Details

sample80.0ms

Algorithm

intervals

Results

43.0ms

653×

body

valid

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	47	14
1	110	13
2	335	13
3	1059	13
4	3442	13
5	5001	13

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 13.2b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* c z) (* i a))
4.7b	(* x (- (* y z) (* t a)))
6.0b	(* b (- (* c z) (* i a)))
6.5b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

720×	`prod-diff`
653×	`add-sqr-sqrt`
395×	`*-un-lft-identity`
385×	`associate-r`
381×	`associate-l`
371×	`add-cube-cbrt`
292×	`distribute-rgt-in` `distribute-lft-in`
135×	`unswap-sqr`
123×	`*-commutative`
12×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`diff-log` `fma-udef`

Counts

4 → 832

Calls

4 calls:

21.0ms	(- (* c z) (* i a))
28.0ms	(* x (- (* y z) (* t a)))
28.0ms	(* b (- (* c z) (* i a)))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

series859.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* c z) (* i a))
80.0ms	(* x (- (* y z) (* t a)))
81.0ms	(* b (- (* c z) (* i a)))
654.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

simplify174.0ms

Algorithm

egg-herbie

Counts

844 → 844

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	1736	13531
1	5001	9255

prune801.0ms

Filtered

844 candidates to 157 candidates (81.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	828	16	844
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	829	16	845

Merged error: 7.0b

Counts

845 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

4.7b	(* x (- (* y z) (* t a)))
4.8b	(* b (* c z))
6.5b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* i a))))))
6.6b	(* b (- (* i a)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

288×	`prod-diff`
285×	`add-sqr-sqrt`
204×	`associate-r`
170×	`*-un-lft-identity`
166×	`associate-l`
162×	`add-cube-cbrt`
146×	`distribute-rgt-in` `distribute-lft-in`
60×	`unswap-sqr`
54×	`*-commutative`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`sub-neg` `associate-*r/`
1×	`neg-mul-1` `flip3--` `distribute-rgt-neg-out` `flip--` `fma-udef`

Counts

4 → 411

Calls

4 calls:

28.0ms	(* x (- (* y z) (* t a)))
8.0ms	(* b (* c z))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* i a))))))
10.0ms	(* b (- (* i a)))

series805.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* x (- (* y z) (* t a)))
29.0ms	(* b (* c z))
663.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* b (- (* i a))))))
31.0ms	(* b (- (* i a)))

simplify170.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1204	5934
1	4498	4175
2	5001	4175

prune609.0ms

Filtered

423 candidates to 120 candidates (71.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	412	11	423
Fresh	10	5	15
Picked	1	0	1
Done	0	0	0
Total	423	16	439

Merged error: 6.8b

Counts

439 → 16

localize22.0ms

Local error

Found 4 expressions with local error:

4.7b	(* x (- (* y z) (* t a)))
4.8b	(* b (* c z))
5.2b	(* (* b (- a)) i)
6.5b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* (* b (- a)) i))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

288×	`prod-diff`
284×	`add-sqr-sqrt`
183×	`associate-r`
179×	`associate-l`
168×	`*-un-lft-identity`
160×	`add-cube-cbrt`
146×	`distribute-rgt-in` `distribute-lft-in`
61×	`unswap-sqr`
53×	`*-commutative`
16×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`sub-neg` `associate-*r/`
1×	`distribute-lft-neg-out` `neg-mul-1` `flip3--` `distribute-rgt-neg-out` `flip--` `fma-udef`

Counts

4 → 406

Calls

4 calls:

31.0ms	(* x (- (* y z) (* t a)))
8.0ms	(* b (* c z))
10.0ms	(* (* b (- a)) i)
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* (* b (- a)) i))))

series816.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* x (- (* y z) (* t a)))
29.0ms	(* b (* c z))
37.0ms	(* (* b (- a)) i)
669.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* (* b (- a)) i))))

simplify169.0ms

Algorithm

egg-herbie

Counts

418 → 418

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1184	5930
1	4350	4166
2	5001	4166

prune568.0ms

Filtered

418 candidates to 113 candidates (73.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	414	4	418
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	419	15	434

Merged error: 6.6b

Counts

434 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

4.7b	(* x (- (* y z) (* t a)))
4.7b	(* (* b (- (* (cbrt a) (cbrt a)))) (* (cbrt a) i))
4.8b	(* b (* c z))
6.5b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* (* b (- (* (cbrt a) (cbrt a)))) (* (cbrt a) i)))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-sqr-sqrt`
288×	`prod-diff`
259×	`associate-r`
245×	`associate-l`
187×	`*-un-lft-identity`
179×	`add-cube-cbrt`
146×	`distribute-rgt-in` `distribute-lft-in`
81×	`unswap-sqr`
56×	`*-commutative`
38×	`cbrt-prod`
28×	`add-cbrt-cube`
27×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
23×	`pow1` `add-exp-log`
17×	`cbrt-unprod`
12×	`swap-sqr` `pow-prod-down` `prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`sub-neg` `associate-*r/`
1×	`distribute-lft-neg-out` `neg-mul-1` `flip3--` `distribute-rgt-neg-out` `flip--` `fma-udef`

Counts

4 → 479

Calls

4 calls:

31.0ms	(* x (- (* y z) (* t a)))
41.0ms	(* (* b (- (* (cbrt a) (cbrt a)))) (* (cbrt a) i))
12.0ms	(* b (* c z))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* (* b (- (* (cbrt a) (cbrt a)))) (* (cbrt a) i)))))

series892.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* x (- (* y z) (* t a)))
57.0ms	(* (* b (- (* (cbrt a) (cbrt a)))) (* (cbrt a) i))
35.0ms	(* b (* c z))
718.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* b (* c z)) (* (* b (- (* (cbrt a) (cbrt a)))) (* (cbrt a) i)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

491 → 491

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1527	6863
1	5001	4967

prune925.0ms

Filtered

491 candidates to 178 candidates (63.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	491	0	491
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	491	15	506

Merged error: 6.6b

Counts

506 → 15

regimes877.0ms

Accuracy

39.6% (4.3b remaining)

Error of 9.2b against oracle of 4.9b and baseline of 12.1b

bsearch272.0ms

Steps

Iters	Range		Point
9	7.544721836480686e+105	5.091940200331415e+111	1.4437934549332887e+106
9	-7.175444757484693e+28	-4.844041260676378e+21	-1.1751140434009048e+28

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	32
1	94	32
2	99	32
3	99	32

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

19253×

body

valid