Details

analyze16.0ms (0.9%)

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
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample152.0ms (9%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 45 to 27 computations (40% saved)

simplify112.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune3.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 80 to 44 computations (45% saved)

localize8.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	3.6b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	31.3b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series42.0ms (2.5%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
12.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
8.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

rewrite15.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 64

Calls

3 calls:

6.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
3.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
3.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

simplify100.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

485×	`fma-def_binary64`
328×	`times-frac_binary64`
299×	`associate-/l*_binary64`
294×	`fma-neg_binary64`
248×	`associate-/r*_binary64`

Counts

136 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	2837
1	356	2636
2	1254	2600
3	4560	2600
4	5037	2600

prune90.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	4	137

Error

0.3b

Counts

137 → 4

Alt Table

Status	Error	Program
▶	30.2b	1
	37.4b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	33.3b	-1
✓	31.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 3942 to 2061 computations (47.7% saved)

localize0.0ms (0%)

prune3.0ms (0.2%)

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

0.3b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	30.2b	1
	37.4b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
▶	33.3b	-1
✓	31.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 54 to 37 computations (31.5% saved)

localize0.0ms (0%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Error

0.3b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	30.2b	1
▶	37.4b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	33.3b	-1
✓	31.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 51 to 34 computations (33.3% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	16.9b	(/.f64 (.f64 x x) (.f64 y y))

series56.0ms (3.3%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(/.f64 (.f64 x x) (.f64 y y))
26.0ms	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)

rewrite6.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
4×	`cbrt-unprod_binary64`
4×	`cbrt-undiv_binary64`
4×	`div-exp_binary64`

Counts

2 → 33

Calls

2 calls:

4.0ms	(/.f64 (.f64 x x) (.f64 y y))
0.0ms	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)

simplify63.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

537×	`times-frac_binary64`
413×	`fma-def_binary64`
366×	`*-commutative_binary64`
344×	`unswap-sqr_binary64`
334×	`associate-/l*_binary64`

Counts

81 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1134
1	139	971
2	467	946
3	1988	923
4	3211	923
5	4982	923

prune22.0ms (1.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	53	4	57

Error

0.3b

Counts

57 → 4

Alt Table

Status	Error	Program
✓	30.2b	1
✓	37.4b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	33.3b	-1
✓	31.9b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 834 to 348 computations (58.3% saved)

regimes153.0ms (9%)

Accuracy

Total 11.8b remaining (97%)

Threshold costs 0b (0%)

Counts

10 → 5

Compiler

Compiled 967 to 627 computations (35.2% saved)

bsearch63.0ms (3.7%)

Steps

Iters	Range		Point
5	4.091312197211709e+122	9.156220450366902e+122	6.904674213912628e+122
8	4.5453559530252217e-156	2.6069563685244264e-153	1.8162755885967747e-154
8	-3.254812911222365e-106	-4.9966956754840317e-110	-4.496742760871901e-109
10	-6.537115956139072e+114	-4.350980272221332e+102	-4.9056520310025977e+114

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`
3×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	91
1	40	91
2	54	91
3	60	91
4	64	91
5	65	91
6	63	91

end1.0ms (0.1%)

Compiler: Compiled 65 to 42 computations (35.4% saved)

sample773.0ms (45.7%)

Algorithm

1×

intervals

Results

504.0ms

8000×

body

128

valid

Compiler

Compiled 128 to 83 computations (35.2% saved)

Details

analyze16.0ms (0.9%)

sample152.0ms (9%)

simplify112.0ms (6.6%)

prune3.0ms (0.2%)

localize8.0ms (0.5%)

series42.0ms (2.5%)

rewrite15.0ms (0.9%)

simplify100.0ms (5.9%)

prune90.0ms (5.3%)

localize0.0ms (0%)

prune3.0ms (0.2%)

localize0.0ms (0%)

prune2.0ms (0.1%)

localize6.0ms (0.4%)

series56.0ms (3.3%)

rewrite6.0ms (0.4%)

simplify63.0ms (3.7%)

prune22.0ms (1.3%)

regimes153.0ms (9%)

bsearch63.0ms (3.7%)

simplify6.0ms (0.3%)

end1.0ms (0.1%)

sample773.0ms (45.7%)

Profiling