Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	259×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	5×	body	1280	valid
1.0ms	8×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 22.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.8b	(+ x (/ (* (- y z) (- t x)) (- a z)))
18.0b	(/ (* (- 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))
8.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series309.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (- y z) (- t x))
144.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
128.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

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

prune213.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	11	91

Merged error: 3.6b

Counts

91 → 11

localize13.0ms

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)))))

rewrite53.0ms

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))
35.0ms	(* (/ (- 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)))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a z))
152.0ms	(cbrt (- a z))
291.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
150.0ms	(+ 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

prune390.0ms

Filtered

146 candidates to 102 candidates (69.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	1	8	9
Picked	1	0	1
Done	1	0	1
Total	143	14	157

Merged error: 3.6b

Counts

157 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
8.4b	(+ 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 (- a z))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
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))))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
154.0ms	(cbrt (- a z))
146.0ms	(cbrt (- a z))
151.0ms	(+ 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))))))

simplify36.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	264	825
1	818	753
2	5001	744

prune333.0ms

Filtered

68 candidates to 59 candidates (86.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	68	14	82

Merged error: 3.6b

Counts

82 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(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)))))
7.9b	(+ 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`
166×	`add-sqr-sqrt`
115×	`cbrt-prod`
103×	`*-un-lft-identity`
80×	`associate-l`
76×	`cbrt-div`
61×	`associate-r`
59×	`add-cube-cbrt`
42×	`associate-/r/`
36×	`add-exp-log`
33×	`flip3--` `flip--`
22×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
21×	`frac-times`
20×	`unswap-sqr`
14×	`cbrt-undiv` `div-exp`
11×	`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 → 230

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
95.0ms	(* (/ (/ (- 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))))))

series749.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a z))
148.0ms	(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)))))
154.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1343	4962
1	5001	4723

prune927.0ms

Filtered

242 candidates to 201 candidates (83.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	238	4	242
Fresh	4	8	12
Picked	0	1	1
Done	0	1	1
Total	242	14	256

Merged error: 3.6b

Counts

256 → 14

regimes361.0ms

Accuracy

19.1% (6.4b remaining)

Error of 10.5b against oracle of 4.1b and baseline of 12.1b

bsearch108.0ms

Steps

Iters	Range		Point
8	9.57374001919587e-186	7.221890555412899e-183	9.477473214863088e-184
7	-9.829566173255385e-222	-5.236032066965215e-223	-9.000457573034878e-222

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	55
1	44	55

end0.0ms

sample790.0ms

Algorithm

intervals

Results

314.0ms	7781×	body	80	valid
73.0ms	468×	body	640	valid
51.0ms	276×	body	1280	valid
44.0ms	397×	body	320	valid
20.0ms	267×	body	160	valid
5.0ms	23×	body	2560	valid