Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.9s (43.4%)

Results

884.0ms	2109×	body	2048	valid
423.0ms	4274×	body	128	valid
347.0ms	1056×	body	1024	valid
127.0ms	524×	body	512	valid
52.0ms	293×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

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

17.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	1.9b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series3.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

2.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
2.0ms	(atan.f64 (+.f64 N 1))

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
392×	`unsub-neg_binary64`
319×	`distribute-rgt-in_binary64`
308×	`unswap-sqr_binary64`
275×	`times-frac_binary64`

Counts

40 → 48

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	72	836
1	128	555
2	354	501
3	1262	498
4	2924	498
5	4651	491
6	4824	491

prune36.0ms (0.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	1	49

Error

0.5b

Counts

49 → 1

Alt Table

Status	Error	Program
▶	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 908 to 499 computations (45% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series2.0ms (0%)

Counts

1 → 0

Calls

1 calls:

1.0ms

(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

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 → 9

Calls

1 calls:

0.0ms

(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

simplify133.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

9 → 10

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	156
1	21	133
2	29	133
3	41	133
4	54	133
5	61	133
6	93	133
7	157	133
8	335	133
9	641	133
10	645	133
11	775	133
12	929	133
13	1097	133
14	1326	133
15	1627	133
16	1975	133
17	2450	133
18	3068	133
19	3264	133
20	3438	133
21	3552	133
22	3599	133
23	3651	133
24	4529	133
25	4833	133

prune9.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	8	2	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	8	3	11

Error

0.5b

Counts

11 → 3

Alt Table

Status	Error	Program
	11.2b	(cbrt.f64 (.f64 (.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
▶	1.1b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 252 to 154 computations (38.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	0.6b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
✓	14.7b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series5.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
1.0ms	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

5.0ms	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

simplify109.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

498×	`log-prod_binary64`
465×	`*-commutative_binary64`
441×	`unswap-sqr_binary64`
425×	`log-div_binary64`
306×	`sqr-pow_binary64`

Counts

80 → 75

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	52	1385
1	75	1281
2	181	1233
3	389	1149
4	720	1054
5	1324	1054
6	2519	1040
7	4285	1040
8	4994	1040
9	4835	1040

prune107.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	108	6	114

Error

0.4b

Counts

114 → 6

Alt Table

Status	Error	Program
	5.1b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	11.2b	(cbrt.f64 (.f64 (.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	1.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (*.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
▶	1.7b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (sqrt.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
✓	1.1b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 3140 to 1955 computations (37.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
✓	0.7b	(*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
✓	6.9b	(sqrt.f64 (*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
✓	15.2b	(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series1.0s (24.1%)

Counts

3 → 36

Calls

3 calls:

347.0ms

(sqrt.f64 (*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))

346.0ms

(*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))

345.0ms

(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
39×	`sqrt-prod_binary64`
27×	`cbrt-prod_binary64`
26×	`pow1_binary64`
23×	`sqrt-pow1_binary64`

Counts

3 → 108

Calls

3 calls:

8.0ms

(*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))

3.0ms

(sqrt.f64 (*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))

1.0ms

(cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

simplify132.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

497×	`unswap-sqr_binary64`
465×	`log-prod_binary64`
414×	`associate-+l+_binary64`
398×	`distribute-rgt-in_binary64`
368×	`distribute-lft-in_binary64`

Counts

144 → 105

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	93	2394
1	117	2226
2	306	2177
3	735	2016
4	1397	2010
5	4562	2010
6	4946	2010
7	4935	2010

prune434.0ms (10.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	268	1	269
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	268	7	275

Error

0.4b

Counts

275 → 7

Alt Table

Status	Error	Program
	5.1b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (.f64 (*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	11.2b	(cbrt.f64 (.f64 (.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	2.2b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (sqrt.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (exp.f64 (log.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))) (*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	1.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (*.f64 (cbrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))
✓	1.7b	(.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (sqrt.f64 (.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))) (*.f64 (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
✓	1.1b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))

Compiler

Compiled 19299 to 12175 computations (36.9% saved)

regimes99.0ms (2.3%)

Accuracy

Total 0.0b remaining (9.7%)

Threshold costs 0.0b (9.7%)

Counts

45 → 1

Compiler

Compiled 3034 to 1998 computations (34.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	9	11
2	8	11

end171.0ms (4%)

Compiler: Compiled 289 to 186 computations (35.6% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze1.0ms (0%)

sample1.9s (43.4%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series3.0ms (0.1%)

rewrite7.0ms (0.2%)

simplify73.0ms (1.7%)

prune36.0ms (0.8%)

localize4.0ms (0.1%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify133.0ms (3.1%)

prune9.0ms (0.2%)

localize7.0ms (0.2%)

series5.0ms (0.1%)

rewrite11.0ms (0.2%)

simplify109.0ms (2.5%)

prune107.0ms (2.5%)

localize12.0ms (0.3%)

series1.0s (24.1%)

rewrite20.0ms (0.5%)

simplify132.0ms (3.1%)

prune434.0ms (10.1%)

regimes99.0ms (2.3%)

simplify2.0ms (0%)

end171.0ms (4%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11