Details

sample10.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune1.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 13.9b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

13.9b

(/ x (+ (* x x) 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
15×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`distribute-lft-out`
5×	`associate-/r*`
4×	`associate-l`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

10.0ms

(/ x (+ (* x x) 1.0))

series66.0ms

Counts

1 → 3

Calls

1 calls:

65.0ms

(/ x (+ (* x x) 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	168	245
1	565	224
2	1921	218
3	5002	212

prune57.0ms

Filtered

42 candidates to 29 candidates (31.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	3	43

Merged error: 0b

Counts

43 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.9b	(/ x (+ (pow (* x x) 3) (pow 1.0 3)))
11.8b	(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
23.2b	(* (/ x (+ (pow (* x x) 3) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

rewrite723.0ms

Algorithm

rewrite-expression-head

Rules

1661×	`add-sqr-sqrt`
1282×	`associate-l`
1266×	`associate-+r+`
1260×	`prod-diff`
1104×	`*-un-lft-identity`
816×	`add-cube-cbrt`
605×	`associate-r`
552×	`swap-sqr`
483×	`unswap-sqr`
424×	`distribute-rgt-in` `distribute-lft-in`
254×	`*-commutative`
117×	`pow1`
82×	`distribute-lft-out`
81×	`fma-def`
61×	`times-frac`
46×	`distribute-lft-out--`
40×	`unpow-prod-down` `pow-unpow` `associate-/r*` `sum-cubes`
36×	`pow-prod-up`
32×	`frac-times`
24×	`pow-prod-down`
23×	`add-exp-log` `add-cbrt-cube`
22×	`pow-sqr`
20×	`flip3-+` `flip-+`
18×	`pow-plus`
16×	`associate-*l/`
13×	`pow2`
12×	`associate-/l*`
10×	`prod-exp` `cbrt-unprod`
9×	`add-log-exp`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r/` `log1p-expm1-u`
3×	`+-commutative` `sub-neg`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `sum-log` `div-inv`
1×	`associate-+r-` `diff-log`

Counts

4 → 1720

Calls

4 calls:

17.0ms	(* (* x x) (* x x))
18.0ms	(/ x (+ (pow (* x x) 3) (pow 1.0 3)))
222.0ms	(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
282.0ms	(* (/ x (+ (pow (* x x) 3) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

series456.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* x x) (* x x))
235.0ms	(/ x (+ (pow (* x x) 3) (pow 1.0 3)))
45.0ms	(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
136.0ms	(* (/ x (+ (pow (* x x) 3) (pow 1.0 3))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

simplify380.0ms

Algorithm

egg-herbie

Counts

1732 → 1732

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5001	36277

prune2.8s

Filtered

1732 candidates to 654 candidates (62.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1731	1	1732
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	1732	3	1735

Merged error: 0b

Counts

1735 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (pow x 5))
0.1b	(/ 1 (pow x 3))
20.0b	(- (+ (* 1.0 (/ 1 (pow x 5))) (/ 1 x)) (* 1.0 (/ 1 (pow x 3))))

rewrite605.0ms

Algorithm

rewrite-expression-head

Rules

4033×	`associate-*r/`
3070×	`associate-/r*`
2482×	`frac-sub`
2448×	`frac-add`
2253×	`*-un-lft-identity`
2018×	`associate-/l*`
1771×	`add-sqr-sqrt`
1642×	`add-cube-cbrt`
1000×	`unpow-prod-down`
897×	`un-div-inv`
872×	`clear-num`
573×	`frac-2neg`
344×	`sqr-pow`
301×	`prod-diff`
261×	`times-frac`
196×	`associate-r`
184×	`distribute-lft-out`
171×	`unpow3`
118×	`associate-l`
101×	`div-inv`
56×	`unswap-sqr`
21×	`add-exp-log`
17×	`flip3-+` `flip-+`
12×	`pow-flip` `div-exp`
10×	`distribute-lft-out--`
8×	`add-log-exp` `difference-of-squares`
7×	`pow1` `fma-neg` `*-commutative` `add-cbrt-cube`
6×	`pow-to-exp` `rec-exp` `pow-unpow` `1-exp` `pow-exp`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-pow` `diff-log` `associate--l+` `inv-pow`
1×	`+-commutative` `sub-neg` `flip3--` `sum-log` `flip--`

Counts

3 → 2949

Calls

3 calls:

11.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 3))
186.0ms	(- (+ (* 1.0 (/ 1 (pow x 5))) (/ 1 x)) (* 1.0 (/ 1 (pow x 3))))

series128.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ 1 (pow x 5))
37.0ms	(/ 1 (pow x 3))
45.0ms	(- (+ (* 1.0 (/ 1 (pow x 5))) (/ 1 x)) (* 1.0 (/ 1 (pow x 3))))

simplify832.0ms

Algorithm

egg-herbie

Counts

2958 → 2958

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5596	79226

prune5.2s

Filtered

2958 candidates to 1356 candidates (54.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	2958	0	2958
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	2958	3	2961

Merged error: 0b

Counts

2961 → 3

regimes45.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch60.0ms

Steps

Iters	Range		Point
9	0.0004381094517774334	96283.49646244562	1034.1827258963394
8	-137459.4213561049	-401.9464502943543	-94110.9245102794

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	12
1	32	12

end0.0ms

sample230.0ms

Algorithm

intervals

Results

144.0ms

8000×

body

valid