Details

analyze721.0ms (17.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
21.8%	78%	0.1%	9
49.1%	50.7%	0.1%	10
52.7%	47.2%	0.1%	11
52.7%	47.2%	0.1%	12
71.7%	28.2%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample26.0ms (0.6%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 52 to 40 computations (23.1% saved)

simplify33.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
94×	`distribute-rgt-out_binary64`
88×	`associate-/l*_binary64`
66×	`associate-l_binary64`
65×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	25
1	39	25
2	71	23
3	134	23
4	247	23
5	389	23
6	567	23
7	670	23
8	831	23
9	914	23
10	974	23
11	975	23
12	972	23

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

15.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	15.6b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)
	21.2b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))

Status

Error

Program

▶

15.6b

(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)

21.2b

(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))

Compiler

Compiled 129 to 93 computations (27.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)
✓	0.1b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)
✓	0.1b	(fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984)
✓	15.1b	(/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

2.0ms	(/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248))
0.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)
0.0ms	(fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)
0.0ms	(fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984)

series119.0ms (2.8%)

Counts

4 → 72

Calls

4 calls:

105.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)
5.0ms	(fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984)
5.0ms	(/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248))
4.0ms	(fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)

simplify152.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-neg_binary64`
381×	`fma-def_binary64`
371×	`times-frac_binary64`
198×	`associate-/l/_binary64`
196×	`distribute-rgt-in_binary64`

Counts

131 → 208

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	169	3169
1	401	2956
2	1053	2853
3	3081	2628
4	4830	2624
5	5120	2624

prune286.0ms (6.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	206	2	208
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	206	4	210

Error

0.0b

Counts

210 → 4

Alt Table

Status	Error	Program
▶	10.5b	(fma.f64 y 4992947066835229/72057594037927936 x)
✓	15.6b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)
	16.5b	(+.f64 (fma.f64 5029535718965825/18014398509481984 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x) (.f64 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) (.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992))))
	21.2b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))

Compiler

Compiled 2820 to 1950 computations (30.9% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify20.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune4.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	10.5b	(fma.f64 y 4992947066835229/72057594037927936 x)
✓	15.6b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)
▶	16.5b	(+.f64 (fma.f64 5029535718965825/18014398509481984 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x) (.f64 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) (.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992))))
	21.2b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))

Compiler

Compiled 135 to 97 computations (28.1% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 5029535718965825/18014398509481984 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)
	3.1b	(/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248))
✓	3.1b	(/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248))
✓	20.2b	(.f64 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) (.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992)))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms

(*.f64 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) (*.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992)))

2.0ms

(/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248))

0.0ms

(fma.f64 5029535718965825/18014398509481984 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)

series224.0ms (5.4%)

Counts

3 → 84

Calls

3 calls:

104.0ms

(*.f64 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) (*.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992)))

69.0ms

(fma.f64 5029535718965825/18014398509481984 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)

51.0ms

(/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248))

simplify142.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
458×	`distribute-rgt-in_binary64`
445×	`distribute-lft-in_binary64`
334×	`fma-neg_binary64`
302×	`cancel-sign-sub-inv_binary64`

Counts

162 → 293

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	232	3666
1	609	3052
2	1905	2998
3	4930	2988
4	5078	2988

prune301.0ms (7.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	378	1	379
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	379	4	383

Error

Counts

383 → 4

Alt Table

Status	Error	Program
✓	10.5b	(fma.f64 y 4992947066835229/72057594037927936 x)
✓	15.6b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)
	23.9b	(+.f64 (fma.f64 5029535718965825/18014398509481984 (.f64 2251799813685248/7544303578448747 y) x) (.f64 (/.f64 y (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) (*.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992))))
▶	21.2b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))

Compiler

Compiled 7713 to 5148 computations (33.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
✓	0.1b	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
✓	4.0b	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
✓	20.4b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

4 → 96

Calls

4 calls:

12.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
7.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
6.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
4.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

series141.0ms (3.4%)

Counts

4 → 72

Calls

4 calls:

89.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
38.0ms	(.f64 y (+.f64 (.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
8.0ms	(.f64 (+.f64 (.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
6.0ms	(*.f64 (+.f64 z 1692356830115869/281474976710656) z)

simplify135.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-def_binary64`
582×	`associate-/l*_binary64`
527×	`times-frac_binary64`
219×	`associate-/l/_binary64`
213×	`associate-l_binary64`

Counts

168 → 323

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	223	2953
1	606	2434
2	2136	2398
3	4861	2394
4	4948	2394

prune166.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	322	1	323
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	324	3	327

Error

Counts

327 → 3

Alt Table

Status	Error	Program
	15.7b	(+.f64 x (/.f64 y (/.f64 (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248) (fma.f64 z (fma.f64 4992947066835229/72057594037927936 z 4429125951667411/9007199254740992) 5029535718965825/18014398509481984))))
✓	10.5b	(fma.f64 y 4992947066835229/72057594037927936 x)
✓	15.6b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z 4992947066835229/72057594037927936 4429125951667411/9007199254740992) 5029535718965825/18014398509481984) (fma.f64 z (+.f64 z 1692356830115869/281474976710656) 7544303578448747/2251799813685248)) x)

Compiler

Compiled 5405 to 3885 computations (28.1% saved)

regimes632.0ms (15.1%)

Accuracy

Total 0.1b remaining (93.8%)

Threshold costs 0.1b (93.8%)

Compiler

Compiled 6653 to 4858 computations (27% saved)

bsearch37.0ms (0.9%)

Steps

Iters	Range		Point
8	6241077350.549231	12060132633567.125	8458636247084.303
7	-1.2997463323104397e+26	-1.0788912857079549e+24	-1.0951716603370986e+24

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`*-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	48
1	44	48
2	61	46
3	80	46
4	90	46
5	93	46
6	92	46

end1.0ms (0%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

sample932.0ms (22.3%)

Algorithm

1×

intervals

Results

607.0ms

8000×

body

128

valid

Compiler

Compiled 111 to 81 computations (27% saved)

Iter	Nodes	Cost
0	19	25
1	39	25
2	71	23
3	134	23
4	247	23
5	389	23
6	567	23
7	670	23
8	831	23
9	914	23
10	974	23
11	975	23
12	972	23

Iter	Nodes	Cost
0	19	25
1	39	25
2	71	23
3	134	23
4	247	23
5	389	23
6	567	23
7	670	23
8	831	23
9	914	23
10	974	23
11	975	23
12	972	23

Details

analyze721.0ms (17.2%)

sample26.0ms (0.6%)

simplify33.0ms (0.8%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

rewrite6.0ms (0.1%)

series119.0ms (2.8%)

simplify152.0ms (3.6%)

prune286.0ms (6.8%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify20.0ms (0.5%)

prune4.0ms (0.1%)

localize22.0ms (0.5%)

rewrite12.0ms (0.3%)

series224.0ms (5.4%)

simplify142.0ms (3.4%)

prune301.0ms (7.2%)

localize14.0ms (0.3%)

rewrite34.0ms (0.8%)

series141.0ms (3.4%)

simplify135.0ms (3.2%)

prune166.0ms (4%)

regimes632.0ms (15.1%)

bsearch37.0ms (0.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample932.0ms (22.3%)

Profiling

Iter	Nodes	Cost
0	19	25
1	39	25
2	71	23
3	134	23
4	247	23
5	389	23
6	567	23
7	670	23
8	831	23
9	914	23
10	974	23
11	975	23
12	972	23