Details

analyze172.0ms (9.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
62.5%	6.2%	31.3%	6
65.6%	3.1%	31.3%	7
65.6%	1.6%	32.8%	8
66.4%	0.8%	32.8%	9
66.4%	0.4%	33.2%	10
66.6%	0.2%	33.2%	11
66.6%	0.1%	33.3%	12
66.6%	0%	33.3%	13
66.6%	0%	33.3%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample16.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify161.0ms (8.7%)

Algorithm

1×	egg-herbie

Rules

1355×	`fma-neg_binary64`
877×	`fma-def_binary64`
720×	`distribute-rgt-neg-in_binary64`
564×	`cancel-sign-sub-inv_binary64`
530×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	21	11
2	49	11
3	107	11
4	170	11
5	291	11
6	516	11
7	1002	11
8	1492	11
9	2128	11
10	2734	11
11	3154	11
12	3358	11
13	3535	11
14	4106	11
15	3099	11
16	3528	11
17	4668	11
18	4732	11

prune3.0ms (0.2%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(.f64 x (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))
	0.4b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (.f64 (.f64 x x) x)))

Status

Error

Program

▶

0.1b

(*.f64 x (fma.f64 (*.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))

0.4b

(-.f64 (*.f64 2150310427208497/2251799813685248 x) (*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x)))

Compiler

Compiled 62 to 40 computations (35.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))
✓	0.1b	(fma.f64 (*.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(.f64 x (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))
0.0ms	(fma.f64 (*.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248)

series24.0ms (1.3%)

Counts

2 → 24

Calls

2 calls:

13.0ms	(.f64 x (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))
11.0ms	(fma.f64 (*.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248)

simplify47.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

907×	`distribute-rgt-in_binary64`
906×	`distribute-lft-in_binary64`
386×	`fma-def_binary64`
238×	`associate-l_binary64`
198×	`associate-r_binary64`

Counts

56 → 102

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	716
1	106	613
2	301	613
3	1063	613
4	5380	613

prune52.0ms (2.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	97	5	102
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	98	6	104

Error

0.0b

Counts

104 → 6

Alt Table

Status	Error	Program
▶	0.1b	(.f64 x (fma.f64 x (.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248))
	0.4b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (.f64 (.f64 x x) x)))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248)))
	16.9b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))))
	16.9b	(.f64 x (expm1.f64 (log1p.f64 (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))))
	0.1b	(+.f64 (.f64 (.f64 (.f64 x x) -4647935950575487/36028797018963968) x) (.f64 2150310427208497/2251799813685248 x))

Compiler

Compiled 958 to 612 computations (36.1% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (*.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248)
✓	0.1b	(.f64 x (fma.f64 x (.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(.f64 x (fma.f64 x (.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248))
0.0ms	(fma.f64 x (*.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248)

series27.0ms (1.5%)

Counts

2 → 24

Calls

2 calls:

18.0ms	(.f64 x (fma.f64 x (.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248))
9.0ms	(fma.f64 x (*.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248)

simplify93.0ms (5%)

Algorithm

1×	egg-herbie

Rules

907×	`distribute-rgt-in_binary64`
906×	`distribute-lft-in_binary64`
415×	`fma-def_binary64`
240×	`associate-l_binary64`
204×	`associate-r_binary64`

Counts

56 → 105

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	716
1	107	613
2	301	613
3	1072	613
4	5400	613

prune50.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	105	6	111

Error

0.0b

Counts

111 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 x (fma.f64 x (.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248))
	0.4b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (.f64 (.f64 x x) x)))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248)))
	16.9b	(.f64 x (log.f64 (exp.f64 (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))))
	16.9b	(.f64 x (expm1.f64 (log1p.f64 (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))))
▶	0.1b	(+.f64 (.f64 (.f64 (.f64 x x) -4647935950575487/36028797018963968) x) (.f64 2150310427208497/2251799813685248 x))

Compiler

Compiled 955 to 616 computations (35.5% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 (.f64 x x) -4647935950575487/36028797018963968) x) (.f64 2150310427208497/2251799813685248 x))
✓	0.1b	(.f64 (.f64 (*.f64 x x) -4647935950575487/36028797018963968) x)
✓	0.2b	(.f64 (.f64 x x) -4647935950575487/36028797018963968)

rewrite19.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 59

Calls

3 calls:

6.0ms

(+.f64 (*.f64 (*.f64 (*.f64 x x) -4647935950575487/36028797018963968) x) (*.f64 2150310427208497/2251799813685248 x))

6.0ms

(*.f64 (*.f64 (*.f64 x x) -4647935950575487/36028797018963968) x)

5.0ms

(*.f64 (*.f64 x x) -4647935950575487/36028797018963968)

series42.0ms (2.3%)

Counts

3 → 36

Calls

3 calls:

16.0ms

(*.f64 (*.f64 (*.f64 x x) -4647935950575487/36028797018963968) x)

16.0ms

(+.f64 (*.f64 (*.f64 (*.f64 x x) -4647935950575487/36028797018963968) x) (*.f64 2150310427208497/2251799813685248 x))

10.0ms

(*.f64 (*.f64 x x) -4647935950575487/36028797018963968)

simplify174.0ms (9.4%)

Algorithm

1×	egg-herbie

Rules

365×	`fma-def_binary64`
338×	`cancel-sign-sub-inv_binary64`
335×	`*-commutative_binary64`
297×	`distribute-rgt-in_binary64`
285×	`distribute-rgt-neg-in_binary64`

Counts

95 → 163

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	1054
1	252	900
2	893	892
3	2185	890
4	4603	887
5	5035	887

prune79.0ms (4.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	164	5	169

Error

Counts

169 → 5

Alt Table

Status	Error	Program
	29.2b	(/.f64 (fma.f64 -4623834933361588875239908999009/5070602400912917605986812821504 (.f64 x x) (.f64 (pow.f64 x 6) 21603308600652055932446485287169/1298074214633706907132624082305024)) (.f64 x (fma.f64 -4647935950575487/36028797018963968 (.f64 x x) -2150310427208497/2251799813685248)))
✓	0.1b	(.f64 x (fma.f64 x (.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248))
▶	0.4b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (.f64 (.f64 x x) x)))
	16.9b	(.f64 x (expm1.f64 (log1p.f64 (fma.f64 (.f64 x x) -4647935950575487/36028797018963968 2150310427208497/2251799813685248))))
✓	0.1b	(+.f64 (.f64 (.f64 (.f64 x x) -4647935950575487/36028797018963968) x) (.f64 2150310427208497/2251799813685248 x))

Compiler

Compiled 1575 to 987 computations (37.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 2150310427208497/2251799813685248 x) (.f64 4647935950575487/36028797018963968 (.f64 (.f64 x x) x)))
✓	0.1b	(.f64 (.f64 x x) x)
✓	0.4b	(.f64 4647935950575487/36028797018963968 (.f64 (*.f64 x x) x))

rewrite17.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`pow1_binary64`
20×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 70

Calls

3 calls:

7.0ms

(*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x))

4.0ms

(*.f64 (*.f64 x x) x)

3.0ms

(-.f64 (*.f64 2150310427208497/2251799813685248 x) (*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x)))

series43.0ms (2.3%)

Counts

3 → 36

Calls

3 calls:

15.0ms

(-.f64 (*.f64 2150310427208497/2251799813685248 x) (*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x)))

15.0ms

(*.f64 4647935950575487/36028797018963968 (*.f64 (*.f64 x x) x))

13.0ms

(*.f64 (*.f64 x x) x)

simplify83.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

928×	`fma-def_binary64`
390×	`fma-neg_binary64`
340×	`distribute-rgt-neg-in_binary64`
321×	`distribute-lft-neg-in_binary64`
311×	`cancel-sign-sub-inv_binary64`

Counts

106 → 175

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	945
1	214	836
2	756	824
3	1870	799
4	4683	799
5	4860	799

prune65.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	176	4	180

Error

Counts

180 → 4

Alt Table

Status	Error	Program
	29.2b	(/.f64 (fma.f64 -4623834933361588875239908999009/5070602400912917605986812821504 (.f64 x x) (.f64 (pow.f64 x 6) 21603308600652055932446485287169/1298074214633706907132624082305024)) (.f64 x (fma.f64 -4647935950575487/36028797018963968 (.f64 x x) -2150310427208497/2251799813685248)))
✓	0.1b	(.f64 x (fma.f64 x (.f64 x -4647935950575487/36028797018963968) 2150310427208497/2251799813685248))
	0.4b	(fma.f64 2150310427208497/2251799813685248 x (neg.f64 (.f64 4647935950575487/36028797018963968 (.f64 (*.f64 x x) x))))
✓	0.1b	(+.f64 (.f64 (.f64 (.f64 x x) -4647935950575487/36028797018963968) x) (.f64 2150310427208497/2251799813685248 x))

Compiler

Compiled 1486 to 875 computations (41.1% saved)

regimes79.0ms (4.2%)

Accuracy

Total 0.1b remaining (78.3%)

Threshold costs 0.1b (78.3%)

Compiler

Compiled 966 to 676 computations (30% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	9	11
2	9	11

end0.0ms (0%)

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

sample573.0ms (30.9%)

Algorithm

1×

intervals

Results

291.0ms

8000×

body

128

valid

Compiler

Compiled 76 to 51 computations (32.9% saved)

Details

analyze172.0ms (9.3%)

sample16.0ms (0.8%)

simplify161.0ms (8.7%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

rewrite4.0ms (0.2%)

series24.0ms (1.3%)

simplify47.0ms (2.6%)

prune52.0ms (2.8%)

localize5.0ms (0.3%)

rewrite4.0ms (0.2%)

series27.0ms (1.5%)

simplify93.0ms (5%)

prune50.0ms (2.7%)

localize7.0ms (0.4%)

rewrite19.0ms (1%)

series42.0ms (2.3%)

simplify174.0ms (9.4%)

prune79.0ms (4.3%)

localize6.0ms (0.3%)

rewrite17.0ms (0.9%)

series43.0ms (2.3%)

simplify83.0ms (4.5%)

prune65.0ms (3.5%)

regimes79.0ms (4.2%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample573.0ms (30.9%)

Profiling