Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	259×	body	80	valid
2.0ms	15×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	5×	body	1280	valid
1.0ms	8×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

Filtered

1 candidates to 1 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: 15.0b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.0b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/ (- t x) (- a z))
1.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series148.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- t x) (- a z))
94.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune196.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	61	11	72

Merged error: 5.0b

Counts

72 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.6b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.9b	(* (- y z) (/ (- t x) (- a z)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 128

Calls

3 calls:

9.0ms	(/ (- t x) (- a z))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
18.0ms	(* (- y z) (/ (- t x) (- a z)))

series340.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- t x) (- a z))
154.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
135.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify59.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	488	901
1	2066	849
2	5001	847

prune315.0ms

Filtered

137 candidates to 96 candidates (70.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	5	4	9
Picked	1	0	1
Done	0	1	1
Total	136	12	148

Merged error: 2.2b

Counts

148 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.1b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
28×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 145

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
43.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series772.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- a z))
156.0ms	(cbrt (- a z))
302.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
160.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	757	1897
1	3339	1727
2	5002	1624

prune451.0ms

Filtered

157 candidates to 116 candidates (73.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	156	13	169

Merged error: 2.2b

Counts

169 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
1.0b	(* (/ (- y z) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
5.8b	(/ (* (/ (- y z) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))) (cbrt (- a z)))
7.2b	(+ x (/ (* (/ (- y z) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))) (cbrt (- a z))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

136×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
100×	`times-frac`
71×	`cbrt-prod`
48×	`add-cube-cbrt`
46×	`associate-r` `associate-l`
34×	`add-exp-log`
29×	`distribute-lft-out--` `difference-of-squares`
21×	`add-cbrt-cube`
13×	`cbrt-undiv` `div-exp`
9×	`unswap-sqr`
8×	`cbrt-div` `prod-exp` `associate-/r*` `cbrt-unprod`
6×	`pow1` `associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`fma-def` `div-inv` `associate-/l/`
2×	`frac-times` `associate-r/` `associate-l/`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow1/3` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `distribute-lft-out` `associate-/l`

Counts

4 → 201

Calls

4 calls:

3.0ms	(cbrt (- a z))
54.0ms	(* (/ (- y z) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
25.0ms	(/ (* (/ (- y z) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))) (cbrt (- a z)))
9.0ms	(+ x (/ (* (/ (- y z) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))) (cbrt (- a z))))

series994.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (- a z))
181.0ms	(* (/ (- y z) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
505.0ms	(/ (* (/ (- y z) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))) (cbrt (- a z)))
158.0ms	(+ x (/ (* (/ (- y z) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))) (cbrt (- a z))))

simplify107.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	949	2505
1	3821	2347
2	5001	2291

prune516.0ms

Filtered

213 candidates to 148 candidates (69.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	0	10	10
Picked	1	0	1
Done	0	2	2
Total	213	13	226

Merged error: 2.1b

Counts

226 → 13

regimes381.0ms

Accuracy

52.3% (4.2b remaining)

Error of 7.9b against oracle of 3.7b and baseline of 12.5b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	29
1	34	29

end0.0ms

sample824.0ms

Algorithm

intervals

Results

319.0ms	7783×	body	80	valid
73.0ms	469×	body	640	valid
54.0ms	276×	body	1280	valid
45.0ms	397×	body	320	valid
20.0ms	264×	body	160	valid
5.0ms	23×	body	2560	valid