Details

sample28.0ms

Algorithm

intervals

Results

11.0ms	254×	body	80	valid
2.0ms	16×	body	320	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	1280	valid
1.0ms	8×	body	160	valid

simplify74.0ms

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: 12.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.6b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.6b	(* (- y z) (/ (- t x) (- a z)))

rewrite37.0ms

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))
6.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
18.0ms	(* (- y z) (/ (- t x) (- a z)))

series324.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (- t x) (- a z))
149.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
126.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify59.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	473	869
1	2012	820
2	5002	820

prune311.0ms

Filtered

128 candidates to 88 candidates (68.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	114	14	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	14	129

Merged error: 3.8b

Counts

129 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
1.5b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`cbrt-prod`
54×	`associate-r`
52×	`times-frac`
34×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
18×	`add-cbrt-cube`
14×	`flip3--` `flip--`
13×	`pow1`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `pow1/3` `div-exp`
6×	`add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

3.0ms	(cbrt (- a z))
14.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
38.0ms	(* (/ (- 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)))))

series718.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (- a z))
122.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
295.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
152.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify119.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	844	2163
1	4193	1974
2	5003	1855

prune503.0ms

Filtered

187 candidates to 125 candidates (66.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	187	14	201

Merged error: 3.8b

Counts

201 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
0.6b	(cbrt (cbrt (- a z)))
1.6b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
5.8b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite135.0ms

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` `add-log-exp`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 235

Calls

4 calls:

9.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
4.0ms	(cbrt (cbrt (- a z)))
102.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
4.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series734.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
153.0ms	(cbrt (cbrt (- a z)))
297.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
159.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1420	5129
1	5001	4883

prune1.0s

Filtered

247 candidates to 204 candidates (82.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	247	14	261

Merged error: 3.8b

Counts

261 → 14

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
0.6b	(cbrt (cbrt (- a z)))
0.8b	(* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (cbrt (- a z))))))
6.7b	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-exp-log`
154×	`times-frac`
110×	`associate-l`
106×	`add-cbrt-cube`
72×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`cbrt-undiv` `div-exp`
63×	`cbrt-prod`
59×	`prod-exp` `cbrt-unprod`
58×	`cbrt-div`
56×	`add-cube-cbrt` `sqrt-prod`
22×	`associate-/r/`
20×	`flip3--` `flip--`
13×	`frac-times`
9×	`pow1` `associate-*r/`
8×	`sqrt-div` `div-inv` `distribute-lft-out--` `difference-of-squares`
7×	`associate-*l/`
6×	`add-log-exp`
3×	`pow-prod-down`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

4 → 230

Calls

4 calls:

9.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
4.0ms	(cbrt (cbrt (- a z)))
95.0ms	(* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (cbrt (- a z))))))
4.0ms	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

series737.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
146.0ms	(cbrt (cbrt (- a z)))
302.0ms	(* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (cbrt (- a z))))))
160.0ms	(+ x (* (/ (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (* (/ (/ (cbrt (- y z)) (cbrt (- a z))) (sqrt (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

simplify81.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1352	8708
1	5002	7306

prune966.0ms

Filtered

242 candidates to 163 candidates (67.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	242	14	256

Merged error: 3.8b

Counts

256 → 14

regimes327.0ms

Accuracy

13.3% (7.1b remaining)

Error of 11.6b against oracle of 4.5b and baseline of 12.7b

bsearch144.0ms

Steps

Iters	Range		Point
11	1.308338291096473e-218	4.0270067770998085e-199	5.231201158574908e-200
10	-6.578304950363068e-253	-3.874621936503089e-267	-6.246485851912935e-261

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	27
1	37	27

end0.0ms

sample822.0ms

Algorithm

intervals

Results

328.0ms	7715×	body	80	valid
80.0ms	500×	body	640	valid
54.0ms	264×	body	1280	valid
54.0ms	438×	body	320	valid
23.0ms	283×	body	160	valid
3.0ms	13×	body	2560	valid

Details

sample28.0ms

simplify74.0ms

prune2.0ms

localize10.0ms

rewrite37.0ms

series324.0ms

simplify59.0ms

prune311.0ms

localize15.0ms

rewrite68.0ms

series718.0ms

simplify119.0ms

prune503.0ms

localize19.0ms

rewrite135.0ms

series734.0ms

simplify73.0ms

prune1.0s

localize32.0ms

rewrite128.0ms

series737.0ms

simplify81.0ms

prune966.0ms

regimes327.0ms

bsearch144.0ms

simplify1.0ms

end0.0ms

sample822.0ms

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