Details

sample16.0ms

Algorithm

intervals

Results

7.0ms

260×

body

valid

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	6
1	67	6
2	145	6
3	241	6
4	301	6
5	355	6
6	396	6
7	444	6
8	529	6
9	744	6
10	2218	6
11	5001	6

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: 19.7b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ t1 u) (+ t1 u))
19.4b	(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
9×	`pow1`
8×	`add-sqr-sqrt` `frac-times` `associate-/r/`
6×	`add-cube-cbrt` `swap-sqr` `distribute-lft-out`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-r` `associate-l` `associate-l/`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-lft-neg-out` `pow2` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `times-frac` `pow-plus` `distribute-frac-neg` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `associate-/l*` `unswap-sqr`

Counts

2 → 74

Calls

2 calls:

8.0ms	(* (+ t1 u) (+ t1 u))
11.0ms	(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

series88.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(* (+ t1 u) (+ t1 u))
74.0ms	(/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))

simplify61.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	390	509
1	2114	426
2	5002	422

prune114.0ms

Filtered

80 candidates to 45 candidates (56.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Merged error: 0.0b

Counts

81 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t1) (+ t1 u))
0.0b	(/ v (+ t1 u))
1.3b	(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

125×	`*-un-lft-identity`
108×	`times-frac`
81×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
46×	`associate-l`
28×	`distribute-lft-out`
27×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r`
13×	`associate-/l*`
9×	`neg-mul-1`
8×	`associate-/r*` `associate-/r/`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `distribute-frac-neg` `clear-num`
1×	`distribute-lft-neg-out` `neg-sub0` `frac-times` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

3 → 198

Calls

3 calls:

7.0ms	(/ (- t1) (+ t1 u))
5.0ms	(/ v (+ t1 u))
26.0ms	(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (- t1) (+ t1 u))
23.0ms	(/ v (+ t1 u))
115.0ms	(* (/ (- t1) (+ t1 u)) (/ v (+ t1 u)))

simplify63.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	602	1313
1	2728	1228
2	5002	1224

prune312.0ms

Filtered

207 candidates to 140 candidates (67.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	202	5	207
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	203	8	211

Merged error: 0b

Counts

211 → 8

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ v (+ t1 u))
0.0b	(/ (+ t1 u) t1)
0.5b	(/ -1 (/ (+ t1 u) t1))
1.3b	(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

225×	`times-frac`
184×	`*-un-lft-identity`
141×	`add-sqr-sqrt`
120×	`add-cube-cbrt`
53×	`associate-l`
34×	`add-exp-log` `add-cbrt-cube`
32×	`distribute-lft-out`
23×	`associate-/r*`
18×	`associate-r`
14×	`cbrt-undiv` `div-exp`
12×	`div-inv`
10×	`associate-/l*`
6×	`pow1` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`associate-/l/`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 257

Calls

4 calls:

5.0ms	(/ v (+ t1 u))
5.0ms	(/ (+ t1 u) t1)
8.0ms	(/ -1 (/ (+ t1 u) t1))
32.0ms	(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ v (+ t1 u))
21.0ms	(/ (+ t1 u) t1)
42.0ms	(/ -1 (/ (+ t1 u) t1))
116.0ms	(* (/ -1 (/ (+ t1 u) t1)) (/ v (+ t1 u)))

simplify115.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	852	1849
1	4285	1726
2	5001	1636

prune403.0ms

Filtered

269 candidates to 180 candidates (66.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	268	1	269
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	270	7	277

Merged error: 0b

Counts

277 → 7

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ v (+ t1 u))
1.1b	(/ (* (- t1) (/ v (+ t1 u))) (+ t1 u))
6.3b	(* (- t1) (/ v (+ t1 u)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
29×	`times-frac`
25×	`add-cube-cbrt`
19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r`
10×	`associate-l`
9×	`distribute-lft-out`
8×	`associate-/r*`
6×	`cbrt-undiv` `div-exp` `associate-/r/`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `associate-/l*`
3×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`distribute-lft-neg-out` `frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`neg-mul-1` `distribute-frac-neg` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

3 → 113

Calls

3 calls:

5.0ms	(/ v (+ t1 u))
14.0ms	(/ (* (- t1) (/ v (+ t1 u))) (+ t1 u))
11.0ms	(* (- t1) (/ v (+ t1 u)))

series142.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ v (+ t1 u))
72.0ms	(/ (* (- t1) (/ v (+ t1 u))) (+ t1 u))
46.0ms	(* (- t1) (/ v (+ t1 u)))

simplify51.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	392	679
1	2087	600
2	5002	600

prune172.0ms

Filtered

122 candidates to 85 candidates (69.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	122	7	129

Merged error: 0b

Counts

129 → 7

regimes88.0ms

Accuracy

91% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.3b

bsearch47.0ms

Steps

Iters	Range		Point
10	1.4671444672834564e-31	2.0974460280779343e-21	1.7403205571924323e-26
3	-2.9420474193088848e+19	-2.475160526658403e+19	-2.7961452653556097e+19

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	12
1	37	12
2	39	12
3	39	12

end0.0ms

sample384.0ms

Algorithm

intervals

Results

217.0ms

8245×

body

valid