Details

sample73.0ms

Algorithm

intervals

Results

39.0ms

588×

body

valid

simplify123.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

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: 13.9b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
3.9b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
5.8b	(* b (- (* c z) (* i a)))
6.8b	(* x (- (* y z) (* t a)))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

1705×	`add-sqr-sqrt`
1552×	`prod-diff`
1059×	`*-un-lft-identity`
1049×	`associate-r`
881×	`associate-l`
707×	`add-cube-cbrt`
584×	`distribute-rgt-in` `distribute-lft-in`
411×	`unswap-sqr`
292×	`associate--l+` `associate--r+`
235×	`*-commutative`
176×	`distribute-lft-out--` `difference-of-squares`
20×	`fma-neg`
12×	`associate-*r/`
9×	`sub-neg`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`flip3--` `flip--`
6×	`add-log-exp`
4×	`expm1-log1p-u` `frac-sub` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`diff-log` `fma-udef`

Counts

4 → 1684

Calls

4 calls:

118.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
27.0ms	(* b (- (* c z) (* i a)))
31.0ms	(* x (- (* y z) (* t a)))

series944.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
581.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
67.0ms	(* b (- (* c z) (* i a)))
77.0ms	(* x (- (* y z) (* t a)))

simplify407.0ms

Algorithm

egg-herbie

Counts

1696 → 1696

Iterations

Useful iterations: 1 (79.0ms)

Iter	Nodes	Cost
0	3583	34141
1	5001	29306

prune3.9s

Filtered

1696 candidates to 672 candidates (39.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	1682	14	1696
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1683	14	1697

Merged error: 5.7b

Counts

1697 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

3.9b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (- (* z (* b c)) (* a (* i b)))))
4.5b	(* a (* i b))
5.9b	(* z (* b c))
6.8b	(* x (- (* y z) (* t a)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

288×	`prod-diff`
282×	`add-sqr-sqrt`
185×	`associate-r`
166×	`*-un-lft-identity`
163×	`associate-l`
158×	`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`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `flip--` `fma-udef`

Counts

4 → 398

Calls

4 calls:

1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (- (* z (* b c)) (* a (* i b)))))
8.0ms	(* a (* i b))
8.0ms	(* z (* b c))
30.0ms	(* x (- (* y z) (* t a)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

565.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (- (* z (* b c)) (* a (* i b)))))
26.0ms	(* a (* i b))
28.0ms	(* z (* b c))
74.0ms	(* x (- (* y z) (* t a)))

simplify178.0ms

Algorithm

egg-herbie

Counts

410 → 410

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1150	5868
1	4312	4107
2	5001	4107

prune489.0ms

Filtered

410 candidates to 105 candidates (25.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	403	7	410
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	412	12	424

Merged error: 5.7b

Counts

424 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

3.9b	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (- (* z (* b c)) (* a (* i b)))))
4.5b	(* a (* i b))
4.9b	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
5.9b	(* z (* b c))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

627×	`add-sqr-sqrt`
584×	`distribute-rgt-in` `distribute-lft-in`
576×	`prod-diff`
359×	`associate-r`
343×	`associate-l`
321×	`*-un-lft-identity`
313×	`add-cube-cbrt`
171×	`unswap-sqr`
106×	`*-commutative`
49×	`add-cbrt-cube`
47×	`cbrt-prod`
43×	`cbrt-unprod`
26×	`pow1` `add-exp-log`
14×	`pow-prod-down` `prod-exp`
12×	`swap-sqr`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
1×	`flip3--` `flip--` `fma-udef`

Counts

4 → 773

Calls

4 calls:

1.0ms	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (- (* z (* b c)) (* a (* i b)))))
8.0ms	(* a (* i b))
65.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
8.0ms	(* z (* b c))

series841.0ms

Counts

4 → 12

Calls

4 calls:

680.0ms	(fma (- (* c t) (* i y)) j (- (* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a)))) (- (* z (* b c)) (* a (* i b)))))
26.0ms	(* a (* i b))
109.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (- (* y z) (* t a))))
26.0ms	(* z (* b c))

simplify258.0ms

Algorithm

egg-herbie

Counts

785 → 785

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	3950	18436
1	5003	16137

prune992.0ms

Filtered

785 candidates to 174 candidates (22.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	783	2	785
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	783	14	797

Merged error: 5.7b

Counts

797 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

5.9b	(* z (* b c))
8.6b	(cbrt (- (* y z) (* t a)))
8.6b	(cbrt (- (* y z) (* t a)))
8.6b	(cbrt (- (* y z) (* t a)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`cbrt-prod`
18×	`associate-l`
16×	`unswap-sqr`
15×	`associate-r`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`add-cube-cbrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`cbrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`*-commutative`

Counts

4 → 102

Calls

4 calls:

8.0ms	(* z (* b c))
13.0ms	(cbrt (- (* y z) (* t a)))
13.0ms	(cbrt (- (* y z) (* t a)))
13.0ms	(cbrt (- (* y z) (* t a)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* z (* b c))
121.0ms	(cbrt (- (* y z) (* t a)))
121.0ms	(cbrt (- (* y z) (* t a)))
127.0ms	(cbrt (- (* y z) (* t a)))

simplify144.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 3 (132.0ms)

Iter	Nodes	Cost
0	358	812
1	1280	770
2	4231	752
3	5001	749

prune698.0ms

Filtered

114 candidates to 87 candidates (76.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	113	15	128

Merged error: 5.7b

Counts

128 → 15

regimes933.0ms

Accuracy

19.2% (6.6b remaining)

Error of 11.5b against oracle of 4.9b and baseline of 13.0b

bsearch167.0ms

Steps

Iters	Range		Point
7	5.112354082747014e-82	8.023798505972276e-80	1.459038361406735e-81
7	-1.3914269606383e-57	-1.2601024812054653e-59	-1.188456493586694e-58

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	25
1	51	25

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s

19492×

body

valid