Details

analyze182.0ms (8.1%)

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
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
74.9%	25%	0.2%	11
74.9%	25%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample901.0ms (40.3%)

Infinites

24.7% of outputs are infinite.

Results

700.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify71.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	11

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	5.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) t)
✓	5.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)

series31.0ms (1.4%)

Counts

2 → 76

Calls

2 calls:

22.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)
9.0ms	(/.f64 (-.f64 z x) t)

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

7.0ms	(/.f64 (-.f64 z x) t)
0.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)

simplify57.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-rgt-in_binary64`
694×	`distribute-lft-in_binary64`
580×	`times-frac_binary64`
456×	`fma-def_binary64`
219×	`div-sub_binary64`

Counts

126 → 76

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	112	1693
1	247	1350
2	554	1350
3	1352	1350
4	4976	1350

prune59.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	71	7	78

Error

0.0b

Counts

78 → 7

Alt Table

Status	Error	Program
	5.0b	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)
	8.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	31.3b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x) 3))
✓	5.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	36.7b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)))
	31.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x) (fma.f64 y (/.f64 (-.f64 z x) t) x)) (fma.f64 y (/.f64 (-.f64 z x) t) x)))

Compiler

Compiled 1268 to 382 computations (69.9% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series16.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

16.0ms

(fma.f64 (/.f64 y t) (-.f64 z x) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 y t) (-.f64 z x) x)

simplify65.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
389×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
294×	`times-frac_binary64`

Counts

58 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	87	635
2	197	623
3	473	623
4	2335	623
5	4674	623
6	5331	623

prune15.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	24	7	31

Error

0.0b

Counts

31 → 7

Alt Table

Status	Error	Program
▶	5.0b	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)
	8.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	31.3b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x) 3))
✓	5.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	36.7b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)))
	31.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x) (fma.f64 y (/.f64 (-.f64 z x) t) x)) (fma.f64 y (/.f64 (-.f64 z x) t) x)))

Compiler

Compiled 485 to 173 computations (64.3% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 z x) (/.f64 1 t))
✓	5.0b	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)

series26.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

17.0ms	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)
9.0ms	(*.f64 (-.f64 z x) (/.f64 1 t))

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
11×	`add-exp-log_binary64`

Counts

2 → 54

Calls

2 calls:

7.0ms	(*.f64 (-.f64 z x) (/.f64 1 t))
0.0ms	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)

simplify79.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-def_binary64`
444×	`times-frac_binary64`
328×	`distribute-rgt-neg-out_binary64`
324×	`distribute-lft-neg-out_binary64`
261×	`distribute-rgt-in_binary64`

Counts

138 → 101

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	120	1703
1	269	1326
2	757	1326
3	2026	1326
4	4512	1326
5	5245	1326

prune71.0ms (3.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	101	7	108

Error

0.0b

Counts

108 → 7

Alt Table

Status	Error	Program
✓	5.0b	(fma.f64 y (*.f64 (-.f64 z x) (/.f64 1 t)) x)
▶	8.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	31.3b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x) 3))
✓	5.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	36.7b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z x) t) x)))
	23.3b	(fma.f64 y (/.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) t) (+.f64 z x)) x)

Compiler

Compiled 1701 to 698 computations (59% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y z) t) x)
✓	3.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
✓	3.9b	(/.f64 (*.f64 y z) t)
✓	5.3b	(/.f64 (*.f64 y x) t)

series72.0ms (3.2%)

Counts

4 → 24

Calls

4 calls:

27.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
17.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
16.0ms	(/.f64 (*.f64 y x) t)
11.0ms	(/.f64 (*.f64 y z) t)

rewrite33.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
28×	`prod-diff_binary64`
28×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`

Counts

4 → 126

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
6.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
6.0ms	(/.f64 (*.f64 y x) t)
3.0ms	(/.f64 (*.f64 y z) t)

simplify117.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

928×	`times-frac_binary64`
635×	`fma-def_binary64`
193×	`cancel-sign-sub-inv_binary64`
170×	`neg-mul-1_binary64`
162×	`distribute-rgt-neg-in_binary64`

Counts

150 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	3546
1	539	2223
2	1887	1903
3	4439	1903
4	4992	1903
5	4889	1903

prune106.0ms (4.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	1	2	3
Picked	0	1	1
Done	1	2	3
Total	186	7	193

Error

Counts

193 → 7

Alt Table

Status	Error	Program
	25.8b	(/.f64 y (/.f64 t (-.f64 z x)))
	31.3b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x) 3))
✓	5.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	8.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 y x) t))
	8.6b	(-.f64 (fma.f64 (.f64 y z) (/.f64 1 t) x) (/.f64 (.f64 y x) t))
	23.3b	(fma.f64 y (/.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) t) (+.f64 z x)) x)

Compiler

Compiled 4380 to 807 computations (81.6% saved)

regimes179.0ms (8%)

Accuracy

Total 0.7b remaining (98.8%)

Threshold costs 0.7b (98.8%)

Counts

28 → 3

Compiler

Compiled 2076 to 1228 computations (40.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	69
1	38	69
2	47	69
3	58	69
4	64	69
5	67	69
6	68	69
7	67	69

end96.0ms (4.3%)

Compiler: Compiled 207 to 111 computations (46.4% saved)

Details

analyze182.0ms (8.1%)

sample901.0ms (40.3%)

simplify71.0ms (3.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series31.0ms (1.4%)

rewrite10.0ms (0.5%)

simplify57.0ms (2.5%)

prune59.0ms (2.6%)

localize5.0ms (0.2%)

series16.0ms (0.7%)

rewrite1.0ms (0%)

simplify65.0ms (2.9%)

prune15.0ms (0.6%)

localize10.0ms (0.4%)

series26.0ms (1.2%)

rewrite13.0ms (0.6%)

simplify79.0ms (3.6%)

prune71.0ms (3.2%)

localize8.0ms (0.4%)

series72.0ms (3.2%)

rewrite33.0ms (1.5%)

simplify117.0ms (5.2%)

prune106.0ms (4.8%)

regimes179.0ms (8%)

bsearch1.0ms (0%)

simplify4.0ms (0.2%)

end96.0ms (4.3%)

Profiling