Details

sample93.0ms

Algorithm

intervals

Results

47.0ms

644×

body

valid

simplify84.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune15.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 13.0b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* y z) (* t a))
3.6b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
4.9b	(* b (- (* c z) (* t i)))
7.4b	(* x (- (* y z) (* t a)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l` `add-log-exp`
5×	`sub-neg` `prod-diff`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log` `fma-udef`

Counts

4 → 82

Calls

4 calls:

4.0ms	(- (* y z) (* t a))
1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
6.0ms	(* b (- (* c z) (* t i)))
6.0ms	(* x (- (* y z) (* t a)))

series760.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* y z) (* t a))
586.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
66.0ms	(* b (- (* c z) (* t i)))
66.0ms	(* x (- (* y z) (* t a)))

simplify46.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	376	645
1	1500	568
2	5001	568

prune394.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	80	14	94
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	81	15	96

Merged error: 4.3b

Counts

96 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* y z) (* t a))
3.8b	(* j (- (* c a) (* y i)))
4.9b	(* b (- (* c z) (* t i)))
7.4b	(* x (- (* y z) (* t a)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l`
7×	`sub-neg` `prod-diff`
6×	`associate-*r/` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log`

Counts

4 → 100

Calls

4 calls:

4.0ms	(- (* y z) (* t a))
6.0ms	(* j (- (* c a) (* y i)))
6.0ms	(* b (- (* c z) (* t i)))
6.0ms	(* x (- (* y z) (* t a)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* y z) (* t a))
66.0ms	(* j (- (* c a) (* y i)))
66.0ms	(* b (- (* c z) (* t i)))
65.0ms	(* x (- (* y z) (* t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	476	643
1	1969	572
2	5001	572

prune498.0ms

Filtered

112 candidates to 79 candidates (70.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	109	18	127

Merged error: 4.0b

Counts

127 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

3.8b	(* j (- (* c a) (* y i)))
4.9b	(* b (- (* c z) (* t i)))
7.4b	(* x (- (* y z) (* t a)))
50.9b	(fma (- i) y (* i y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l`
6×	`sub-neg` `associate-*r/` `prod-diff`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 94

Calls

4 calls:

6.0ms	(* j (- (* c a) (* y i)))
6.0ms	(* b (- (* c z) (* t i)))
6.0ms	(* x (- (* y z) (* t a)))
1.0ms	(fma (- i) y (* i y))

series222.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* j (- (* c a) (* y i)))
66.0ms	(* b (- (* c z) (* t i)))
66.0ms	(* x (- (* y z) (* t a)))
25.0ms	(fma (- i) y (* i y))

simplify51.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	456	602
1	1902	532
2	5002	532

prune440.0ms

Filtered

106 candidates to 74 candidates (69.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	16	17
Picked	1	0	1
Done	0	0	0
Total	107	17	124

Merged error: 4.0b

Counts

124 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (cbrt b) (- (* c z) (* t i)))
3.5b	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
3.6b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
7.4b	(* x (- (* y z) (* t a)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
18×	`distribute-rgt-in` `distribute-lft-in`
15×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
10×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sub-neg` `associate-*r/` `prod-diff`
7×	`associate-r`
4×	`cbrt-prod` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 108

Calls

4 calls:

7.0ms	(* (cbrt b) (- (* c z) (* t i)))
12.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
1.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
6.0ms	(* x (- (* y z) (* t a)))

series1.2s

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (cbrt b) (- (* c z) (* t i)))
99.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))
817.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* t i))))))
66.0ms	(* x (- (* y z) (* t a)))

simplify78.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	563	1204
1	2492	956
2	5001	877

prune390.0ms

Filtered

120 candidates to 80 candidates (66.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	120	17	137

Merged error: 3.9b

Counts

137 → 17

regimes836.0ms

Accuracy

-2.4% (8.0b remaining)

Error of 12.3b against oracle of 4.3b and baseline of 12.1b

bsearch165.0ms

Steps

Iters	Range		Point
6	2.624618586072339e-241	1.76781680232472e-240	4.6110464469355526e-241
9	-6.0558494946520626e-148	-3.1700500742314277e-153	-6.672488131467256e-152

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	29
1	76	29
2	84	29
3	84	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

18904×

body

valid