Details

sample82.0ms

Algorithm

intervals

Results

45.0ms

582×

body

valid

simplify109.0ms

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 (100.0%)

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: 11.8b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* c z) (* t i))
3.2b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
4.8b	(* b (- (* c z) (* t i)))
6.1b	(* x (- (* y z) (* t a)))

rewrite149.0ms

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:

19.0ms	(- (* c z) (* t i))
1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
29.0ms	(* b (- (* c z) (* t i)))
37.0ms	(* x (- (* y z) (* t a)))

series911.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* c z) (* t i))
691.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
85.0ms	(* b (- (* c z) (* t i)))
93.0ms	(* x (- (* y z) (* t a)))

simplify179.0ms

Algorithm

egg-herbie

Counts

844 → 844

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	1737	13531
1	5001	9255

prune835.0ms

Filtered

844 candidates to 157 candidates (18.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	829	15	844
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	830	15	845

Merged error: 4.8b

Counts

845 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* c a) (* y i))
3.2b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (fma (* c 1) z (- (* i t))))))
4.8b	(* b (fma (* c 1) z (- (* i t))))
6.1b	(* x (- (* y z) (* t a)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

432×	`prod-diff`
401×	`add-sqr-sqrt`
243×	`*-un-lft-identity`
233×	`associate-r` `associate-l`
227×	`add-cube-cbrt`
147×	`distribute-rgt-in` `distribute-lft-in`
83×	`unswap-sqr`
75×	`*-commutative`
12×	`fma-neg`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-udef`
2×	`flip3--` `associate-*r/` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
1×	`diff-log`

Counts

4 → 532

Calls

4 calls:

18.0ms	(- (* c a) (* y i))
1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (fma (* c 1) z (- (* i t))))))
4.0ms	(* b (fma (* c 1) z (- (* i t))))
37.0ms	(* x (- (* y z) (* t a)))

series897.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* c a) (* y i))
687.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (fma (* c 1) z (- (* i t))))))
90.0ms	(* b (fma (* c 1) z (- (* i t))))
78.0ms	(* x (- (* y z) (* t a)))

simplify191.0ms

Algorithm

egg-herbie

Counts

544 → 544

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1463	8287
1	4483	5463
2	5001	5463

prune654.0ms

Filtered

544 candidates to 113 candidates (20.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	531	13	544
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	541	18	559

Merged error: 4.0b

Counts

559 → 18

localize36.0ms

Local error

Found 4 expressions with local error:

5.9b	(cbrt (- (* c a) (* y i)))
5.9b	(cbrt (- (* c a) (* y i)))
5.9b	(cbrt (- (* c a) (* y i)))
6.1b	(* x (- (* y z) (* t a)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

299×	`add-sqr-sqrt`
288×	`prod-diff`
185×	`*-un-lft-identity`
163×	`associate-l`
155×	`associate-r`
153×	`add-cube-cbrt`
146×	`distribute-rgt-in` `distribute-lft-in`
65×	`unswap-sqr`
49×	`*-commutative`
33×	`cbrt-prod`
16×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`sub-neg` `associate-*r/`
1×	`pow-prod-down` `prod-exp` `cbrt-unprod`

Counts

4 → 391

Calls

4 calls:

14.0ms	(cbrt (- (* c a) (* y i)))
13.0ms	(cbrt (- (* c a) (* y i)))
13.0ms	(cbrt (- (* c a) (* y i)))
30.0ms	(* x (- (* y z) (* t a)))

series526.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- (* c a) (* y i)))
143.0ms	(cbrt (- (* c a) (* y i)))
141.0ms	(cbrt (- (* c a) (* y i)))
90.0ms	(* x (- (* y z) (* t a)))

simplify145.0ms

Algorithm

egg-herbie

Counts

403 → 403

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	1053	6116
1	3257	4387
2	5001	4081

prune711.0ms

Filtered

403 candidates to 101 candidates (25.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	399	4	403
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	403	18	421

Merged error: 4.0b

Counts

421 → 18

localize30.0ms

Local error

Found 4 expressions with local error:

4.8b	(* b (fma (* c 1) z (- (* i t))))
7.9b	(cbrt (- (* y z) (* t a)))
7.9b	(cbrt (- (* y z) (* t a)))
7.9b	(cbrt (- (* y z) (* t a)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
33×	`cbrt-prod` `*-un-lft-identity`
15×	`associate-l`
13×	`unswap-sqr`
12×	`distribute-lft-out--` `difference-of-squares`
9×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `associate-r` `flip--`
2×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

4.0ms	(* b (fma (* c 1) z (- (* i t))))
14.0ms	(cbrt (- (* y z) (* t a)))
22.0ms	(cbrt (- (* y z) (* t a)))
14.0ms	(cbrt (- (* y z) (* t a)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* b (fma (* c 1) z (- (* i t))))
142.0ms	(cbrt (- (* y z) (* t a)))
153.0ms	(cbrt (- (* y z) (* t a)))
143.0ms	(cbrt (- (* y z) (* t a)))

simplify108.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	321	859
1	966	805
2	3219	783
3	5002	765

prune472.0ms

Filtered

103 candidates to 80 candidates (77.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	103	18	121

Merged error: 4.0b

Counts

121 → 18

regimes6.1s

Accuracy

-6% (8.3b remaining)

Error of 12.8b against oracle of 4.5b and baseline of 12.3b

bsearch242.0ms

Steps

Iters	Range		Point
8	-8.795068997917619e-296	-1.0979383505437052e-299	-7.680446822110556e-296
10	-3.2574874288383606e-225	-2.8457850991393653e-236	-1.3862453169432524e-235

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	81
1	87	81
2	87	81

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s

19417×

body

valid