Details

sample31.0ms

Algorithm

intervals

Results

15.0ms

270×

body

valid

simplify143.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	43	8
2	75	8
3	120	8
4	156	8
5	189	8
6	265	8
7	451	8
8	1023	8
9	3632	8
10	5001	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 26.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.0b	(* z (- t a))
1.3b	(+ (* x y) (* z (- t a)))
25.8b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
54×	`prod-diff`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
44×	`associate-+r+`
33×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `sub-neg`
5×	`associate-r`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`+-commutative` `associate-*r/` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 153

Calls

4 calls:

6.0ms	(+ y (* z (- b y)))
8.0ms	(* z (- t a))
7.0ms	(+ (* x y) (* z (- t a)))
9.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ y (* z (- b y)))
44.0ms	(* z (- t a))
46.0ms	(+ (* x y) (* z (- t a)))
374.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify88.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	608	1288
1	2360	956
2	5001	942

prune522.0ms

Filtered

165 candidates to 109 candidates (66.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	154	11	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	11	166

Merged error: 26.0b

Counts

166 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
0.3b	(fma x y (* z (- t a)))
25.9b	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
72×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
68×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`div-exp`
7×	`pow1`
6×	`div-inv` `associate-/l*`
5×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`sub-neg` `rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num`
1×	`flip3--` `pow-flip` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 163

Calls

4 calls:

8.0ms	(* z (- t a))
6.0ms	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
1.0ms	(fma x y (* z (- t a)))
4.0ms	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

series1.5s

Counts

4 → 12

Calls

4 calls:

45.0ms	(* z (- t a))
1.3s	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
51.0ms	(fma x y (* z (- t a)))
173.0ms	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

simplify74.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	520	1776
1	2146	1503
2	5001	1426

prune425.0ms

Filtered

175 candidates to 96 candidates (54.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	175	11	186

Merged error: 13.3b

Counts

186 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ 1 (/ (fma x y (* z (- t a))) (fma (- b y) z y))))
0.2b	(/ 1 (/ (fma x y (* z (- t a))) (fma (- b y) z y)))
0.3b	(fma x y (* z (- t a)))
25.8b	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
60×	`add-exp-log` `associate-/r*`
43×	`div-exp`
23×	`div-inv`
20×	`add-cbrt-cube`
15×	`rec-exp` `1-exp`
10×	`cbrt-undiv`
9×	`associate-/l*`
7×	`pow1`
6×	`associate-/r/`
5×	`pow-flip`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `inv-pow`
1×	`fma-udef` `remove-double-div`

Counts

4 → 338

Calls

4 calls:

13.0ms	(/ 1 (/ 1 (/ (fma x y (* z (- t a))) (fma (- b y) z y))))
6.0ms	(/ 1 (/ (fma x y (* z (- t a))) (fma (- b y) z y)))
1.0ms	(fma x y (* z (- t a)))
3.0ms	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

series1.2s

Counts

4 → 12

Calls

4 calls:

617.0ms	(/ 1 (/ 1 (/ (fma x y (* z (- t a))) (fma (- b y) z y))))
164.0ms	(/ 1 (/ (fma x y (* z (- t a))) (fma (- b y) z y)))
60.0ms	(fma x y (* z (- t a)))
368.0ms	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

simplify91.0ms

Algorithm

egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	966	4941
1	5001	4158

prune767.0ms

Filtered

350 candidates to 177 candidates (50.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	349	1	350
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	350	11	361

Merged error: 13.3b

Counts

361 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- b y) z y)
0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
25.8b	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

1.0ms	(fma (- b y) z y)
7.0ms	(* z (- t a))
1.0ms	(fma x y (* z (- t a)))
3.0ms	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

series494.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(fma (- b y) z y)
38.0ms	(* z (- t a))
59.0ms	(fma x y (* z (- t a)))
366.0ms	(/ (fma x y (* z (- t a))) (fma (- b y) z y))

simplify58.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	307	774
1	1107	590
2	5001	584

prune234.0ms

Filtered

107 candidates to 64 candidates (59.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	107	11	118

Merged error: 13.3b

Counts

118 → 11

regimes456.0ms

Accuracy

27.4% (9.1b remaining)

Error of 20.0b against oracle of 10.9b and baseline of 23.4b

bsearch134.0ms

Steps

Iters	Range		Point
9	56430094903984.445	8.948503618249613e+21	8.82264572808663e+21
11	-6.636271424916035e+171	-4.91450804605582e+144	-1.8042740951690393e+145

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	25	9

end0.0ms

sample696.0ms

Algorithm

intervals

Results

374.0ms

8440×

body

valid