Details

sample85.0ms

Algorithm

intervals

Results

50.0ms

586×

body

valid

simplify88.0ms

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

prune11.0ms

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: 13.2b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* y z) (* t a))
4.8b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
5.0b	(* b (- (* c z) (* i a)))
6.8b	(* 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 t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
6.0ms	(* b (- (* c z) (* i a)))
6.0ms	(* x (- (* y z) (* t a)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* y z) (* t a))
559.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
62.0ms	(* b (- (* c z) (* i a)))
67.0ms	(* x (- (* y z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

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

prune411.0ms

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: 4.8b

Counts

95 → 16

localize26.0ms

Local error

Found 4 expressions with local error:

4.8b	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
5.0b	(* b (- (* c z) (* i a)))
6.8b	(* x (fma y z (- (* a t))))
49.7b	(fma (- a) t (* a t))

rewrite12.0ms

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

series3.5s

Counts

4 → 12

Calls

4 calls:

3.3s	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
65.0ms	(* b (- (* c z) (* i a)))
65.0ms	(* x (fma y z (- (* a t))))
29.0ms	(fma (- a) t (* a t))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	315	624
1	1247	538
2	5002	538

prune392.0ms

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: 4.8b

Counts

98 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (cbrt b) (- (* c z) (* i a)))
3.1b	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
4.8b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))))
6.8b	(* x (- (* y z) (* t a)))

rewrite29.0ms

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

series1.1s

Counts

4 → 12

Calls

4 calls:

262.0ms	(* (cbrt b) (- (* c z) (* i a)))
97.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
662.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))))
68.0ms	(* x (- (* y z) (* t a)))

simplify78.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	559	1204
1	2479	956
2	5003	877

prune662.0ms

Filtered

120 candidates to 80 candidates (66.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	120	15	135

Merged error: 4.7b

Counts

135 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

4.3b	(* z (* b c))
4.6b	(* a (* i b))
4.8b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* z (* b c)) (- (* a (* i b))))))
6.8b	(* x (- (* y z) (* t a)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

5.0ms	(* z (* b c))
5.0ms	(* a (* i b))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* z (* b c)) (- (* a (* i b))))))
6.0ms	(* x (- (* y z) (* t a)))

series650.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* z (* b c))
30.0ms	(* a (* i b))
533.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* z (* b c)) (- (* a (* i b))))))
62.0ms	(* x (- (* y z) (* t a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	374	544
1	1413	461
2	5002	461

prune284.0ms

Filtered

90 candidates to 61 candidates (67.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	90	15	105

Merged error: 4.7b

Counts

105 → 15

regimes790.0ms

Accuracy

1.8% (7.4b remaining)

Error of 12.6b against oracle of 5.3b and baseline of 12.7b

bsearch206.0ms

Steps

Iters	Range		Point
6	1.5606685024061335e+129	1.079971610501906e+130	1.0677468285707515e+130
9	-2.2814576340551837e+103	-1.6263070950360542e+97	-2.1032420279727952e+103

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	22
1	64	22
2	64	22

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s

18824×

body

valid