Details

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample537.0ms (22%)

Infinites

26% of outputs are infinite.

Results

461.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify25.0ms (1%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-def_binary64`
257×	`fma-neg_binary64`
76×	`cancel-sign-sub-inv_binary64`
55×	`sub-neg_binary64`
32×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	54	11
3	122	11
4	222	9
5	361	9
6	423	9
7	587	9
8	645	9
9	664	9
10	593	9

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 33 to 25 computations (24.2% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
✓	0.1b	(fma.f64 x -3/25 -253/1000)

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
2.0ms	(fma.f64 x -3/25 -253/1000)

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
0.0ms	(fma.f64 x -3/25 -253/1000)

simplify75.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-l_binary64`
533×	`fma-neg_binary64`
477×	`associate-r_binary64`
446×	`unsub-neg_binary64`
418×	`times-frac_binary64`

Counts

44 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	455
1	77	344
2	166	341
3	592	341
4	2915	341
5	4504	341
6	5515	341

prune38.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	32	6	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	7	39

Error

0.0b

Counts

39 → 7

Alt Table

Status	Error	Program
	9.4b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1) 3))
	49.1b	(fma.f64 x (*.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) (sqrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
	0.3b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000)) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
	5.0b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1))) (cbrt.f64 (fma.f64 x (fma.f64 x -3/25 -253/1000) 1)))

Compiler

Compiled 571 to 445 computations (22.1% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
✓	0.1b	(*.f64 253/1000 x)
✓	0.2b	(*.f64 3/25 (pow.f64 x 2))

series8.0ms (0.3%)

Counts

3 → 3

Calls

3 calls:

3.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
3.0ms	(*.f64 3/25 (pow.f64 x 2))
2.0ms	(*.f64 253/1000 x)

rewrite18.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`associate-r_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 63

Calls

3 calls:

9.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
4.0ms	(*.f64 3/25 (pow.f64 x 2))
3.0ms	(*.f64 253/1000 x)

simplify108.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
484×	`associate-l_binary64`
452×	`distribute-rgt-out_binary64`
388×	`associate-r_binary64`
351×	`cancel-sign-sub-inv_binary64`

Counts

66 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	705
1	226	611
2	573	582
3	2216	580
4	4154	580
5	4978	580
6	4929	580

prune163.0ms (6.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	93	6	99

Error

0.0b

Counts

99 → 6

Alt Table

Status	Error	Program
	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
	49.1b	(fma.f64 x (*.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) (sqrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
	0.3b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000)) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) (cbrt.f64 (fma.f64 x -3/25 -253/1000))) 1)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))

Compiler

Compiled 1669 to 1330 computations (20.3% saved)

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x))
	0.1b	(*.f64 253/1000 x)
✓	0.1b	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))
✓	0.2b	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))

series29.0ms (1.2%)

Counts

3 → 24

Calls

3 calls:

12.0ms	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))
11.0ms	(+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x))
6.0ms	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))

rewrite28.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
12×	`associate-l_binary64`
10×	`sqrt-prod_binary64`
10×	`add-cbrt-cube_binary64`

Counts

3 → 74

Calls

3 calls:

10.0ms	(.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))
9.0ms	(+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x))
6.0ms	(*.f64 (sqrt.f64 3/25) (pow.f64 x 2))

simplify145.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-neg_binary64`
382×	`unswap-sqr_binary64`
375×	`*-commutative_binary64`
290×	`fma-def_binary64`
219×	`distribute-rgt-in_binary64`

Counts

98 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	102	1180
1	255	1111
2	819	1068
3	1879	1040
4	3901	1000
5	4918	1000
6	4947	1000

prune252.0ms (10.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	2	1	3
Picked	0	1	1
Done	1	1	2
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 3/25) (cbrt.f64 3/25))) (.f64 (sqrt.f64 (cbrt.f64 3/25)) (.f64 (sqrt.f64 3/25) (pow.f64 x 2)))) (*.f64 253/1000 x)))
	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 (sqrt.f64 3/25)) (.f64 x (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)))) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))

Compiler

Compiled 2826 to 2374 computations (16% saved)

localize17.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 253/1000 x)
✓	0.2b	(.f64 x (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 3/25)) (.f64 x (*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2))))
✓	0.3b	(*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2))

series47.0ms (1.9%)

Counts

3 → 36

Calls

3 calls:

19.0ms	(*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2))
19.0ms	(.f64 x (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)))
9.0ms	(.f64 (sqrt.f64 (sqrt.f64 3/25)) (.f64 x (*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2))))

rewrite26.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
22×	`prod-exp_binary64`
19×	`add-cbrt-cube_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`

Counts

3 → 82

Calls

3 calls:

11.0ms	(.f64 (sqrt.f64 (sqrt.f64 3/25)) (.f64 x (*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2))))
6.0ms	(.f64 x (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)))
4.0ms	(*.f64 x (pow.f64 (sqrt.f64 3/25) 3/2))

simplify158.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-def_binary64`
557×	`unswap-sqr_binary64`
530×	`*-commutative_binary64`
308×	`associate-/l*_binary64`
261×	`log-prod_binary64`

Counts

118 → 117

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	1842
1	244	1596
2	828	1542
3	1361	1303
4	2577	1253
5	4360	1253
6	4951	1253

prune315.0ms (12.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	139	5	144

Error

Counts

144 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 1 (+.f64 (.f64 (.f64 x (sqrt.f64 3/25)) (.f64 x (sqrt.f64 3/25))) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 (sqrt.f64 3/25)) (.f64 x (.f64 x (pow.f64 (sqrt.f64 3/25) 3/2)))) (.f64 253/1000 x)))
	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 (sqrt.f64 3/25)) (.f64 (pow.f64 (sqrt.f64 3/25) 3/2) (.f64 x x))) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 3/25) (.f64 (sqrt.f64 3/25) (pow.f64 x 2))) (*.f64 253/1000 x)))

Compiler

Compiled 3342 to 2743 computations (17.9% saved)

regimes221.0ms (9.1%)

Accuracy

Total 0.1b remaining (92.1%)

Threshold costs 0.1b (92.1%)

Counts

38 → 1

Compiler

Compiled 1600 to 1314 computations (17.9% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`distribute-lft-neg-in_binary64`
8×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	24	28
2	32	28
3	53	28
4	69	28
5	84	28
6	91	28
7	94	28
8	95	28
9	93	28

end183.0ms (7.5%)

Compiler: Compiled 120 to 101 computations (15.8% saved)

Details

analyze1.0ms (0%)

sample537.0ms (22%)

simplify25.0ms (1%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify75.0ms (3.1%)

prune38.0ms (1.6%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite18.0ms (0.8%)

simplify108.0ms (4.4%)

prune163.0ms (6.7%)

localize15.0ms (0.6%)

series29.0ms (1.2%)

rewrite28.0ms (1.2%)

simplify145.0ms (5.9%)

prune252.0ms (10.3%)

localize17.0ms (0.7%)

series47.0ms (1.9%)

rewrite26.0ms (1.1%)

simplify158.0ms (6.5%)

prune315.0ms (12.9%)

regimes221.0ms (9.1%)

simplify8.0ms (0.3%)

end183.0ms (7.5%)

Profiling