Details

sample74.0ms

Algorithm

intervals

Results

38.0ms

629×

body

valid

simplify89.0ms

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

prune14.0ms

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: 13.4b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* y z) (* t a))
3.7b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
5.6b	(* b (- (* c z) (* i a)))
7.2b	(* x (- (* y z) (* t a)))

rewrite19.0ms

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)))

series805.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* y z) (* t a))
610.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
71.0ms	(* b (- (* c z) (* i a)))
72.0ms	(* 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

prune545.0ms

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: 4.5b

Counts

95 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

5.6b	(* b (- (* c z) (* i a)))
8.4b	(cbrt (- (* y z) (* t a)))
8.4b	(cbrt (- (* y z) (* t a)))
8.4b	(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) (* i a)))
3.0ms	(cbrt (- (* y z) (* t a)))
3.0ms	(cbrt (- (* y z) (* t a)))
3.0ms	(cbrt (- (* y z) (* t a)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* b (- (* c z) (* i a)))
125.0ms	(cbrt (- (* y z) (* t a)))
121.0ms	(cbrt (- (* y z) (* t a)))
119.0ms	(cbrt (- (* y z) (* t a)))

simplify109.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	336	646
1	1159	598
2	4181	580
3	5001	580

prune422.0ms

Filtered

85 candidates to 71 candidates (83.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	85	13	98

Merged error: 4.5b

Counts

98 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (cbrt b) (- (* c z) (* i a)))
3.3b	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
3.7b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))))
7.2b	(* x (- (* y z) (* t a)))

rewrite30.0ms

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)))
13.0ms	(* (* (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)))

series1.2s

Counts

4 → 12

Calls

4 calls:

281.0ms	(* (cbrt b) (- (* c z) (* i a)))
112.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
725.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))))
70.0ms	(* x (- (* y z) (* t a)))

simplify80.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (68.0ms)

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

prune458.0ms

Filtered

120 candidates to 79 candidates (65.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	121	12	133

Merged error: 4.5b

Counts

133 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

3.7b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* z (* b c)) (- (* a (* i b))))))
3.7b	(* a (* i b))
5.1b	(* z (* b c))
7.2b	(* x (- (* y z) (* t a)))

rewrite20.0ms

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:

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

series727.0ms

Counts

4 → 12

Calls

4 calls:

586.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (+ (* z (* b c)) (- (* a (* i b))))))
30.0ms	(* a (* i b))
30.0ms	(* z (* b c))
81.0ms	(* x (- (* y z) (* t a)))

simplify47.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (10.0ms)

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

prune326.0ms

Filtered

90 candidates to 61 candidates (67.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	89	13	102

Merged error: 4.3b

Counts

102 → 13

regimes750.0ms

Accuracy

-0.9% (7.4b remaining)

Error of 12.6b against oracle of 5.2b and baseline of 12.5b

bsearch246.0ms

Steps

Iters	Range		Point
8	5.547902844096734e+142	6.559931041703192e+145	3.241757727781201e+143
11	-6.6613309156198935e+81	-2.7763509787006124e+53	-6.573971523973346e+81

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	31
1	54	31

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.2s

18700×

body

valid