Details

sample93.0ms

Algorithm

intervals

Results

50.0ms

581×

body

valid

simplify87.0ms

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

prune12.0ms

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: 12.4b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* y z) (* t a))
4.5b	(* x (- (* y z) (* t a)))
4.8b	(* b (- (* c z) (* i a)))
5.1b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i 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))
6.0ms	(* x (- (* y z) (* t a)))
6.0ms	(* b (- (* c z) (* i a)))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

series714.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* y z) (* t a))
68.0ms	(* x (- (* y z) (* t a)))
68.0ms	(* b (- (* c z) (* i a)))
542.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	373	645
1	1485	568
2	5001	568

prune434.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	78	16	94
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	79	17	96

Merged error: 4.7b

Counts

96 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* c t) (* i y))
4.5b	(* x (fma y z (- (* t a))))
4.8b	(* b (- (* c z) (* i a)))
5.1b	(fma (- (* c t) (* i y)) j (- (* x (fma y z (- (* t a)))) (* b (- (* c z) (* i a)))))

rewrite16.0ms

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` `add-log-exp`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u`
3×	`sub-neg` `prod-diff` `fma-udef`
2×	`flip3--` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log`

Counts

4 → 76

Calls

4 calls:

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

series771.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* c t) (* i y))
69.0ms	(* x (fma y z (- (* t a))))
74.0ms	(* b (- (* c z) (* i a)))
585.0ms	(fma (- (* c t) (* i y)) j (- (* x (fma y z (- (* t a)))) (* b (- (* c z) (* i a)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	374	606
1	1439	529
2	5002	529

prune363.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	88	17	105

Merged error: 3.7b

Counts

105 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* y z) (* t a))
4.5b	(* x (- (* y z) (* t a)))
4.8b	(* b (- (* c z) (* i a)))
6.2b	(* j (- (* c t) (* i y)))

rewrite28.0ms

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:

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

series247.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* y z) (* t a))
73.0ms	(* x (- (* y z) (* t a)))
70.0ms	(* b (- (* c z) (* i a)))
66.0ms	(* j (- (* c t) (* i y)))

simplify64.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	478	643
1	1976	572
2	5001	572

prune455.0ms

Filtered

112 candidates to 82 candidates (73.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	112	17	129

Merged error: 3.7b

Counts

129 → 17

localize29.0ms

Local error

Found 4 expressions with local error:

4.5b	(* x (- (* y z) (* t a)))
4.8b	(* b (- (* c z) (* i a)))
6.2b	(* j (fma c t (- (* y i))))
49.2b	(fma (- y) i (* y i))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

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

series235.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* x (- (* y z) (* t a)))
68.0ms	(* b (- (* c z) (* i a)))
68.0ms	(* j (fma c t (- (* y i))))
29.0ms	(fma (- y) i (* y i))

simplify51.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	411	562
1	1680	493
2	5002	493

prune390.0ms

Filtered

100 candidates to 71 candidates (71.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	101	16	117

Merged error: 3.7b

Counts

117 → 16

regimes861.0ms

Accuracy

1.6% (7.6b remaining)

Error of 12.0b against oracle of 4.4b and baseline of 12.1b

bsearch163.0ms

Steps

Iters	Range		Point
8	2.8059840969933902e-217	1.1999274532176383e-214	7.99154773277492e-217
5	-4.745853485790696e-139	-1.6786546600989055e-139	-1.714942722626056e-139

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	34
1	58	34
2	58	34

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

19134×

body

valid