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 (48%)

Results

914.0ms	2137×	body	2048	valid
449.0ms	4293×	body	128	valid
334.0ms	1038×	body	1024	valid
143.0ms	520×	body	512	valid
53.0ms	268×	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

16.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	1.8b	(-.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))

rewrite6.0ms (0.1%)

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

simplify73.0ms (1.8%)

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

prune27.0ms (0.7%)

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)

localize6.0ms (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)))

series1.0ms (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)))

simplify129.0ms (3.2%)

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

prune11.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	7	3	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	7	4	11

Error

0.4b

Counts

11 → 4

Alt Table

Status	Error	Program
▶	1.0b	(*.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)))))
	10.7b	(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))) 3))
	1.8b	(exp.f64 (log.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 242 to 154 computations (36.4% saved)

localize6.0ms (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)))))
✓	13.0b	(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)))))

rewrite12.0ms (0.3%)

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))))

simplify106.0ms (2.6%)

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

prune112.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	106	9	115

Error

0.4b

Counts

115 → 9

Alt Table

Status	Error	Program
	2.1b	(.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)))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	2.0b	(.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))))))
	1.5b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (.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 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	1.5b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (.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))))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	1.2b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	4.8b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))
▶	0.8b	(.f64 (.f64 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)))))))
	1.1b	(.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (.f64 (sqrt.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 3412 to 2138 computations (37.3% saved)

localize13.0ms (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)))
	0.6b	(*.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)))))
	13.0b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
✓	13.5b	(cbrt.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))))))

series343.0ms (8.5%)

Counts

1 → 12

Calls

1 calls:

343.0ms

(cbrt.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))))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`cbrt-prod_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

3.0ms

(cbrt.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))))))

simplify69.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

813×	`associate-/r/_binary64`
619×	`log-prod_binary64`
449×	`associate-l_binary64`
350×	`distribute-rgt-out_binary64`
295×	`associate-r_binary64`

Counts

23 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	21	334
1	32	334
2	66	334
3	133	334
4	374	330
5	1654	330
6	2945	330
7	3838	330
8	5314	330

prune695.0ms (17.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	390	0	390
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	390	9	399

Error

0.4b

Counts

399 → 9

Alt Table

Status	Error	Program
	2.1b	(.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)))))) (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2))
✓	0.5b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))
	2.0b	(.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))))))
	1.5b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (.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 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	1.5b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (sqrt.f64 (.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))))) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	1.2b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (*.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))
	4.8b	(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (cbrt.f64 (pow.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 3)))
✓	0.8b	(.f64 (.f64 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)))))))
	1.1b	(.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (.f64 (sqrt.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 26702 to 16688 computations (37.5% saved)

regimes256.0ms (6.4%)

Accuracy

Total 0.0b remaining (14.8%)

Threshold costs 0.0b (14.8%)

Counts

113 → 1

Compiler

Compiled 9000 to 5922 computations (34.2% 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

end188.0ms (4.7%)

Compiler: Compiled 349 to 228 computations (34.7% 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 (48%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize9.0ms (0.2%)

series3.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify73.0ms (1.8%)

prune27.0ms (0.7%)

localize6.0ms (0.1%)

series1.0ms (0%)

rewrite1.0ms (0%)

simplify129.0ms (3.2%)

prune11.0ms (0.3%)

localize6.0ms (0.2%)

series5.0ms (0.1%)

rewrite12.0ms (0.3%)

simplify106.0ms (2.6%)

prune112.0ms (2.8%)

localize13.0ms (0.3%)

series343.0ms (8.5%)

rewrite3.0ms (0.1%)

simplify69.0ms (1.7%)

prune695.0ms (17.3%)

regimes256.0ms (6.4%)

simplify2.0ms (0%)

end188.0ms (4.7%)

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