Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	248×	body	80	valid
2.0ms	15×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	8×	body	160	valid

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1498	6
6	3410	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: 25.8b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.9b	(+ x (/ (* (- y z) (- t x)) (- a z)))
20.4b	(/ (* (- y z) (- t x)) (- a z))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series299.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* (- y z) (- t x))
144.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
122.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify58.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	466	583
1	2158	534
2	5001	534

prune228.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	12	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 4.7b

Counts

91 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.4b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.3b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite52.0ms

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))
36.0ms	(* (/ (- 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)))))

series724.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (- a z))
143.0ms	(cbrt (- a z))
287.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
148.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (71.0ms)

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

prune397.0ms

Filtered

146 candidates to 103 candidates (70.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	143	15	158

Merged error: 4.6b

Counts

158 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
9.0b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

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

series587.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- t x))
142.0ms	(cbrt (- t x))
146.0ms	(cbrt (- t x))
150.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	260	825
1	810	753
2	5002	742

prune327.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	69	14	83

Merged error: 3.4b

Counts

83 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.2b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.7b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
98×	`times-frac`
84×	`cbrt-prod`
74×	`*-un-lft-identity`
69×	`add-exp-log`
61×	`associate-r`
44×	`cbrt-div`
42×	`add-cbrt-cube`
36×	`add-cube-cbrt`
29×	`associate-l`
27×	`cbrt-undiv` `div-exp`
24×	`prod-exp` `cbrt-unprod`
19×	`distribute-lft-out--` `difference-of-squares`
18×	`associate-/r/`
15×	`flip3--` `flip--`
12×	`unswap-sqr`
9×	`frac-times`
6×	`pow1` `add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`div-inv`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 183

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
65.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
3.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series739.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (- a z))
148.0ms	(cbrt (- a z))
297.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
150.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1131	4150
1	5001	3682

prune675.0ms

Filtered

195 candidates to 147 candidates (75.4%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	194	15	209

Merged error: 3.4b

Counts

209 → 15

regimes508.0ms

Accuracy

23.7% (7.0b remaining)

Error of 10.3b against oracle of 3.4b and baseline of 12.5b

bsearch70.0ms

Steps

Iters	Range		Point
7	3.0056805004922944e+190	1.625455215461017e+192	9.100194368894704e+191
4	-3.542713222812643e+246	-2.135390510436753e+246	-3.216598382673023e+246

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	33
1	39	33

end0.0ms

sample740.0ms

Algorithm

intervals

Results

282.0ms	7827×	body	80	valid
60.0ms	462×	body	640	valid
48.0ms	292×	body	1280	valid
44.0ms	427×	body	320	valid
20.0ms	266×	body	160	valid
7.0ms	20×	body	2560	valid