Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	252×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	13×	body	1280	valid
1.0ms	15×	body	320	valid
0.0ms	4×	body	160	valid

simplify63.0ms

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: 28.5b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.0b	(+ x (/ (* (- y z) (- t x)) (- a z)))
21.0b	(/ (* (- 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))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series303.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(* (- y z) (- t x))
146.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
124.0ms	(/ (* (- 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

prune244.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 5.0b

Counts

91 → 11

localize13.0ms

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)))) (/ (- t x) (cbrt (- a z))))
7.3b	(+ 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)))))

series728.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (- a z))
146.0ms	(cbrt (- a z))
290.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
151.0ms	(+ 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 (68.0ms)

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

prune428.0ms

Filtered

146 candidates to 104 candidates (71.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	138	8	146
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	143	14	157

Merged error: 4.9b

Counts

157 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
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 (- 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))))))

series754.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
144.0ms	(cbrt (- a z))
138.0ms	(cbrt (- a z))
323.0ms	(+ 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))))))

simplify37.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (28.0ms)

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

prune354.0ms

Filtered

68 candidates to 59 candidates (86.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

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

Merged error: 4.9b

Counts

82 → 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))
9.8b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (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 (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- a z))
144.0ms	(cbrt (- a z))
148.0ms	(cbrt (- a z))
152.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (cbrt (- a z))) (cbrt (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	266	842
1	840	735
2	5001	724

prune323.0ms

Filtered

68 candidates to 59 candidates (86.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	68	14	82

Merged error: 4.9b

Counts

82 → 14

regimes385.0ms

Accuracy

8.3% (7.3b remaining)

Error of 12.0b against oracle of 4.7b and baseline of 12.7b

bsearch69.0ms

Steps

Iters	Range		Point
5	1.2493217098294225e-111	2.715832765458057e-111	1.8049874192490836e-111
6	-6.172682213460419e-74	-4.559231648305547e-75	-6.227068275249967e-75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	41
1	43	41

end0.0ms

sample719.0ms

Algorithm

intervals

Results

256.0ms	7750×	body	80	valid
69.0ms	502×	body	640	valid
44.0ms	433×	body	320	valid
42.0ms	283×	body	1280	valid
17.0ms	277×	body	160	valid
3.0ms	15×	body	2560	valid