Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
2.0ms	16×	body	1280	valid
2.0ms	19×	body	640	valid
2.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	74	5
3	128	5
4	252	5
5	374	5
6	514	5
7	642	5
8	777	5
9	1010	5
10	1686	5
11	5001	5

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: 21.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.6b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
5.9b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt`
5×	`pow1` `associate-l` `add-log-exp`
4×	`times-frac` `associate-l/` `associate-/r`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

6.0ms	(* (- 1.0 x) y)
7.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series142.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* (- 1.0 x) y)
66.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
46.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	338	401
1	1456	359
2	5001	359

prune124.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.0b

Counts

73 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
3.6b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3--` `flip--` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 88

Calls

3 calls:

5.0ms	(/ y (+ y 1.0))
12.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
3.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series144.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ y (+ y 1.0))
46.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
64.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	400	572
1	1790	526
2	5002	526

prune141.0ms

Filtered

97 candidates to 70 candidates (72.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	97	4	101

Merged error: 0.0b

Counts

101 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.1b	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
5.1b	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
16.9b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (- 1.0 x) y)
13.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- 1.0 x) y)
77.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
154.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
86.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	567	1027
1	3078	900
2	5001	900

prune181.0ms

Filtered

117 candidates to 82 candidates (70.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	117	4	121

Merged error: 0.0b

Counts

121 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

5.9b	(/ (* (- 1.0 x) y) (+ y 1.0))
5.9b	(/ (* (- 1.0 x) y) (+ y 1.0))
5.9b	(/ (* (- 1.0 x) y) (+ y 1.0))
9.9b	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ y 1.0)) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
28×	`times-frac`
21×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/r*`
11×	`distribute-lft-out`
8×	`associate-/r/` `associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`associate-*l/`
5×	`difference-of-squares`
4×	`pow1` `flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `div-inv` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
1×	`div-sub`

Counts

4 → 122

Calls

4 calls:

12.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
8.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
12.0ms	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ y 1.0)) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
47.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
394.0ms	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ y 1.0)) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	431	1543
1	2019	1406
2	5001	1406

prune235.0ms

Filtered

134 candidates to 98 candidates (73.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	134	4	138

Merged error: 0.0b

Counts

138 → 4

regimes148.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.7b

bsearch92.0ms

Steps

Iters	Range		Point
9	172312.70592171172	58211804231.258	94936908.52428018
10	-4.445579369187069e+17	-1822035.3400642718	-21195722.51507012

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	14
1	33	14

end0.0ms

sample518.0ms

Algorithm

intervals

Results

181.0ms	6058×	body	80	valid
83.0ms	757×	body	640	valid
56.0ms	371×	body	1280	valid
47.0ms	550×	body	320	valid
15.0ms	264×	body	160	valid