Details

analyze305.0ms (11.6%)

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 15 to 10 computations (33.3% saved)

sample935.0ms (35.7%)

Infinites

24.2% of outputs are infinite.

Results

814.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify65.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	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
	5.2b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	4.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series58.0ms (2.2%)

Counts

3 → 144

Calls

3 calls:

33.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
19.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

6.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
5.0ms	(*.f64 y (-.f64 z t))
5.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

simplify78.0ms (3%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
517×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
448×	`fma-def_binary64`
124×	`associate-l_binary64`

Counts

236 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2898
1	425	2525
2	1558	2355
3	5186	2355

prune96.0ms (3.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	145	5	150

Error

0.0b

Counts

150 → 5

Alt Table

Status	Error	Program
	36.4b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
	5.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	4.6b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
	5.2b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	4.6b	(+.f64 (/.f64 (*.f64 y (-.f64 z t)) a) x)

Compiler

Compiled 2585 to 743 computations (71.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series28.0ms (1.1%)

Counts

1 → 60

Calls

1 calls:

28.0ms

(+.f64 (/.f64 (*.f64 y (-.f64 z t)) a) x)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`fma-def_binary64`
5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`times-frac_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 21

Calls

1 calls:

6.0ms

(+.f64 (/.f64 (*.f64 y (-.f64 z t)) a) x)

simplify68.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

922×	`fma-neg_binary64`
522×	`associate-/l*_binary64`
295×	`times-frac_binary64`
229×	`associate-/r/_binary64`
198×	`distribute-rgt-in_binary64`

Counts

81 → 44

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	1276
1	144	973
2	414	834
3	1850	834
4	4498	834
5	5265	834

prune96.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	157	5	162

Error

Counts

162 → 5

Alt Table

Status	Error	Program
	36.4b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
	5.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	4.6b	(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)
▶	1.7b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
✓	4.6b	(+.f64 (/.f64 (*.f64 y (-.f64 z t)) a) x)

Compiler

Compiled 2672 to 738 computations (72.4% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.7b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series25.0ms (0.9%)

Counts

1 → 60

Calls

1 calls:

25.0ms

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

simplify68.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

429×	`distribute-lft-neg-out_binary64`
429×	`distribute-rgt-neg-out_binary64`
368×	`distribute-rgt-in_binary64`
367×	`distribute-lft-in_binary64`
237×	`distribute-rgt-out_binary64`

Counts

70 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	1133
1	75	750
2	165	733
3	447	733
4	2165	733
5	4627	733
6	4940	733

prune17.0ms (0.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	26	5	31

Error

Counts

31 → 5

Alt Table

Status	Error	Program
	36.4b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
	5.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
▶	4.6b	(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)
✓	1.7b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
✓	4.6b	(+.f64 (/.f64 (*.f64 y (-.f64 z t)) a) x)

Compiler

Compiled 397 to 135 computations (66% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z t))
✓	4.6b	(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)

series23.0ms (0.9%)

Counts

1 → 60

Calls

1 calls:

23.0ms

(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) 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 (-.f64 z t)) (/.f64 1 a) x)

simplify74.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

596×	`distribute-rgt-neg-out_binary64`
438×	`distribute-lft-in_binary64`
438×	`distribute-rgt-in_binary64`
395×	`associate-l_binary64`
360×	`associate-r_binary64`

Counts

70 → 32

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	1169
1	83	860
2	186	733
3	552	733
4	2869	733
5	4618	733
6	5085	733

prune70.0ms (2.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	99	5	104

Error

Counts

104 → 5

Alt Table

Status	Error	Program
	36.4b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
	5.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	4.6b	(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)
✓	1.7b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
✓	4.6b	(+.f64 (/.f64 (*.f64 y (-.f64 z t)) a) x)

Compiler

Compiled 1805 to 621 computations (65.6% saved)

regimes481.0ms (18.4%)

Accuracy

Total 0.3b remaining (94.5%)

Threshold costs 0.3b (94.5%)

Counts

43 → 3

Compiler

Compiled 6435 to 3982 computations (38.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	57
1	28	57
2	32	57
3	34	57
4	35	57
5	34	57

end67.0ms (2.6%)

Compiler: Compiled 162 to 85 computations (47.5% saved)

Details

analyze305.0ms (11.6%)

sample935.0ms (35.7%)

simplify65.0ms (2.5%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series58.0ms (2.2%)

rewrite21.0ms (0.8%)

simplify78.0ms (3%)

prune96.0ms (3.7%)

localize7.0ms (0.3%)

series28.0ms (1.1%)

rewrite7.0ms (0.3%)

simplify68.0ms (2.6%)

prune96.0ms (3.7%)

localize6.0ms (0.2%)

series25.0ms (0.9%)

rewrite1.0ms (0%)

simplify68.0ms (2.6%)

prune17.0ms (0.7%)

localize7.0ms (0.3%)

series23.0ms (0.9%)

rewrite1.0ms (0%)

simplify74.0ms (2.8%)

prune70.0ms (2.7%)

regimes481.0ms (18.4%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end67.0ms (2.6%)

Profiling