Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	239×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	10×	body	1280	valid
1.0ms	14×	body	320	valid
0.0ms	7×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	44	6
2	122	6
3	327	6
4	868	6
5	1727	6
6	3544	6
7	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: 13.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.6b	(+ x (* (- y z) (/ (- t x) (- a z))))
3.0b	(* (- y z) (/ (- t x) (- a z)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`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/`
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 → 119

Calls

3 calls:

8.0ms	(/ (- t x) (- a z))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
17.0ms	(* (- y z) (/ (- t x) (- a z)))

series329.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- t x) (- a z))
148.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
130.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	473	869
1	2012	820
2	5001	820

prune297.0ms

Filtered

128 candidates to 88 candidates (68.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	116	12	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	12	129

Merged error: 4.6b

Counts

129 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.9b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`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`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
40.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series749.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
148.0ms	(cbrt (- a z))
296.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
157.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	744	1831
1	3287	1663
2	5001	1576

prune403.0ms

Filtered

146 candidates to 103 candidates (70.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	144	14	158

Merged error: 4.5b

Counts

158 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
3.0b	(* (- y z) (* (- t x) (/ 1 (- a z))))
4.3b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 146

Calls

4 calls:

6.0ms	(/ 1 (- a z))
14.0ms	(* (- t x) (/ 1 (- a z)))
15.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
6.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (- a z))
53.0ms	(* (- t x) (/ 1 (- a z)))
129.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
154.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	585	1027
1	2810	910
2	5002	865

prune302.0ms

Filtered

158 candidates to 99 candidates (62.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	157	15	172

Merged error: 4.5b

Counts

172 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (- y z) (/ (- t x) (- a z)))
3.0b	(* (- y z) (/ (- t x) (- a z)))
3.0b	(* (- y z) (/ (- t x) (- a z)))
8.4b	(+ x (* (* (cbrt (* (- y z) (/ (- t x) (- a z)))) (cbrt (* (- y z) (/ (- t x) (- a z))))) (cbrt (* (- y z) (/ (- t x) (- a z))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

121×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
93×	`associate-r`
78×	`times-frac`
40×	`add-cube-cbrt`
33×	`distribute-lft-out--` `difference-of-squares`
19×	`add-exp-log` `add-cbrt-cube`
15×	`associate-l`
10×	`pow1`
9×	`flip3--` `flip--`
6×	`frac-times` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 179

Calls

4 calls:

18.0ms	(* (- y z) (/ (- t x) (- a z)))
18.0ms	(* (- y z) (/ (- t x) (- a z)))
17.0ms	(* (- y z) (/ (- t x) (- a z)))
3.0ms	(+ x (* (* (cbrt (* (- y z) (/ (- t x) (- a z)))) (cbrt (* (- y z) (/ (- t x) (- a z))))) (cbrt (* (- y z) (/ (- t x) (- a z))))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- y z) (/ (- t x) (- a z)))
129.0ms	(* (- y z) (/ (- t x) (- a z)))
132.0ms	(* (- y z) (/ (- t x) (- a z)))
156.0ms	(+ x (* (* (cbrt (* (- y z) (/ (- t x) (- a z)))) (cbrt (* (- y z) (/ (- t x) (- a z))))) (cbrt (* (- y z) (/ (- t x) (- a z))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	388	1573
1	1711	1397
2	5002	1369

prune488.0ms

Filtered

191 candidates to 128 candidates (67.0%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	1	11	12
Picked	0	1	1
Done	0	2	2
Total	191	15	206

Merged error: 4.5b

Counts

206 → 15

regimes346.0ms

Accuracy

6.2% (7.9b remaining)

Error of 12.2b against oracle of 4.2b and baseline of 12.7b

bsearch111.0ms

Steps

Iters	Range		Point
10	6.583784058470612e-211	1.0350117034000376e-200	1.2457411842631624e-202
8	-7.400235156808656e-134	-1.6001195191711304e-137	-1.1780764679783897e-136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	26
1	41	26

end0.0ms

sample699.0ms

Algorithm

intervals

Results

251.0ms	7788×	body	80	valid
56.0ms	483×	body	640	valid
40.0ms	258×	body	1280	valid
40.0ms	423×	body	320	valid
16.0ms	277×	body	160	valid
3.0ms	18×	body	2560	valid