Details

sample81.0ms

Algorithm

intervals

Results

45.0ms

574×

body

valid

simplify110.0ms

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

prune15.0ms

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: 13.0b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* y z) (* t a))
4.1b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
5.1b	(* b (- (* c z) (* t i)))
6.6b	(* x (- (* y z) (* t a)))

rewrite20.0ms

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)))
7.0ms	(* x (- (* y z) (* t a)))

series840.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* y z) (* t a))
633.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
79.0ms	(* b (- (* c z) (* t i)))
78.0ms	(* x (- (* y z) (* t a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (15.0ms)

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

prune480.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	78	16	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	16	95

Merged error: 5.6b

Counts

95 → 16

localize27.0ms

Local error

Found 4 expressions with local error:

4.1b	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
5.1b	(* b (- (* c z) (* t i)))
6.6b	(* x (fma y z (- (* a t))))
48.9b	(fma (- a) t (* a t))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

1.0ms	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
7.0ms	(* b (- (* c z) (* t i)))
4.0ms	(* x (fma y z (- (* a t))))
1.0ms	(fma (- a) t (* a t))

series4.0s

Counts

4 → 12

Calls

4 calls:

3.8s	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
74.0ms	(* b (- (* c z) (* t i)))
82.0ms	(* x (fma y z (- (* a t))))
34.0ms	(fma (- a) t (* a t))

simplify55.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	310	624
1	1230	538
2	5001	538

prune435.0ms

Filtered

82 candidates to 58 candidates (70.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	83	15	98

Merged error: 5.6b

Counts

98 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

6.6b	(* x (- (* y z) (* t a)))
7.2b	(cbrt (- (* c z) (* t i)))
7.2b	(cbrt (- (* c z) (* t i)))
7.2b	(cbrt (- (* c z) (* t i)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

7.0ms	(* x (- (* y z) (* t a)))
4.0ms	(cbrt (- (* c z) (* t i)))
4.0ms	(cbrt (- (* c z) (* t i)))
4.0ms	(cbrt (- (* c z) (* t i)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* x (- (* y z) (* t a)))
136.0ms	(cbrt (- (* c z) (* t i)))
136.0ms	(cbrt (- (* c z) (* t i)))
144.0ms	(cbrt (- (* c z) (* t i)))

simplify121.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	340	646
1	1165	598
2	4148	580
3	5001	580

prune539.0ms

Filtered

85 candidates to 74 candidates (87.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	85	15	100

Merged error: 5.6b

Counts

100 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

5.1b	(* b (- (* c z) (* t i)))
6.6b	(* x (- (* y z) (* t a)))
6.6b	(* x (- (* y z) (* t a)))
6.6b	(* x (- (* y z) (* t a)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

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

series280.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* b (- (* c z) (* t i)))
66.0ms	(* x (- (* y z) (* t a)))
71.0ms	(* x (- (* y z) (* t a)))
72.0ms	(* x (- (* y z) (* t a)))

simplify47.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	306	736
1	1264	652
2	5002	652

prune507.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	124	15	139

Merged error: 5.6b

Counts

139 → 15

regimes790.0ms

Accuracy

-4.4% (7.5b remaining)

Error of 12.6b against oracle of 5.1b and baseline of 12.3b

bsearch187.0ms

Steps

Iters	Range		Point
8	-2.893485506202003e-290	-6.670336256007826e-293	-2.0021764565690793e-290
7	-1.237110658175894e-259	-3.528016645140009e-261	-3.569033422717177e-261

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	57
1	59	57

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.7s

19043×

body

valid