Details

analyze466.0ms (16%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.6s (56.2%)

Results

864.0ms	2794×	body	1024	valid
289.0ms	1359×	body	512	valid
243.0ms	3132×	body	128	valid
106.0ms	675×	body	256	valid
103.0ms	296×	body	2048	valid
1.0ms	2×	body	2048	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))
	41.8b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 41 to 25 computations (39% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 x)
✓	0.3b	(/.f64 (exp.f64 x) (expm1.f64 x))

series13.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
2.0ms	(expm1.f64 x)

rewrite86.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

103× egg-rr

Counts

2 → 103

Calls

2 calls:

84.0ms	((/.f64 (exp.f64 x) (expm1.f64 x)) (expm1.f64 x))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	98	11
2	1250	11
3	4894	11
4	5321	11
0	0	0
1	0	0

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

804×	`unswap-sqr_binary64`
534×	`fma-def_binary64`
487×	`distribute-lft-out_binary64`
366×	`fma-neg_binary64`
361×	`*-commutative_binary64`

Counts

127 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	180
1	78	176
2	182	174
3	494	168
4	1472	168
5	2433	168
6	4835	168
7	4933	168

prune61.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	119	3	122

Error

0.2b

Counts

122 → 3

Alt Table

Status	Error	Program
	21.3b	(+.f64 1/2 (/.f64 1 x))
▶	0.3b	(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
	41.8b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 1516 to 677 computations (55.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 x)
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
✓	0.3b	(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))

series24.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
10.0ms	(/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))

rewrite109.0ms (3.8%)

Algorithm

2×	batch-egg-rewrite

Rules

79× egg-rr

Counts

2 → 79

Calls

2 calls:

108.0ms	((/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)) (*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	162	18
2	1934	18
3	4986	18
4	4981	18
5	5027	18
0	0	0
1	0	0

simplify113.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-def_binary64`
705×	`unswap-sqr_binary64`
495×	`associate-l_binary64`
451×	`distribute-rgt-neg-in_binary64`
446×	`fma-neg_binary64`

Counts

103 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	273
1	91	241
2	212	235
3	525	233
4	1222	233
5	2745	233
6	4031	233
7	4853	233
8	4968	233
9	4995	233
10	4816	233

prune69.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Error

0.2b

Counts

143 → 3

Alt Table

Status	Error	Program
▶	21.3b	(+.f64 1/2 (/.f64 1 x))
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
	41.8b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 2125 to 920 computations (56.7% saved)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.2b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	21.3b	(+.f64 1/2 (/.f64 1 x))
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
▶	41.8b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 35 to 23 computations (34.3% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
✓	4.4b	(-.f64 (exp.f64 x) 1)

series10.0ms (0.4%)

Counts

2 → 8

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.0ms	(-.f64 (exp.f64 x) 1)

rewrite49.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

77× egg-rr

Counts

2 → 77

Calls

2 calls:

47.0ms	((-.f64 (exp.f64 x) 1) (/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	125	11
2	1561	11
3	5047	11
0	0	0
1	0	0

simplify53.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

804×	`unswap-sqr_binary64`
534×	`fma-def_binary64`
487×	`distribute-lft-out_binary64`
361×	`*-commutative_binary64`
360×	`fma-neg_binary64`

Counts

85 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	92
1	71	88
2	175	86
3	485	80
4	1458	80
5	2398	80
6	4846	80
7	4961	80

prune37.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	90	3	93

Error

0.2b

Counts

93 → 3

Alt Table

Status	Error	Program
✓	21.3b	(+.f64 1/2 (/.f64 1 x))
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 (exp.f64 x)) 1) (/.f64 (sqrt.f64 (exp.f64 x)) (expm1.f64 x)))
✓	41.8b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 1019 to 443 computations (56.5% saved)

regimes52.0ms (1.8%)

Accuracy

Total 0.1b remaining (20.3%)

Threshold costs 0.1b (20.3%)

Counts

27 → 1

Compiler

Compiled 839 to 571 computations (31.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	12	17
2	11	17

end47.0ms (1.6%)

Compiler: Compiled 49 to 30 computations (38.8% saved)

Details

analyze466.0ms (16%)

sample1.6s (56.2%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series13.0ms (0.4%)

rewrite86.0ms (3%)

simplify57.0ms (1.9%)

prune61.0ms (2.1%)

localize6.0ms (0.2%)

series24.0ms (0.8%)

rewrite109.0ms (3.8%)

simplify113.0ms (3.9%)

prune69.0ms (2.4%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

series10.0ms (0.4%)

rewrite49.0ms (1.7%)

simplify53.0ms (1.8%)

prune37.0ms (1.3%)

regimes52.0ms (1.8%)

simplify2.0ms (0.1%)

end47.0ms (1.6%)

Profiling