Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
37.5%	12.5%	50%	3
43.7%	6.2%	50%	4
46.8%	3.1%	50%	5
48.4%	1.6%	50%	6
49.2%	0.8%	50%	7
49.6%	0.4%	50%	8
49.8%	0.2%	50%	9
49.9%	0.1%	50%	10
49.9%	0%	50%	11
49.9%	0%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample11.9s (88.5%)

Results

9.7s	4385×	body	2048	valid
1.6s	2053×	body	1024	valid
413.0ms	1012×	body	512	valid
142.0ms	521×	body	256	valid
44.0ms	285×	body	128	valid

Compiler

Compiled 38 to 25 computations (34.2% saved)

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-def_binary64`
278×	`fma-neg_binary64`
235×	`times-frac_binary64`
176×	`div-sub_binary64`
119×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	11	11
2	18	11
3	29	11
4	56	11
5	86	11
6	150	11
7	238	11
8	380	11
9	714	11
10	1628	11
11	2249	11
12	2882	11
13	2945	11
14	2983	11
15	2993	11

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (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

31.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.2b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
✓	2.0b	(-.f64 x (sin.f64 x))

series15.0ms (0.1%)

Counts

2 → 18

Calls

2 calls:

13.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite103.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

864×	`log1p-expm1-u_binary64`
864×	`expm1-log1p-u_binary64`
591×	`prod-diff_binary64`
254×	`egg-rr`
75×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	140	17
2	2168	17

Stop Event

1×	node limit

Counts

2 → 254

Calls

2 calls:

92.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
92.0ms	(-.f64 x (sin.f64 x))

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-def_binary64`
478×	`cancel-sign-sub-inv_binary64`
387×	`unswap-sqr_binary64`
346×	`fma-neg_binary64`
272×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	272
1	133	266
2	344	262
3	1234	248
4	4380	248

Stop Event

1×	node limit

Counts

272 → 274

prune152.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	271	3	274
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	272	3	275

Error

0.2b

Counts

275 → 3

Alt Table

Status	Error	Program
	11.0b	(/.f64 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 (pow.f64 x 5) -1/120 (*.f64 1/5040 (pow.f64 x 7)))) (tan.f64 x))
	31.1b	(+.f64 (fma.f64 1 (/.f64 x (tan.f64 x)) (neg.f64 (/.f64 (sin.f64 x) (tan.f64 x)))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (sin.f64 x) (tan.f64 x)))) (sqrt.f64 (/.f64 (sin.f64 x) (tan.f64 x))) (/.f64 (sin.f64 x) (tan.f64 x))))
▶	0.4b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))

Compiler

Compiled 10481 to 2844 computations (72.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 x 6) -11/15120)
✓	0.1b	(fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))
✓	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))

series14.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
4.0ms	(fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))
3.0ms	(*.f64 (pow.f64 x 6) -11/15120)

rewrite48.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

448×	`log-prod_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
181×	`pow3_binary64`
171×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	274	42
2	2836	42

Stop Event

1×	node limit

Counts

3 → 75

Calls

3 calls:

46.0ms	(*.f64 (pow.f64 x 6) -11/15120)
46.0ms	(fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))
46.0ms	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))

simplify29.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-neg_binary64`
774×	`cancel-sign-sub-inv_binary64`
366×	`associate-l_binary64`
285×	`unswap-sqr_binary64`
275×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	456
1	54	454
2	127	420
3	446	420
4	2464	420

Stop Event

1×	node limit

Counts

111 → 87

prune110.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Error

0.1b

Counts

90 → 7

Alt Table

Status	Error	Program
	11.0b	(/.f64 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 (pow.f64 x 5) -1/120 (*.f64 1/5040 (pow.f64 x 7)))) (tan.f64 x))
	31.1b	(+.f64 (fma.f64 1 (/.f64 x (tan.f64 x)) (neg.f64 (/.f64 (sin.f64 x) (tan.f64 x)))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (sin.f64 x) (tan.f64 x)))) (sqrt.f64 (/.f64 (sin.f64 x) (tan.f64 x))) (/.f64 (sin.f64 x) (tan.f64 x))))
	21.5b	(cbrt.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 3))
▶	0.4b	(pow.f64 (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 2)
	0.9b	(pow.f64 (cbrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 3)
	53.0b	(/.f64 (+.f64 (pow.f64 (.f64 1/6 (.f64 x x)) 3) (pow.f64 (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)) 3)) (fma.f64 (.f64 1/6 (.f64 x x)) (.f64 1/6 (.f64 x x)) (-.f64 (pow.f64 (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)) 2) (.f64 (.f64 1/6 (.f64 x x)) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))))
✓	0.4b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))

Compiler

Compiled 2135 to 1539 computations (27.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))
✓	0.2b	(pow.f64 (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 2)
	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
✓	27.8b	(sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))

series39.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

31.0ms

(pow.f64 (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120)))) 2)

8.0ms

(sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))))

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`log-prod_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
196×	`log-pow_binary64`
152×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	44
1	335	44
2	3225	44

Stop Event

1×	node limit

Counts

2 → 71

Calls

2 calls:

50.0ms

(pow.f64 (sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120)))) 2)

50.0ms

(sqrt.f64 (fma.f64 1/6 (*.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))))

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-neg_binary64`
342×	`fma-def_binary64`
225×	`associate-/r*_binary64`
222×	`associate-r_binary64`
213×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	709
1	292	616
2	1007	576
3	4501	576

Stop Event

1×	node limit

Counts

95 → 105

prune279.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	171	5	176
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	173	10	183

Error

0.1b

Counts

183 → 10

Alt Table

Status	Error	Program
	16.6b	(fma.f64 (.f64 1/6 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
	31.1b	(+.f64 (fma.f64 1 (/.f64 x (tan.f64 x)) (neg.f64 (/.f64 (sin.f64 x) (tan.f64 x)))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (sin.f64 x) (tan.f64 x)))) (sqrt.f64 (/.f64 (sin.f64 x) (tan.f64 x))) (/.f64 (sin.f64 x) (tan.f64 x))))
	11.0b	(/.f64 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 (pow.f64 x 5) -1/120 (*.f64 1/5040 (pow.f64 x 7)))) (tan.f64 x))
	0.5b	(.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 1/4) (.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 1/4) (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))))
	0.8b	(.f64 (cbrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))) (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))))
▶	0.4b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
	21.5b	(cbrt.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 3))
	0.9b	(pow.f64 (cbrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 3)
	0.4b	(pow.f64 (fma.f64 (sqrt.f64 1/6) x (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 1/6)) -23/720)) 2)
✓	0.4b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))

Compiler

Compiled 4773 to 3632 computations (23.9% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
✓	0.1b	(.f64 x (.f64 x 1/6))
✓	0.3b	(*.f64 x 1/6)

series9.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
2.0ms	(.f64 x (.f64 x 1/6))
2.0ms	(*.f64 x 1/6)

rewrite42.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

734×	`log1p-expm1-u_binary64`
734×	`expm1-log1p-u_binary64`
153×	`log1p-udef_binary64`
149×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	189	25
2	2039	25

Stop Event

1×	node limit

Counts

3 → 51

Calls

3 calls:

41.0ms	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
41.0ms	(.f64 x (.f64 x 1/6))
41.0ms	(*.f64 x 1/6)

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
666×	`fma-neg_binary64`
395×	`distribute-rgt-neg-in_binary64`
349×	`cancel-sign-sub-inv_binary64`
336×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	297
1	30	279
2	63	279
3	186	279
4	750	279
5	1829	279
6	3094	279
7	4840	279

Stop Event

1×	node limit

Counts

87 → 58

prune95.0ms (0.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	53	5	58
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	57	11	68

Error

0.0b

Counts

68 → 11

Alt Table

Status	Error	Program
	31.1b	(+.f64 (fma.f64 1 (/.f64 x (tan.f64 x)) (neg.f64 (/.f64 (sin.f64 x) (tan.f64 x)))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (sin.f64 x) (tan.f64 x)))) (sqrt.f64 (/.f64 (sin.f64 x) (tan.f64 x))) (/.f64 (sin.f64 x) (tan.f64 x))))
	16.5b	(fma.f64 (pow.f64 x 4) -23/360 (sqrt.f64 (*.f64 (pow.f64 x 4) 1/36)))
	0.8b	(.f64 (cbrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))) (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))))
	0.4b	(fma.f64 (pow.f64 x 4) -23/360 (pow.f64 (*.f64 x (sqrt.f64 1/6)) 2))
	1.0b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (pow.f64 (cbrt.f64 (.f64 x 1/6)) 3)))
	11.0b	(/.f64 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 (pow.f64 x 5) -1/120 (*.f64 1/5040 (pow.f64 x 7)))) (tan.f64 x))
	0.5b	(.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 1/4) (.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 1/4) (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))))
✓	0.4b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
✓	0.4b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
	15.9b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (sqrt.f64 (.f64 1/36 (*.f64 x x)))))
	33.3b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (pow.f64 (sqrt.f64 (.f64 x 1/6)) 2)))

Compiler

Compiled 1048 to 789 computations (24.7% saved)

regimes160.0ms (1.2%)

Accuracy

Total 0.3b remaining (87.1%)

Threshold costs 0.3b (87.1%)

Counts

91 → 1

Compiler

Compiled 2956 to 2136 computations (27.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	22	25
2	31	25
3	53	25
4	62	25
5	68	25
6	70	25

Stop Event

1×

saturated

end209.0ms (1.5%)

Compiler: Compiled 286 to 206 computations (28% saved)

Details

analyze4.0ms (0%)

sample11.9s (88.5%)

simplify33.0ms (0.2%)

prune1.0ms (0%)

localize6.0ms (0%)

series15.0ms (0.1%)

rewrite103.0ms (0.8%)

simplify36.0ms (0.3%)

prune152.0ms (1.1%)

localize8.0ms (0.1%)

series14.0ms (0.1%)

rewrite48.0ms (0.4%)

simplify29.0ms (0.2%)

prune110.0ms (0.8%)

localize12.0ms (0.1%)

series39.0ms (0.3%)

rewrite52.0ms (0.4%)

simplify41.0ms (0.3%)

prune279.0ms (2.1%)

localize6.0ms (0%)

series9.0ms (0.1%)

rewrite42.0ms (0.3%)

simplify41.0ms (0.3%)

prune95.0ms (0.7%)

regimes160.0ms (1.2%)

simplify3.0ms (0%)

end209.0ms (1.5%)

Profiling