Details

sample93.0ms

Algorithm

intervals

Results

54.0ms

682×

body

valid

simplify86.0ms

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: 13.5b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* y z) (* t a))
4.3b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
5.3b	(* b (- (* c z) (* t i)))
7.0b	(* 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)))

series708.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* y z) (* t a))
538.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
66.0ms	(* b (- (* c z) (* t i)))
64.0ms	(* x (- (* y z) (* t a)))

simplify73.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (17.0ms)

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

prune412.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	13	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 5.7b

Counts

95 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

4.3b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (- (* c z) (* t i))) (* b (fma (- i) t (* i t))))))
5.3b	(* b (- (* c z) (* t i)))
7.0b	(* x (- (* y z) (* t a)))
49.5b	(fma (- i) t (* i 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×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `prod-diff` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

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

series3.6s

Counts

4 → 12

Calls

4 calls:

3.4s	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (+ (* b (- (* c z) (* t i))) (* b (fma (- i) t (* i t))))))
70.0ms	(* b (- (* c z) (* t i)))
71.0ms	(* x (- (* y z) (* t a)))
26.0ms	(fma (- i) t (* i t))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	363	664
1	1472	577
2	5001	577

prune408.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	89	12	101

Merged error: 5.7b

Counts

101 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

6.9b	(cbrt (- (* c z) (* t i)))
6.9b	(cbrt (- (* c z) (* t i)))
6.9b	(cbrt (- (* c z) (* t i)))
7.0b	(* x (- (* y z) (* t a)))

rewrite18.0ms

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:

3.0ms	(cbrt (- (* c z) (* t i)))
3.0ms	(cbrt (- (* c z) (* t i)))
3.0ms	(cbrt (- (* c z) (* t i)))
6.0ms	(* x (- (* y z) (* t a)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (- (* c z) (* t i)))
115.0ms	(cbrt (- (* c z) (* t i)))
115.0ms	(cbrt (- (* c z) (* t i)))
68.0ms	(* x (- (* y z) (* t a)))

simplify106.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (33.0ms)

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

prune444.0ms

Filtered

85 candidates to 74 candidates (87.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 5.7b

Counts

97 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

5.3b	(* b (- (* c z) (* t i)))
8.3b	(cbrt (- (* y z) (* t a)))
8.3b	(cbrt (- (* y z) (* t a)))
8.3b	(cbrt (- (* y z) (* t a)))

rewrite18.0ms

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:

6.0ms	(* b (- (* c z) (* t i)))
3.0ms	(cbrt (- (* y z) (* t a)))
3.0ms	(cbrt (- (* y z) (* t a)))
3.0ms	(cbrt (- (* y z) (* t a)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* b (- (* c z) (* t i)))
112.0ms	(cbrt (- (* y z) (* t a)))
113.0ms	(cbrt (- (* y z) (* t a)))
115.0ms	(cbrt (- (* y z) (* t a)))

simplify102.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	335	646
1	1158	598
2	4180	580
3	5001	580

prune521.0ms

Filtered

85 candidates to 71 candidates (83.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	83	14	97

Merged error: 5.7b

Counts

97 → 14

regimes774.0ms

Accuracy

2.9% (7.2b remaining)

Error of 12.8b against oracle of 5.5b and baseline of 13.0b

bsearch193.0ms

Steps

Iters	Range		Point
7	3.510338304119835e-162	2.5956730567631496e-160	3.971405507871879e-161
8	-4.455368298511299e-208	-1.7010959355894162e-211	-8.249689110649005e-210

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	56
1	62	56
2	73	56
3	73	56

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.5s

19075×

body

valid