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)

sample12.0s (91.9%)

Results

9.7s	4442×	body	2048	valid
1.6s	2027×	body	1024	valid
425.0ms	1035×	body	512	valid
150.0ms	494×	body	256	valid
37.0ms	258×	body	128	valid

Compiler

Compiled 38 to 25 computations (34.2% saved)

simplify35.0ms (0.3%)

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

27.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.4b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
✓	2.7b	(-.f64 x (sin.f64 x))

series13.0ms (0.1%)

Counts

2 → 18

Calls

2 calls:

10.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite101.0ms (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:

91.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
91.0ms	(-.f64 x (sin.f64 x))

simplify35.0ms (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

prune149.0ms (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
▶	0.4b	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))
	9.8b	(/.f64 (-.f64 (+.f64 (.f64 1/5040 (pow.f64 x 7)) (.f64 1/6 (pow.f64 x 3))) (*.f64 1/120 (pow.f64 x 5))) (tan.f64 x))
	60.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 x))) (cbrt.f64 (/.f64 x (tan.f64 x)))) (cbrt.f64 (/.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x)))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (*.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)))))

Compiler

Compiled 10535 to 2866 computations (72.8% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))
2.0ms	(fma.f64 (*.f64 x x) -23/360 1/6)

rewrite34.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

594×	`log1p-expm1-u_binary64`
594×	`expm1-log1p-u_binary64`
296×	`log-prod_binary64`
171×	`pow2_binary64`
120×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	144	22
2	1632	22

Stop Event

1×	node limit

Counts

2 → 50

Calls

2 calls:

33.0ms	(fma.f64 (*.f64 x x) -23/360 1/6)
33.0ms	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))

simplify32.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-def_binary64`
536×	`fma-neg_binary64`
418×	`distribute-rgt-neg-in_binary64`
409×	`cancel-sign-sub-inv_binary64`
351×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	270
1	36	252
2	82	234
3	238	234
4	940	234
5	2254	234
6	3791	234

Stop Event

1×	node limit

Counts

74 → 61

prune56.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	59	5	64

Error

0.0b

Counts

64 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))
	0.5b	(.f64 (.f64 x x) (exp.f64 (log.f64 (fma.f64 x (*.f64 x -23/360) 1/6))))
	9.8b	(/.f64 (-.f64 (+.f64 (.f64 1/5040 (pow.f64 x 7)) (.f64 1/6 (pow.f64 x 3))) (*.f64 1/120 (pow.f64 x 5))) (tan.f64 x))
	60.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 x))) (cbrt.f64 (/.f64 x (tan.f64 x)))) (cbrt.f64 (/.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x)))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (*.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)))))
▶	0.4b	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -23/360) 1/6))) 2)

Compiler

Compiled 1068 to 664 computations (37.8% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 x (*.f64 x -23/360) 1/6))
✓	0.0b	(.f64 x (sqrt.f64 (fma.f64 x (.f64 x -23/360) 1/6)))
✓	0.2b	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -23/360) 1/6))) 2)
✓	0.5b	(*.f64 x -23/360)

series47.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

31.0ms	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -23/360) 1/6))) 2)
6.0ms	(.f64 x (sqrt.f64 (fma.f64 x (.f64 x -23/360) 1/6)))
4.0ms	(sqrt.f64 (fma.f64 x (*.f64 x -23/360) 1/6))
3.0ms	(*.f64 x -23/360)

rewrite48.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

796×	`log1p-expm1-u_binary64`
796×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
90×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	208	41
2	2250	41

Stop Event

1×	node limit

Counts

4 → 77

Calls

4 calls:

46.0ms	(sqrt.f64 (fma.f64 x (*.f64 x -23/360) 1/6))
46.0ms	(.f64 x (sqrt.f64 (fma.f64 x (.f64 x -23/360) 1/6)))
46.0ms	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -23/360) 1/6))) 2)
46.0ms	(*.f64 x -23/360)

simplify42.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-neg_binary64`
291×	`associate-/r*_binary64`
241×	`fma-def_binary64`
236×	`sub-neg_binary64`
209×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	913
1	309	811
2	997	785
3	3993	783

Stop Event

1×	node limit

Counts

125 → 133

prune106.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	132	6	138

Error

0.0b

Counts

138 → 6

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))
	0.5b	(.f64 (.f64 x x) (exp.f64 (log.f64 (fma.f64 x (*.f64 x -23/360) 1/6))))
▶	0.3b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
	9.8b	(/.f64 (-.f64 (+.f64 (.f64 1/5040 (pow.f64 x 7)) (.f64 1/6 (pow.f64 x 3))) (*.f64 1/120 (pow.f64 x 5))) (tan.f64 x))
	60.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 x))) (cbrt.f64 (/.f64 x (tan.f64 x)))) (cbrt.f64 (/.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x)))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (*.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)))))
✓	0.4b	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -23/360) 1/6))) 2)

Compiler

Compiled 2530 to 1944 computations (23.2% 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)

series15.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

10.0ms	(.f64 x (.f64 x 1/6))
3.0ms	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
1.0ms	(*.f64 x 1/6)

rewrite41.0ms (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:

40.0ms	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
40.0ms	(.f64 x (.f64 x 1/6))
40.0ms	(*.f64 x 1/6)

simplify39.0ms (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

prune50.0ms (0.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	58	6	64

Error

0.0b

Counts

64 → 6

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (.f64 x x) (fma.f64 (*.f64 x x) -23/360 1/6))
	0.5b	(.f64 (.f64 x x) (exp.f64 (log.f64 (fma.f64 x (*.f64 x -23/360) 1/6))))
✓	0.3b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
	9.8b	(/.f64 (-.f64 (+.f64 (.f64 1/5040 (pow.f64 x 7)) (.f64 1/6 (pow.f64 x 3))) (*.f64 1/120 (pow.f64 x 5))) (tan.f64 x))
	60.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 x (tan.f64 x))) (cbrt.f64 (/.f64 x (tan.f64 x)))) (cbrt.f64 (/.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2))))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x)))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) (*.f64 (/.f64 (sin.f64 x) (cbrt.f64 (tan.f64 x))) (/.f64 1 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)))))
✓	0.4b	(pow.f64 (.f64 x (sqrt.f64 (fma.f64 x (.f64 x -23/360) 1/6))) 2)

Compiler

Compiled 929 to 689 computations (25.8% saved)

regimes81.0ms (0.6%)

Accuracy

Total 0.3b remaining (86.9%)

Threshold costs 0.3b (86.9%)

Counts

54 → 1

Compiler

Compiled 1492 to 1020 computations (31.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	14	21

Stop Event

1×

saturated

end99.0ms (0.8%)

Compiler: Compiled 163 to 100 computations (38.7% saved)

Details

analyze4.0ms (0%)

sample12.0s (91.9%)

simplify35.0ms (0.3%)

prune1.0ms (0%)

localize4.0ms (0%)

series13.0ms (0.1%)

rewrite101.0ms (0.8%)

simplify35.0ms (0.3%)

prune149.0ms (1.1%)

localize5.0ms (0%)

series5.0ms (0%)

rewrite34.0ms (0.3%)

simplify32.0ms (0.2%)

prune56.0ms (0.4%)

localize6.0ms (0%)

series47.0ms (0.4%)

rewrite48.0ms (0.4%)

simplify42.0ms (0.3%)

prune106.0ms (0.8%)

localize6.0ms (0%)

series15.0ms (0.1%)

rewrite41.0ms (0.3%)

simplify39.0ms (0.3%)

prune50.0ms (0.4%)

regimes81.0ms (0.6%)

simplify2.0ms (0%)

end99.0ms (0.8%)

Profiling