Details

sample50.0ms

Algorithm

intervals

Results

23.0ms

487×

body

valid

simplify128.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	33	9
1	87	9
2	260	8
3	872	8
4	2436	8
5	4957	8
6	5001	8

prune16.0ms

Filtered

1 candidates to 1 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: 1.8b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (* (- (fma c b a)) (* c i)))
0.0b	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i))))
0.0b	(fma x y (* z t))
5.5b	(* (- (fma c b a)) (* c i))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

59×	`associate-r`
41×	`add-sqr-sqrt`
29×	`associate-l`
18×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
14×	`unswap-sqr`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`distribute-lft-neg-out` `neg-mul-1` `fma-udef`
1×	`distribute-rgt-neg-out`

Counts

4 → 116

Calls

4 calls:

19.0ms	(* 2.0 (* (- (fma c b a)) (* c i)))
1.0ms	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i))))
1.0ms	(fma x y (* z t))
11.0ms	(* (- (fma c b a)) (* c i))

series930.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* 2.0 (* (- (fma c b a)) (* c i)))
742.0ms	(fma 2.0 (fma x y (* z t)) (* 2.0 (* (- (fma c b a)) (* c i))))
41.0ms	(fma x y (* z t))
67.0ms	(* (- (fma c b a)) (* c i))

simplify90.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	449	786
1	2369	697
2	5003	695

prune369.0ms

Filtered

128 candidates to 96 candidates (25.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 1.7b

Counts

130 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma t z (* x y))
0.0b	(* 2.0 (* (- (fma c b a)) (* c i)))
0.0b	(fma 2.0 (fma t z (* x y)) (* 2.0 (* (- (fma c b a)) (* c i))))
5.5b	(* (- (fma c b a)) (* c i))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

59×	`associate-r`
41×	`add-sqr-sqrt`
29×	`associate-l`
18×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
14×	`unswap-sqr`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`distribute-lft-neg-out` `neg-mul-1` `fma-udef`
1×	`distribute-rgt-neg-out`

Counts

4 → 116

Calls

4 calls:

1.0ms	(fma t z (* x y))
21.0ms	(* 2.0 (* (- (fma c b a)) (* c i)))
1.0ms	(fma 2.0 (fma t z (* x y)) (* 2.0 (* (- (fma c b a)) (* c i))))
12.0ms	(* (- (fma c b a)) (* c i))

series941.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma t z (* x y))
80.0ms	(* 2.0 (* (- (fma c b a)) (* c i)))
745.0ms	(fma 2.0 (fma t z (* x y)) (* 2.0 (* (- (fma c b a)) (* c i))))
70.0ms	(* (- (fma c b a)) (* c i))

simplify96.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	447	786
1	2367	697
2	5001	695

prune375.0ms

Filtered

128 candidates to 94 candidates (26.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	128	8	136

Merged error: 1.7b

Counts

136 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
0.6b	(cbrt i)
2.2b	(* (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))) (cbrt i))
3.9b	(* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

326×	`add-sqr-sqrt`
229×	`associate-r`
206×	`unswap-sqr`
129×	`associate-l`
95×	`cbrt-prod`
81×	`add-cbrt-cube`
75×	`cbrt-unprod`
39×	`add-cube-cbrt` `*-un-lft-identity`
33×	`pow1` `add-exp-log`
26×	`swap-sqr`
21×	`pow-prod-down` `prod-exp`
15×	`*-commutative`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-out`
2×	`neg-mul-1` `pow1/3`
1×	`distribute-rgt-neg-out`

Counts

4 → 268

Calls

4 calls:

1.0ms	(cbrt i)
1.0ms	(cbrt i)
70.0ms	(* (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))) (cbrt i))
32.0ms	(* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))

series739.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt i)
187.0ms	(cbrt i)
113.0ms	(* (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))) (cbrt i))
240.0ms	(* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))

simplify70.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1099	3018
1	5001	2567

prune1.0s

Filtered

280 candidates to 212 candidates (24.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	277	3	280
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	280	8	288

Merged error: 0.3b

Counts

288 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))
10.8b	(cbrt (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))))
10.8b	(cbrt (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))))
10.8b	(cbrt (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

515×	`associate-r`
456×	`add-sqr-sqrt`
394×	`cbrt-prod`
262×	`unswap-sqr`
85×	`associate-l`
69×	`add-cube-cbrt` `*-un-lft-identity`
46×	`swap-sqr`
26×	`*-commutative`
21×	`add-cbrt-cube`
15×	`cbrt-unprod`
13×	`pow1` `add-exp-log`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
6×	`pow-prod-down` `prod-exp`
4×	`expm1-log1p-u` `neg-mul-1` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`distribute-lft-neg-out`

Counts

4 → 381

Calls

4 calls:

37.0ms	(* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))
50.0ms	(cbrt (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))))
54.0ms	(cbrt (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))))
53.0ms	(cbrt (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))))

series1.8s

Counts

4 → 12

Calls

4 calls:

232.0ms	(* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))
498.0ms	(cbrt (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))))
504.0ms	(cbrt (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))))
516.0ms	(cbrt (* 2.0 (* (- (fma c b a)) (* c (* (cbrt i) (cbrt i))))))

simplify208.0ms

Algorithm

egg-herbie

Counts

393 → 393

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1003	5542
1	4636	5398
2	5001	5398

prune1.7s

Filtered

393 candidates to 271 candidates (31.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	392	1	393
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	393	8	401

Merged error: 0.3b

Counts

401 → 8

regimes504.0ms

Accuracy

-51.7% (3.6b remaining)

Error of 3.8b against oracle of 0.2b and baseline of 2.6b

bsearch193.0ms

Steps

Iters	Range		Point
10	7.183657241293898e+123	8.677036478863934e+134	8.546306878700463e+134
8	1.7605528476317036e-100	6.936984512694408e-96	2.4693420887247912e-98

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	31
1	83	31
2	103	31
3	108	31
4	108	31

end0.0ms

sample1.4s

Algorithm

intervals

Results

751.0ms

15077×

body

valid