336×	`frac-sub`
324×	`distribute-lft-out--`
312×	`associate-*r/`
270×	`frac-times`
269×	`associate-/l/`
161×	`associate-/r/` `div-inv`
131×	`clear-num`
114×	`*-commutative`
105×	`frac-2neg`
52×	`un-div-inv`
48×	`flip3-+` `flip-+`
36×	`fma-neg`
33×	`add-exp-log` `add-cbrt-cube`
13×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod`
6×	`sub-div`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `flip--`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down`

Counts

3 → 4346

Calls

3 calls:

22.0ms	(* (/ (+ x 1.0) (sqrt 1.0)) (/ x 1.0))
240.0ms	(/ (- (* 1 (/ x (sqrt 1.0))) (* (/ (+ x 1.0) 1.0) (sqrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (/ x 1.0)))
98.0ms	(- (* 1 (/ x (sqrt 1.0))) (* (/ (+ x 1.0) 1.0) (sqrt 1.0)))

series605.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(* (/ (+ x 1.0) (sqrt 1.0)) (/ x 1.0))
265.0ms	(/ (- (* 1 (/ x (sqrt 1.0))) (* (/ (+ x 1.0) 1.0) (sqrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (/ x 1.0)))
205.0ms	(- (* 1 (/ x (sqrt 1.0))) (* (/ (+ x 1.0) 1.0) (sqrt 1.0)))

simplify1.2s

Algorithm

egg-herbie

Counts

4355 → 4355

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5001	135718

prune7.4s

Filtered

4355 candidates to 2002 candidates (46.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	4354	1	4355
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	4355	3	4358

Merged error: 0.7b

Counts

4358 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.1b	(* (* 1 (/ x 1)) (/ 1.0 (+ x 1.0)))
6.4b	(- (* (* 1 (/ x 1)) (/ 1.0 (+ x 1.0))) (* (sqrt 1.0) (* 1 (sqrt 1.0))))
13.8b	(* (* (/ (+ x 1.0) (sqrt 1.0)) (/ x 1.0)) (* (sqrt 1.0) (/ 1.0 (+ x 1.0))))

rewrite969.0ms

Algorithm

rewrite-expression-head

Rules

7786×	`add-sqr-sqrt`
4764×	`*-un-lft-identity`
3797×	`frac-times`
3411×	`unswap-sqr`
2903×	`associate-r`
2560×	`prod-diff`
2426×	`add-cube-cbrt`
2137×	`associate-/r*`
1960×	`times-frac`
1938×	`associate-l`
1889×	`associate-/l*`
1858×	`associate-*r/`
1657×	`sqrt-prod`
711×	`clear-num`
524×	`frac-2neg`
443×	`distribute-lft-out`
374×	`un-div-inv`
367×	`associate-*l/`
260×	`associate-/l/`
215×	`*-commutative`
174×	`flip3-+` `flip-+`
165×	`difference-of-squares`
120×	`add-exp-log`
96×	`add-cbrt-cube`
88×	`associate-/r/` `div-inv`
65×	`swap-sqr`
64×	`fma-neg`
63×	`prod-exp`
47×	`cbrt-unprod`
33×	`div-exp`
23×	`cbrt-undiv`
21×	`pow1`
11×	`pow-prod-down`
10×	`1-exp` `distribute-lft-out--`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 5341

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
30.0ms	(* (* 1 (/ x 1)) (/ 1.0 (+ x 1.0)))
194.0ms	(- (* (* 1 (/ x 1)) (/ 1.0 (+ x 1.0))) (* (sqrt 1.0) (* 1 (sqrt 1.0))))
120.0ms	(* (* (/ (+ x 1.0) (sqrt 1.0)) (/ x 1.0)) (* (sqrt 1.0) (/ 1.0 (+ x 1.0))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (+ x 1.0))
44.0ms	(* (* 1 (/ x 1)) (/ 1.0 (+ x 1.0)))
82.0ms	(- (* (* 1 (/ x 1)) (/ 1.0 (+ x 1.0))) (* (sqrt 1.0) (* 1 (sqrt 1.0))))
16.0ms	(* (* (/ (+ x 1.0) (sqrt 1.0)) (/ x 1.0)) (* (sqrt 1.0) (/ 1.0 (+ x 1.0))))

simplify1.6s

Algorithm

egg-herbie

Counts

5353 → 5353

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5001	150753

prune12.3s

Filtered

5353 candidates to 3089 candidates (57.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	5353	0	5353
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	5353	3	5356

Merged error: 0.7b

Counts

5356 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (pow x 4))
0.3b	(/ 1 (pow x 3))
0.8b	(/ 1 (pow x 2))
12.8b	(- (/ 1 (pow x 3)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))))

rewrite558.0ms

Algorithm

rewrite-expression-head

Rules

4323×	`associate-/r*`
2576×	`frac-sub`
2548×	`frac-add`
2302×	`*-un-lft-identity`
2010×	`add-sqr-sqrt`
1995×	`add-cube-cbrt`
1823×	`unpow-prod-down`
1695×	`associate-/l*`
609×	`sqr-pow`
565×	`frac-2neg` `clear-num`
516×	`times-frac`
280×	`prod-diff`
221×	`unpow3`
207×	`distribute-lft-out`
186×	`unpow2`
139×	`div-inv`
31×	`add-exp-log`
28×	`fma-neg`
18×	`pow-flip` `div-exp`
14×	`flip3-+` `flip-+`
13×	`distribute-lft-out--`
10×	`pow1` `add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `pow-unpow` `1-exp` `pow-exp` `add-log-exp`
7×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-pow` `inv-pow`
2×	`diff-log` `associate--r+`
1×	`+-commutative` `sub-neg` `flip3--` `sum-log` `flip--`

Counts

4 → 3109

Calls

4 calls:

6.0ms	(/ 1 (pow x 4))
5.0ms	(/ 1 (pow x 3))
11.0ms	(/ 1 (pow x 2))
183.0ms	(- (/ 1 (pow x 3)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(/ 1 (pow x 4))
32.0ms	(/ 1 (pow x 3))
16.0ms	(/ 1 (pow x 2))
32.0ms	(- (/ 1 (pow x 3)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))))

simplify994.0ms

Algorithm

egg-herbie

Counts

3121 → 3121

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	7356	85919

prune6.4s

Filtered

3121 candidates to 1552 candidates (49.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	3120	1	3121
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	3122	2	3124

Merged error: 0b

Counts

3124 → 2

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.4b

bsearch98.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	15130.36829603915
10	-1556119314.230081	-0.05767290693153419	-9261.012486212478

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	30
1	60	30
2	60	30

end0.0ms

sample399.0ms

Algorithm

intervals

Results

135.0ms	1841×	body	640	valid
91.0ms	4308×	body	80	valid
64.0ms	1216×	body	320	valid
23.0ms	635×	body	160	valid