Details

analyze1.8s (15.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample9.2s (78%)

Results

5.7s	2062×	body	2048	valid
2.2s	3117×	body	1024	valid
652.0ms	1552×	body	512	valid
224.0ms	782×	body	256	valid
176.0ms	122×	body	4096	valid
116.0ms	621×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`div-sub_binary64`
430×	`fma-def_binary64`
335×	`times-frac_binary64`
160×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	67	14
5	115	14
6	212	14
7	416	14
8	699	14
9	1176	14
10	1555	14
11	1621	14
12	1652	14
13	1679	14
14	1689	14
15	1693	14
16	1693	14
17	1592	14

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

34.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	34.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.6b	(-.f64 x (sin.f64 x))
✓	1.6b	(-.f64 x (tan.f64 x))

series21.0ms (0.2%)

Counts

3 → 30

Calls

3 calls:

11.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
7.0ms	(-.f64 x (tan.f64 x))
3.0ms	(-.f64 x (sin.f64 x))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

3 → 114

Calls

3 calls:

8.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
3.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
368×	`fma-neg_binary64`
252×	`associate-/l/_binary64`
250×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-in_binary64`

Counts

144 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3004
1	594	2580
2	1993	2458
3	4734	2458
4	4868	2458

prune65.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	3	154

Error

Counts

154 → 3

Alt Table

Status	Error	Program
	34.1b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
▶	29.0b	(fma.f64 9/40 (*.f64 x x) -1/2)
✓	34.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 3141 to 873 computations (72.2% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 9/40 (*.f64 x x) -1/2)

series4.0ms (0%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(fma.f64 9/40 (*.f64 x x) -1/2)

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 9/40 (*.f64 x x) -1/2)

simplify49.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
474×	`unswap-sqr_binary64`
438×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	214
1	30	197
2	59	197
3	156	197
4	622	197
5	2186	197
6	2781	197
7	5149	197

prune8.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	16	3	19

Error

Counts

19 → 3

Alt Table

Status	Error	Program
▶	34.1b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	29.0b	(fma.f64 9/40 (*.f64 x x) -1/2)
✓	34.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 189 to 120 computations (36.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
	1.6b	(-.f64 x (sin.f64 x))
	1.6b	(-.f64 x (tan.f64 x))

series13.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

13.0ms

(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`log-pow_binary64`
31×	`exp-prod_binary64`
25×	`times-frac_binary64`

Counts

1 → 46

Calls

1 calls:

9.0ms

(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
417×	`unswap-sqr_binary64`
355×	`times-frac_binary64`
239×	`associate-/l*_binary64`
218×	`sub-neg_binary64`

Counts

58 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1276
1	300	1230
2	777	1196
3	3125	1180
4	4945	1180
5	4994	1180

prune93.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	234	3	237

Error

Counts

237 → 3

Alt Table

Status	Error	Program
✓	34.1b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	29.0b	(fma.f64 9/40 (*.f64 x x) -1/2)
✓	34.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 5214 to 1474 computations (71.7% saved)

regimes41.0ms (0.4%)

Accuracy

Total 0.0b remaining (8.9%)

Threshold costs 0.0b (8.9%)

Counts

13 → 3

Compiler

Compiled 234 to 166 computations (29.1% saved)

bsearch62.0ms (0.5%)

Steps

Iters	Range		Point
11	5.495478824741389e-14	1687332.7142601968	0.004699430420038539
10	-827217.4268575609	-1.3860547960016512e-6	-0.005143713995356559

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	27	40
2	35	40
3	39	40
4	41	40
5	41	40

end68.0ms (0.6%)

Compiler: Compiled 83 to 57 computations (31.3% saved)

Details

analyze1.8s (15.5%)

sample9.2s (78%)

simplify86.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series21.0ms (0.2%)

rewrite22.0ms (0.2%)

simplify109.0ms (0.9%)

prune65.0ms (0.5%)

localize4.0ms (0%)

series4.0ms (0%)

rewrite1.0ms (0%)

simplify49.0ms (0.4%)

prune8.0ms (0.1%)

localize12.0ms (0.1%)

series13.0ms (0.1%)

rewrite17.0ms (0.1%)

simplify79.0ms (0.7%)

prune93.0ms (0.8%)

regimes41.0ms (0.4%)

bsearch62.0ms (0.5%)

simplify3.0ms (0%)

end68.0ms (0.6%)

Profiling