Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	255×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	12×	body	320	valid
0.0ms	6×	body	160	valid

simplify52.0ms

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: 13.3b

Counts

2 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.3b	(* (- y z) (/ (- t x) (- a z)))

rewrite34.0ms

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:

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:

51.0ms	(/ (- t x) (- a z))
150.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
128.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify58.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (46.0ms)

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

prune352.0ms

Filtered

137 candidates to 97 candidates (70.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	126	11	137
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	127	12	139

Merged error: 3.8b

Counts

139 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.9b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite57.0ms

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))
41.0ms	(* (/ (- 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)))))

series963.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (- a z))
145.0ms	(cbrt (- a z))
511.0ms	(* (/ (- 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)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (74.0ms)

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

prune488.0ms

Filtered

157 candidates to 114 candidates (72.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	157	12	169

Merged error: 3.8b

Counts

169 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
0.6b	(cbrt (cbrt (- a z)))
2.6b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
7.7b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
165×	`add-sqr-sqrt`
119×	`cbrt-prod`
102×	`*-un-lft-identity`
96×	`cbrt-div`
80×	`associate-l`
61×	`associate-r`
60×	`add-cube-cbrt`
42×	`associate-/r/`
38×	`flip3--` `flip--`
36×	`add-exp-log`
25×	`frac-times`
22×	`add-cbrt-cube`
21×	`distribute-lft-out--` `difference-of-squares`
20×	`unswap-sqr`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
6×	`pow1` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 246

Calls

4 calls:

8.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
4.0ms	(cbrt (cbrt (- a z)))
92.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
6.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series715.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
143.0ms	(cbrt (cbrt (- a z)))
293.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
154.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1436	5237
1	5001	4995

prune1.1s

Filtered

258 candidates to 216 candidates (83.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	254	4	258
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	257	13	270

Merged error: 3.1b

Counts

270 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
0.6b	(cbrt (cbrt (- a z)))
2.6b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
10.5b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
164×	`add-sqr-sqrt`
119×	`cbrt-prod`
101×	`*-un-lft-identity`
96×	`cbrt-div`
80×	`associate-l`
61×	`associate-r`
59×	`add-cube-cbrt`
42×	`associate-/r/`
38×	`flip3--` `flip--`
36×	`add-exp-log`
25×	`frac-times`
22×	`add-cbrt-cube`
21×	`distribute-lft-out--` `difference-of-squares`
20×	`unswap-sqr`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
6×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3`
1×	`pow-prod-down` `*-commutative` `fma-udef`

Counts

4 → 240

Calls

4 calls:

9.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
4.0ms	(cbrt (cbrt (- a z)))
94.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
146.0ms	(cbrt (cbrt (- a z)))
301.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
161.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify69.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1383	5174
1	5002	4873

prune1.2s

Filtered

252 candidates to 211 candidates (83.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	252	13	265

Merged error: 3.1b

Counts

265 → 13

regimes329.0ms

Accuracy

21.2% (7.2b remaining)

Error of 10.7b against oracle of 3.5b and baseline of 12.6b

bsearch115.0ms

Steps

Iters	Range		Point
7	2.5859239974450258e-199	1.7648018178292372e-197	1.3516224103259182e-197
10	-5.234781754180975e-130	-3.1530790865620953e-141	-7.654582002881182e-132

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	54
1	45	54

end0.0ms

sample685.0ms

Algorithm

intervals

Results

254.0ms	7849×	body	80	valid
58.0ms	477×	body	640	valid
41.0ms	275×	body	1280	valid
37.0ms	423×	body	320	valid
18.0ms	250×	body	160	valid
3.0ms	14×	body	2560	valid