Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample5.3s (76.5%)

Results

3.7s	4315×	body	2048	valid
1.0s	2046×	body	1024	valid
349.0ms	1002×	body	512	valid
96.0ms	517×	body	256	valid
37.0ms	376×	body	128	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

819×	`div-sub_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	112	13
5	223	13
6	481	13
7	890	13
8	1570	13
9	4778	13
10	5815	13

prune2.0ms (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

Error

26.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	3.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series4.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

2.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
1.0ms	(-.f64 (exp.f64 x) 2)

rewrite55.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

815×	`log1p-expm1-u_binary64`
815×	`expm1-log1p-u_binary64`
536×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`

Counts

2 → 80

Calls

2 calls:

54.0ms	(-.f64 (exp.f64 x) 2)
54.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	181	17
2	2012	17
3	5842	17
0	0	0
1	0	0

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

750×	`unswap-sqr_binary64`
683×	`distribute-rgt-out_binary64`
567×	`associate-l_binary64`
524×	`fma-def_binary64`
411×	`associate-r_binary64`

Counts

96 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	198
1	108	196
2	236	196
3	630	191
4	2026	191
5	4956	191
6	4921	191
7	4962	191

prune75.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	4	98

Error

0.0b

Counts

98 → 4

Alt Table

Status	Error	Program
▶	0.9b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	26.1b	(/.f64 (+.f64 (+.f64 (exp.f64 x) 2) (.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 2) 4))) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))
	26.1b	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
✓	26.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 1590 to 928 computations (41.6% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))

series11.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

4.0ms

(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

4.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

3.0ms

(*.f64 1/20160 (pow.f64 x 8))

rewrite66.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

520×	`log-prod_binary64`
314×	`prod-diff_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
201×	`log-pow_binary64`

Counts

3 → 79

Calls

3 calls:

64.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

64.0ms

(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

64.0ms

(*.f64 1/20160 (pow.f64 x 8))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	318	50
2	2983	50
3	5250	50
0	0	0
1	0	0

simplify159.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

714×	`distribute-rgt-out_binary64`
540×	`sqr-pow_binary64`
414×	`unswap-sqr_binary64`
398×	`*-commutative_binary64`
378×	`distribute-lft-out_binary64`

Counts

103 → 94

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	357
1	61	357
2	129	357
3	333	357
4	1097	357
5	2251	357
6	2328	357
7	2795	357
8	3554	357
9	4571	357
10	4810	357
11	4625	357
12	4856	357
13	4991	357
14	4847	357

prune112.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	93	5	98

Error

0.0b

Counts

98 → 5

Alt Table

Status	Error	Program
▶	1.6b	(pow.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))) 3)
✓	0.9b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	26.1b	(/.f64 (+.f64 (+.f64 (exp.f64 x) 2) (.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 2) 4))) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))
	26.1b	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
✓	26.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 2412 to 1821 computations (24.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	0.4b	(pow.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))) 3)
✓	32.5b	(cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

series26.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

18.0ms

(pow.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))) 3)

7.0ms

(cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

rewrite111.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

314×	`prod-diff_binary64`
262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
235×	`fma-udef_binary64`
192×	`fma-neg_binary64`

Counts

2 → 63

Calls

2 calls:

109.0ms

(pow.f64 (cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))) 3)

109.0ms

(cbrt.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	364	52
2	3362	52
3	4906	52
4	4937	52
5	4672	52
0	0	0
1	0	0

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

560×	`associate-/l/_binary64`
341×	`fma-def_binary64`
300×	`times-frac_binary64`
214×	`unswap-sqr_binary64`
200×	`associate-/l*_binary64`

Counts

87 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	1166
1	300	1118
2	817	880
3	2916	620
4	5003	620

prune215.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	166	5	171

Error

0.0b

Counts

171 → 5

Alt Table

Status	Error	Program
▶	3.6b	(pow.f64 (+.f64 (.f64 1/1224720 (pow.f64 (pow.f64 x 20) 1/3)) (+.f64 (.f64 1/6480 (pow.f64 (pow.f64 x 14) 1/3)) (+.f64 (*.f64 1/36 (pow.f64 (pow.f64 x 8) 1/3)) (pow.f64 (pow.f64 x 2) 1/3)))) 3)
✓	0.9b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	26.1b	(/.f64 (+.f64 (+.f64 (exp.f64 x) 2) (.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 2) 4))) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))
	26.1b	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
✓	26.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 4837 to 3832 computations (20.8% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(pow.f64 (pow.f64 x 20) 1/3)
✓	8.2b	(pow.f64 (pow.f64 x 14) 1/3)
✓	13.8b	(pow.f64 (pow.f64 x 8) 1/3)
✓	34.3b	(pow.f64 (pow.f64 x 2) 1/3)

series110.0ms (1.6%)

Counts

4 → 0

Calls

4 calls:

32.0ms	(pow.f64 (pow.f64 x 2) 1/3)
27.0ms	(pow.f64 (pow.f64 x 14) 1/3)
26.0ms	(pow.f64 (pow.f64 x 20) 1/3)
25.0ms	(pow.f64 (pow.f64 x 8) 1/3)

rewrite78.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

526×	`log-prod_binary64`
223×	`log-pow_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
191×	`pow3_binary64`

Counts

4 → 94

Calls

4 calls:

77.0ms	(pow.f64 (pow.f64 x 20) 1/3)
77.0ms	(pow.f64 (pow.f64 x 14) 1/3)
77.0ms	(pow.f64 (pow.f64 x 8) 1/3)
77.0ms	(pow.f64 (pow.f64 x 2) 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	330	24
2	2969	24
3	4977	24
4	4755	24
0	0	0
1	0	0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune136.0ms (2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	94	5	99

Error

0.0b

Counts

99 → 5

Alt Table

Status	Error	Program
✓	3.6b	(pow.f64 (+.f64 (.f64 1/1224720 (pow.f64 (pow.f64 x 20) 1/3)) (+.f64 (.f64 1/6480 (pow.f64 (pow.f64 x 14) 1/3)) (+.f64 (*.f64 1/36 (pow.f64 (pow.f64 x 8) 1/3)) (pow.f64 (pow.f64 x 2) 1/3)))) 3)
	25.6b	(pow.f64 (+.f64 (.f64 1/1224720 (pow.f64 (pow.f64 x 20) 1/3)) (+.f64 (.f64 1/6480 (pow.f64 (pow.f64 x 14) 1/3)) (+.f64 (.f64 1/36 (pow.f64 (pow.f64 x 8) 1/3)) (-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 x x)))) 1)))) 3)
✓	0.9b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	26.1b	(/.f64 (+.f64 (+.f64 (exp.f64 x) 2) (.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 2) 4))) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))
✓	26.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 3357 to 2815 computations (16.1% saved)

regimes84.0ms (1.2%)

Accuracy

Total 0.5b remaining (97.2%)

Threshold costs 0.5b (97.2%)

Counts

42 → 1

Compiler

Compiled 1360 to 1042 computations (23.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	16	25
2	16	25

end122.0ms (1.8%)

Compiler: Compiled 156 to 121 computations (22.4% saved)

Details

analyze5.0ms (0.1%)

sample5.3s (76.5%)

simplify56.0ms (0.8%)

prune2.0ms (0%)

localize10.0ms (0.2%)

series4.0ms (0.1%)

rewrite55.0ms (0.8%)

simplify80.0ms (1.2%)

prune75.0ms (1.1%)

localize13.0ms (0.2%)

series11.0ms (0.2%)

rewrite66.0ms (1%)

simplify159.0ms (2.3%)

prune112.0ms (1.6%)

localize12.0ms (0.2%)

series26.0ms (0.4%)

rewrite111.0ms (1.6%)

simplify55.0ms (0.8%)

prune215.0ms (3.1%)

localize28.0ms (0.4%)

series110.0ms (1.6%)

rewrite78.0ms (1.1%)

simplify6.0ms (0.1%)

prune136.0ms (2%)

regimes84.0ms (1.2%)

simplify2.0ms (0%)

end122.0ms (1.8%)

Profiling