Details

analyze239.0ms (15.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample25.0ms (1.7%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify232.0ms (15.1%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	19	9
3	29	9
4	45	9
5	68	9
6	108	9
7	242	9
8	447	9
9	724	9
10	1531	9
11	2311	9
12	2365	9
13	2601	9
14	2749	9
15	2747	9
16	2824	9
17	3083	9
18	3646	9
19	4638	9
20	4883	9
21	4925	9
22	4936	9
23	4933	9
24	6185	9

prune2.0ms (0.2%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series5.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`sqrt-prod_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64`
2×	`difference-of-squares_binary64`
2×	`sqrt-div_binary64`

Counts

1 → 19

Calls

1 calls:

3.0ms

(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify63.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

501×	`fma-neg_binary64`
320×	`times-frac_binary64`
249×	`distribute-rgt-neg-in_binary64`
249×	`unswap-sqr_binary64`
245×	`neg-mul-1_binary64`

Counts

31 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	503
1	217	482
2	591	473
3	2037	469
4	4433	469
5	4967	469

prune41.0ms (2.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	2	46

Error

Counts

46 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶	0.0b	(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))

Compiler

Compiled 673 to 502 computations (25.4% saved)

localize11.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.0b	(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
✓	1.0b	(expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

series9.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
4.0ms	(expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-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:

0.0ms	(expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0ms	(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))

simplify108.0ms (7%)

Algorithm

1×	egg-herbie

Rules

828×	`times-frac_binary64`
502×	`fma-neg_binary64`
285×	`distribute-rgt-neg-in_binary64`
271×	`distribute-lft-neg-in_binary64`
210×	`fma-def_binary64`

Counts

46 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	754
1	237	693
2	678	678
3	2313	671
4	4750	671
5	5665	671

prune102.0ms (6.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	107	2	109

Error

Counts

109 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.0b	(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))

Compiler

Compiled 1639 to 1248 computations (23.9% saved)

regimes37.0ms (2.4%)

Accuracy

Total 0.0b remaining (6.8%)

Threshold costs 0.0b (6.8%)

Counts

5 → 1

Compiler

Compiled 146 to 116 computations (20.5% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	19	9
3	23	9
4	25	9
5	24	9

end1.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample644.0ms (42%)

Algorithm

1×

intervals

Results

349.0ms

8000×

body

128

valid

Compiler

Compiled 32 to 24 computations (25% saved)

Details

analyze239.0ms (15.6%)

sample25.0ms (1.7%)

simplify232.0ms (15.1%)

prune2.0ms (0.2%)

localize3.0ms (0.2%)

series5.0ms (0.3%)

rewrite3.0ms (0.2%)

simplify63.0ms (4.1%)

prune41.0ms (2.7%)

localize11.0ms (0.7%)

series9.0ms (0.6%)

rewrite3.0ms (0.2%)

simplify108.0ms (7%)

prune102.0ms (6.7%)

regimes37.0ms (2.4%)

simplify5.0ms (0.3%)

end1.0ms (0%)

sample644.0ms (42%)

Profiling