Details

analyze1.9s (15.3%)

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
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample6.6s (51.6%)

Results

4.1s	4243×	body	2048	valid
1.5s	1957×	body	1024	valid
532.0ms	1013×	body	512	valid
198.0ms	522×	body	256	valid
108.0ms	521×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

686×	`div-sub_binary64`
546×	`sub-neg_binary64`
397×	`neg-mul-1_binary64`
344×	`neg-sub0_binary64`
311×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	31	19
2	72	17
3	203	17
4	532	17
5	1340	17
6	2710	17
7	3748	17
8	4643	17
9	4981	17

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.4b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series10.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
3.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
1.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

simplify120.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

667×	`times-frac_binary64`
628×	`fma-def_binary64`
405×	`fma-neg_binary64`
337×	`associate-/l*_binary64`
292×	`associate-/r*_binary64`

Counts

63 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1379
1	209	1264
2	549	1261
3	1434	1259
4	4502	1259
5	5039	1259

prune100.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	3	61

Error

0.4b

Counts

61 → 3

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
	0.6b	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
	2.0b	(.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 1307 to 946 computations (27.6% saved)

localize24.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.0b	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	0.5b	(asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series10.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
3.0ms	(asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
37×	`times-frac_binary64`

Counts

2 → 82

Calls

2 calls:

15.0ms	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
1.0ms	(asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

simplify248.0ms (2%)

Algorithm

1×	egg-herbie

Rules

907×	`fma-def_binary64`
390×	`fma-neg_binary64`
350×	`distribute-rgt-in_binary64`
308×	`associate-/l*_binary64`
289×	`distribute-lft-in_binary64`

Counts

106 → 102

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	4123
1	213	3340
2	591	2574
3	1761	2574
4	4510	2556
5	4871	2556
6	4876	2556

prune449.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	146	6	152

Error

0.4b

Counts

152 → 6

Alt Table

Status	Error	Program
	61.9b	(/.f64 (-.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (+.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
▶	0.6b	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
	1.9b	(-.f64 (/.f64 (PI.f64) 2) (.f64 (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
	2.4b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 2)) (neg.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.0b	(.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.7b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))

Compiler

Compiled 7149 to 5131 computations (28.2% saved)

localize18.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6)))
✓	0.4b	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))

series12.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

7.0ms	(+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6)))
6.0ms	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`fma-def_binary64`
6×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 32

Calls

2 calls:

9.0ms	(+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6)))
1.0ms	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

754×	`associate-+l+_binary64`
349×	`cancel-sign-sub-inv_binary64`
323×	`distribute-rgt-out_binary64`
279×	`sub-neg_binary64`
212×	`distribute-rgt-in_binary64`

Counts

44 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	735
1	120	659
2	339	659
3	1429	656
4	4569	656
5	5063	656

prune123.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Error

0.4b

Counts

50 → 6

Alt Table

Status	Error	Program
	61.9b	(/.f64 (-.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (+.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	1.9b	(-.f64 (/.f64 (PI.f64) 2) (.f64 (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
	2.4b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 2)) (neg.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
▶	0.6b	(expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))))
	2.0b	(.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.7b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))

Compiler

Compiled 1544 to 1124 computations (27.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1)))
	0.0b	(+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6)))
✓	0.0b	(expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))))
	0.4b	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))

series1.4s (10.8%)

Counts

2 → 24

Calls

2 calls:

1.4s	(log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1)))
6.0ms	(expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

1.0ms	(log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1)))
1.0ms	(expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))))

simplify256.0ms (2%)

Algorithm

1×	egg-herbie

Rules

594×	`sqr-pow_binary64`
514×	`distribute-rgt-out_binary64`
472×	`unswap-sqr_binary64`
367×	`distribute-lft-out_binary64`
356×	`fma-def_binary64`

Counts

46 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	1100
1	50	1011
2	79	1011
3	148	1011
4	367	1011
5	1162	1011
6	2147	1011
7	2256	1011
8	2616	1011
9	3109	1011
10	3936	1011
11	4190	1011
12	4856	1011
13	4957	1011
14	4824	1011

prune144.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Error

0.4b

Counts

82 → 6

Alt Table

Status	Error	Program
	61.9b	(/.f64 (-.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (+.f64 (/.f64 (PI.f64) 2) (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	3.2b	(expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1)))) (cbrt.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))))) (cbrt.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))))))
	1.9b	(-.f64 (/.f64 (PI.f64) 2) (.f64 (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) 2) (cbrt.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
	2.1b	(.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))))) (cbrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1)))))) (cbrt.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))))))
	2.4b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 2)) (neg.f64 (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
✓	0.6b	(expm1.f64 (log1p.f64 (acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))))

Compiler

Compiled 2002 to 1516 computations (24.3% saved)

regimes684.0ms (5.4%)

Accuracy

Total 0.0b remaining (4.2%)

Threshold costs 0.0b (4.2%)

Counts

90 → 1

Compiler

Compiled 9605 to 7336 computations (23.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	22	28
2	25	28
3	27	28
4	28	28
5	27	28

end371.0ms (2.9%)

Compiler: Compiled 277 to 211 computations (23.8% saved)

Details

analyze1.9s (15.3%)

sample6.6s (51.6%)

simplify79.0ms (0.6%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series10.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify120.0ms (0.9%)

prune100.0ms (0.8%)

localize24.0ms (0.2%)

series10.0ms (0.1%)

rewrite37.0ms (0.3%)

simplify248.0ms (2%)

prune449.0ms (3.5%)

localize18.0ms (0.1%)

series12.0ms (0.1%)

rewrite13.0ms (0.1%)

simplify90.0ms (0.7%)

prune123.0ms (1%)

localize23.0ms (0.2%)

series1.4s (10.8%)

rewrite3.0ms (0%)

simplify256.0ms (2%)

prune144.0ms (1.1%)

regimes684.0ms (5.4%)

simplify5.0ms (0%)

end371.0ms (2.9%)

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