Details

analyze44.0ms (1.1%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample67.0ms (1.7%)

Algorithm

1×

intervals

Results

31.0ms	75×	body	2048	valid
13.0ms	132×	body	128	valid
7.0ms	26×	body	1024	valid
3.0ms	13×	body	512	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify21.0ms (0.5%)

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

prune3.0ms (0.1%)

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

13.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

Compiler

Compiled 24 to 18 computations (25% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (+.f64 N 1))
✓	2.2b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series6.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

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

rewrite11.0ms (0.3%)

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:

6.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))

simplify138.0ms (3.5%)

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

prune55.0ms (1.4%)

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

0.4b

Counts

49 → 1

Alt Table

Status	Error	Program
▶	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 908 to 499 computations (45% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(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:

1.0ms

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

simplify166.0ms (4.3%)

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

prune20.0ms (0.5%)

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)))))
	1.7b	(.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)))))
	8.5b	(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)))))
✓	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 312 to 192 computations (38.5% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(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)))))
✓	17.2b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series13.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

7.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))
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)))))

rewrite21.0ms (0.5%)

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:

10.0ms	(*.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)))))
2.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

simplify184.0ms (4.7%)

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

prune217.0ms (5.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	109	6	115

Error

0.4b

Counts

115 → 6

Alt Table

Status	Error	Program
	8.5b	(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)))))
▶	0.6b	(.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)))))))
	1.7b	(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	1.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (.f64 (cbrt.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)))))))
	4.4b	(*.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)))
✓	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 3040 to 1896 computations (37.6% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.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))))))
	0.4b	(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)))) (.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)))))))
	17.2b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))

series11.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

8.0ms

(*.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))))))

3.0ms

(*.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)))))))

rewrite82.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`sqrt-prod_binary64`
83×	`sqrt-pow1_binary64`
78×	`add-sqr-sqrt_binary64`
63×	`pow1_binary64`
43×	`pow1/2_binary64`

Counts

2 → 137

Calls

2 calls:

26.0ms

(*.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)))))))

19.0ms

(*.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))))))

simplify225.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-def_binary64`
529×	`unswap-sqr_binary64`
414×	`log-prod_binary64`
373×	`associate-l_binary64`
351×	`*-commutative_binary64`

Counts

161 → 139

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	86	2476
1	121	2303
2	343	2221
3	1033	2164
4	2172	2164
5	3733	2134
6	4411	2134
7	4881	2134

prune596.0ms (15.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	216	7	223

Error

0.4b

Counts

223 → 7

Alt Table

Status	Error	Program
	1.4b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) 3)))
	1.7b	(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))
	8.5b	(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)))))
✓	0.6b	(.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)))))))
	4.4b	(*.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)))
	0.7b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))) (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N)))))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (fma.f64 N N N))))))))
✓	0.4b	(atan2.f64 1 (+.f64 1 (fma.f64 N N N)))

Compiler

Compiled 7729 to 4973 computations (35.7% saved)

regimes293.0ms (7.5%)

Accuracy

Total 0.0b remaining (11.3%)

Threshold costs 0.0b (11.3%)

Counts

89 → 1

Compiler

Compiled 4548 to 3098 computations (31.9% saved)

simplify4.0ms (0.1%)

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

end1.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample1.7s (42.8%)

Algorithm

1×

intervals

Results

610.0ms	2058×	body	2048	valid
239.0ms	4148×	body	128	valid
233.0ms	1011×	body	1024	valid
83.0ms	509×	body	512	valid
29.0ms	274×	body	256	valid

Compiler

Compiled 226 to 152 computations (32.7% 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

analyze44.0ms (1.1%)

sample67.0ms (1.7%)

simplify21.0ms (0.5%)

prune3.0ms (0.1%)

localize12.0ms (0.3%)

series6.0ms (0.1%)

rewrite11.0ms (0.3%)

simplify138.0ms (3.5%)

prune55.0ms (1.4%)

localize9.0ms (0.2%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify166.0ms (4.3%)

prune20.0ms (0.5%)

localize13.0ms (0.3%)

series13.0ms (0.3%)

rewrite21.0ms (0.5%)

simplify184.0ms (4.7%)

prune217.0ms (5.6%)

localize18.0ms (0.5%)

series11.0ms (0.3%)

rewrite82.0ms (2.1%)

simplify225.0ms (5.8%)

prune596.0ms (15.3%)

regimes293.0ms (7.5%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.7s (42.8%)

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