Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

288×

body

valid

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	5
1	38	5
2	60	5
3	88	5
4	122	5
5	175	5
6	625	5
7	4686	5
8	5001	5

prune7.0ms

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: 8.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- t (* a z))
0.0b	(- x (* y z))
8.1b	(/ (- x (* y z)) (- t (* a z)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-sqr-sqrt`
135×	`*-un-lft-identity`
72×	`prod-diff`
63×	`add-cube-cbrt`
49×	`times-frac`
36×	`associate-l` `distribute-lft-out--` `difference-of-squares`
24×	`unswap-sqr`
18×	`associate-r`
7×	`associate-/r` `associate-/l` `add-log-exp`
6×	`fma-neg` `*-commutative`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 196

Calls

3 calls:

9.0ms	(- t (* a z))
8.0ms	(- x (* y z))
18.0ms	(/ (- x (* y z)) (- t (* a z)))

series145.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(- t (* a z))
33.0ms	(- x (* y z))
69.0ms	(/ (- x (* y z)) (- t (* a z)))

simplify102.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	754	2143
1	2499	1616
2	5003	1608

prune288.0ms

Filtered

205 candidates to 98 candidates (47.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	192	13	205
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	192	14	206

Merged error: 7.5b

Counts

206 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- t (* a z))
0.0b	(- x (* y z))
0.9b	(/ 1 (- t (* a z)))
7.8b	(* (- x (* y z)) (/ 1 (- t (* a z))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
132×	`*-un-lft-identity`
78×	`add-cube-cbrt`
72×	`prod-diff`
45×	`associate-r`
44×	`times-frac`
38×	`associate-l`
28×	`associate-/r*`
26×	`frac-times` `distribute-lft-out--` `difference-of-squares`
22×	`unswap-sqr`
18×	`flip3--` `flip--`
17×	`add-exp-log`
13×	`associate-r/` `associate-/l`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `*-commutative`
6×	`fma-neg`
5×	`clear-num`
4×	`expm1-log1p-u` `frac-2neg` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`un-div-inv`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 263

Calls

4 calls:

9.0ms	(- t (* a z))
13.0ms	(- x (* y z))
9.0ms	(/ 1 (- t (* a z)))
26.0ms	(* (- x (* y z)) (/ 1 (- t (* a z))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- t (* a z))
40.0ms	(- x (* y z))
55.0ms	(/ 1 (- t (* a z)))
70.0ms	(* (- x (* y z)) (/ 1 (- t (* a z))))

simplify131.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	887	2496
1	3588	1877
2	5003	1805

prune375.0ms

Filtered

275 candidates to 129 candidates (46.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	269	6	275
Fresh	6	6	12
Picked	0	1	1
Done	0	1	1
Total	275	14	289

Merged error: 7.5b

Counts

289 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.9b	(/ 1 (- t (* a z)))
2.0b	(+ (- (* (cbrt y) z)) (* (cbrt y) z))
7.8b	(* (+ (- x (* (* (cbrt y) z) (* (cbrt y) (cbrt y)))) (* (* (cbrt y) (cbrt y)) (+ (- (* (cbrt y) z)) (* (cbrt y) z)))) (/ 1 (- t (* a z))))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

187×	`*-un-lft-identity`
169×	`add-sqr-sqrt`
105×	`associate-l`
78×	`frac-times`
72×	`add-cube-cbrt`
69×	`associate-*r/`
56×	`frac-add` `associate-/r*`
47×	`associate-r`
45×	`distribute-lft-neg-in`
44×	`times-frac`
43×	`flip3-+` `flip-+`
37×	`distribute-lft-out--`
36×	`fma-def`
35×	`cbrt-prod`
34×	`distribute-rgt-neg-in`
32×	`distribute-lft-out`
30×	`flip3--` `flip--`
29×	`distribute-rgt-out` `unswap-sqr`
28×	`difference-of-squares`
25×	`associate-/l*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`clear-num`
8×	`frac-2neg` `add-log-exp`
7×	`pow1` `*-commutative`
6×	`associate-*l/`
5×	`neg-mul-1`
4×	`expm1-log1p-u` `distribute-lft1-in` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`un-div-inv`
2×	`cbrt-undiv` `rec-exp` `1-exp` `sum-log` `cbrt-unprod` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `pow-flip` `pow1/3` `pow-prod-down` `neg-log` `inv-pow`

Counts

4 → 330

Calls

4 calls:

1.0ms	(cbrt y)
9.0ms	(/ 1 (- t (* a z)))
33.0ms	(+ (- (* (cbrt y) z)) (* (cbrt y) z))
241.0ms	(* (+ (- x (* (* (cbrt y) z) (* (cbrt y) (cbrt y)))) (* (* (cbrt y) (cbrt y)) (+ (- (* (cbrt y) z)) (* (cbrt y) z)))) (/ 1 (- t (* a z))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(cbrt y)
55.0ms	(/ 1 (- t (* a z)))
2.0ms	(+ (- (* (cbrt y) z)) (* (cbrt y) z))
105.0ms	(* (+ (- x (* (* (cbrt y) z) (* (cbrt y) (cbrt y)))) (* (* (cbrt y) (cbrt y)) (+ (- (* (cbrt y) z)) (* (cbrt y) z)))) (/ 1 (- t (* a z))))

simplify118.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1096	9054
1	5002	7050

prune5.9s

Filtered

342 candidates to 220 candidates (64.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	1	10	11
Picked	1	0	1
Done	0	2	2
Total	343	13	356

Merged error: 7.5b

Counts

356 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- t (* a z))
0.0b	(- x (* y z))
0.7b	(/ 1 (/ (- t (* a z)) (- x (* y z))))
8.1b	(/ (- t (* a z)) (- x (* y z)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

574×	`add-sqr-sqrt`
491×	`*-un-lft-identity`
410×	`times-frac`
182×	`add-cube-cbrt`
154×	`distribute-lft-out--`
152×	`difference-of-squares`
95×	`associate-l`
82×	`unswap-sqr`
72×	`prod-diff`
69×	`associate-/r*`
29×	`associate-/r/`
20×	`associate-/l*`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`flip3--` `flip--`
8×	`div-exp` `add-log-exp`
6×	`fma-neg` `*-commutative` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `clear-num` `log1p-expm1-u` `associate-/l/` `remove-double-div`
3×	`frac-2neg`
2×	`sub-neg` `rec-exp` `diff-log` `1-exp`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 464

Calls

4 calls:

9.0ms	(- t (* a z))
9.0ms	(- x (* y z))
26.0ms	(/ 1 (/ (- t (* a z)) (- x (* y z))))
19.0ms	(/ (- t (* a z)) (- x (* y z)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- t (* a z))
38.0ms	(- x (* y z))
241.0ms	(/ 1 (/ (- t (* a z)) (- x (* y z))))
70.0ms	(/ (- t (* a z)) (- x (* y z)))

simplify108.0ms

Algorithm

egg-herbie

Counts

476 → 476

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	1249	5467
1	5002	4606

prune573.0ms

Filtered

476 candidates to 208 candidates (43.7%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	473	3	476
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	475	14	489

Merged error: 7.5b

Counts

489 → 14

regimes358.0ms

Accuracy

0% (0.9b remaining)

Error of 10.2b against oracle of 9.3b and baseline of 10.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

end0.0ms

sample587.0ms

Algorithm

intervals

Results

303.0ms

8784×

body

valid