Details

analyze743.0ms (6.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.9s (16.5%)

Results

1.3s	7128×	body	128	valid
189.0ms	439×	body	512	valid
180.0ms	335×	body	1024	valid
86.0ms	293×	body	256	valid
46.0ms	61×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify185.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

6.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	7.7b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	14.5b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	2.3b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series97.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

67.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
30.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

10.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

simplify238.0ms (2%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
644×	`fma-neg_binary64`
523×	`cancel-sign-sub-inv_binary64`
397×	`sub-neg_binary64`
195×	`div-sub_binary64`

Counts

160 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4255
1	740	4157
2	2480	3550
3	4430	3531
4	5167	3531

prune232.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	131	8	139

Error

0.0b

Counts

139 → 8

Alt Table

Status	Error	Program
	7.8b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t)))) (+.f64 x y))
	14.5b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
	31.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.9b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	35.7b	(-.f64 (+.f64 y (+.f64 x (.f64 (/.f64 y a) (+.f64 t (/.f64 (.f64 t t) a))))) (+.f64 (/.f64 (.f64 y z) a) (.f64 (/.f64 z a) (.f64 (/.f64 y a) (+.f64 t (/.f64 (.f64 t t) a))))))
	23.9b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
▶	7.7b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	32.2b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 3720 to 1266 computations (66% saved)

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 t z))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
✓	2.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))

series136.0ms (1.2%)

Counts

3 → 132

Calls

3 calls:

66.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
36.0ms	(/.f64 (-.f64 a t) (-.f64 t z))
33.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))

rewrite84.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

22.0ms	(/.f64 (-.f64 a t) (-.f64 t z))
19.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z)))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))

simplify352.0ms (3%)

Algorithm

1×	egg-herbie

Rules

672×	`cancel-sign-sub-inv_binary64`
565×	`sub-neg_binary64`
292×	`fma-neg_binary64`
225×	`+-commutative_binary64`
218×	`associate--r+_binary64`

Counts

346 → 344

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	8897
1	1039	8416
2	3680	8214
3	5459	8214

prune595.0ms (5.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	344	8	352

Error

0.0b

Counts

352 → 8

Alt Table

Status	Error	Program
▶	7.8b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t)))) (+.f64 x y))
	14.5b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
	31.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.9b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	35.7b	(-.f64 (+.f64 y (+.f64 x (.f64 (/.f64 y a) (+.f64 t (/.f64 (.f64 t t) a))))) (+.f64 (/.f64 (.f64 y z) a) (.f64 (/.f64 z a) (.f64 (/.f64 y a) (+.f64 t (/.f64 (.f64 t t) a))))))
	23.9b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
✓	7.7b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	32.2b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 9563 to 2923 computations (69.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
✓	0.5b	(cbrt.f64 (-.f64 a t))
✓	6.5b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t)))) (+.f64 x y))

series293.0ms (2.5%)

Counts

4 → 144

Calls

4 calls:

101.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
79.0ms	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t)))) (+.f64 x y))
58.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))
54.0ms	(cbrt.f64 (-.f64 a t))

rewrite118.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64`
79×	`*-un-lft-identity_binary64`
61×	`cbrt-prod_binary64`
55×	`times-frac_binary64`
54×	`associate-r_binary64`

Counts

4 → 189

Calls

4 calls:

54.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t))))
18.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
4.0ms	(cbrt.f64 (-.f64 a t))
1.0ms	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t)))) (+.f64 x y))

simplify310.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-def_binary64`
411×	`associate-r_binary64`
299×	`associate-l_binary64`
263×	`times-frac_binary64`
262×	`associate-/l*_binary64`

Counts

333 → 380

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	560	10244
1	1506	8821
2	4836	8561
3	5598	8561

prune758.0ms (6.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	480	2	482
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	482	8	490

Error

0.0b

Counts

490 → 8

Alt Table

Status	Error	Program
	31.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.9b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	23.9b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
✓	7.7b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 t z))) (+.f64 x y))
	32.2b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
▶	12.5b	(-.f64 (+.f64 y (fma.f64 (/.f64 y (-.f64 a t)) t x)) (/.f64 (*.f64 y z) (-.f64 a t)))
✓	7.8b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t)))) (+.f64 x y))
	31.8b	(-.f64 (+.f64 y (fma.f64 (/.f64 y a) t x)) (fma.f64 (/.f64 (.f64 y t) a) (/.f64 z a) (/.f64 (.f64 y z) a)))

Compiler

Compiled 17971 to 5923 computations (67% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	5.4b	(fma.f64 (/.f64 y (-.f64 a t)) t x)
✓	6.0b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	6.2b	(+.f64 y (fma.f64 (/.f64 y (-.f64 a t)) t x))

series186.0ms (1.6%)

Counts

4 → 144

Calls

4 calls:

61.0ms	(+.f64 y (fma.f64 (/.f64 y (-.f64 a t)) t x))
51.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
41.0ms	(fma.f64 (/.f64 y (-.f64 a t)) t x)
33.0ms	(/.f64 y (-.f64 a t))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 96

Calls

4 calls:

12.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
4.0ms	(/.f64 y (-.f64 a t))
4.0ms	(+.f64 y (fma.f64 (/.f64 y (-.f64 a t)) t x))
0.0ms	(fma.f64 (/.f64 y (-.f64 a t)) t x)

simplify227.0ms (2%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
358×	`fma-neg_binary64`
325×	`distribute-rgt-in_binary64`
256×	`distribute-lft-in_binary64`
221×	`cancel-sign-sub-inv_binary64`

Counts

240 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	297	4380
1	691	4254
2	2290	3750
3	4684	3750
4	4976	3750

prune439.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	207	7	214

Error

0.0b

Counts

214 → 7

Alt Table

Status	Error	Program
	31.0b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.9b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	28.0b	(-.f64 (+.f64 y (fma.f64 (/.f64 y (-.f64 a t)) t x)) (fma.f64 (/.f64 y a) z (.f64 (/.f64 z a) (.f64 (/.f64 y a) (+.f64 t (/.f64 t (/.f64 a t)))))))
	32.2b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	30.6b	(-.f64 (-.f64 x (.f64 (/.f64 y t) (+.f64 a (/.f64 a (/.f64 t a))))) (/.f64 (.f64 y z) (-.f64 a t)))
✓	7.8b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 t z) (cbrt.f64 (-.f64 a t)))) (+.f64 x y))
	7.7b	(-.f64 (+.f64 y (fma.f64 (/.f64 y (-.f64 a t)) t x)) (/.f64 y (/.f64 (-.f64 a t) z)))

Compiler

Compiled 5560 to 1351 computations (75.7% saved)

regimes4.4s (37.5%)

Accuracy

Total 6.1b remaining (98.8%)

Threshold costs 0b (0%)

Counts

203 → 4

Compiler

Compiled 28908 to 16392 computations (43.3% saved)

bsearch14.0ms (0.1%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

20×	`+-commutative_binary64`
16×	`sub-neg_binary64`
14×	`*-commutative_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	149
1	57	149
2	80	149
3	105	149
4	122	149
5	141	149
6	148	149
7	149	149
8	145	149

end194.0ms (1.7%)

Compiler: Compiled 391 to 170 computations (56.5% saved)

Iter	Nodes	Cost
0	38	149
1	57	149
2	80	149
3	105	149
4	122	149
5	141	149
6	148	149
7	149	149
8	145	149

Iter	Nodes	Cost
0	38	149
1	57	149
2	80	149
3	105	149
4	122	149
5	141	149
6	148	149
7	149	149
8	145	149

Details

analyze743.0ms (6.4%)

sample1.9s (16.5%)

simplify185.0ms (1.6%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

series97.0ms (0.8%)

rewrite19.0ms (0.2%)

simplify238.0ms (2%)

prune232.0ms (2%)

localize20.0ms (0.2%)

series136.0ms (1.2%)

rewrite84.0ms (0.7%)

simplify352.0ms (3%)

prune595.0ms (5.1%)

localize23.0ms (0.2%)

series293.0ms (2.5%)

rewrite118.0ms (1%)

simplify310.0ms (2.7%)

prune758.0ms (6.5%)

localize30.0ms (0.3%)

series186.0ms (1.6%)

rewrite25.0ms (0.2%)

simplify227.0ms (2%)

prune439.0ms (3.8%)

regimes4.4s (37.5%)

bsearch14.0ms (0.1%)

simplify19.0ms (0.2%)

end194.0ms (1.7%)

Profiling

Iter	Nodes	Cost
0	38	149
1	57	149
2	80	149
3	105	149
4	122	149
5	141	149
6	148	149
7	149	149
8	145	149