Details

analyze935.0ms (19.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
16.4%	83.4%	0.2%	9
21.4%	78.4%	0.2%	10
25.9%	73.3%	0.8%	11
28%	70.2%	1.9%	12
39.6%	55.8%	4.6%	13
43.9%	50.4%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample227.0ms (4.7%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	68×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	11

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	5.7b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z x))
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	6.5b	(/.f64 (*.f64 y (-.f64 z x)) t)

series64.0ms (1.3%)

Counts

3 → 104

Calls

3 calls:

34.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
24.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
6.0ms	(*.f64 y (-.f64 z x))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

10.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
6.0ms	(*.f64 y (-.f64 z x))
4.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

simplify106.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
609×	`times-frac_binary64`
591×	`distribute-rgt-in_binary64`
370×	`fma-neg_binary64`
158×	`associate-l_binary64`

Counts

196 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2470
1	431	2151
2	1681	2001
3	4818	2001
4	4992	2001

prune94.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	137	5	142

Error

0.0b

Counts

142 → 5

Alt Table

Status	Error	Program
	7.3b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	7.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	2.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	5.7b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
	27.9b	(+.f64 x (/.f64 (cbrt.f64 (pow.f64 (*.f64 y (-.f64 z x)) 3)) t))

Compiler

Compiled 2478 to 709 computations (71.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series19.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

19.0ms

(fma.f64 (/.f64 y t) (-.f64 z x) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 y t) (-.f64 z x) x)

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
389×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
294×	`times-frac_binary64`

Counts

58 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	87	635
2	197	623
3	473	623
4	2335	623
5	4674	623
6	5331	623

prune17.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	24	5	29

Error

0.0b

Counts

29 → 5

Alt Table

Status	Error	Program
	7.3b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	7.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	2.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
▶	5.7b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
	27.9b	(+.f64 x (/.f64 (cbrt.f64 (pow.f64 (*.f64 y (-.f64 z x)) 3)) t))

Compiler

Compiled 385 to 142 computations (63.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z x))
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
✓	0.4b	(/.f64 1 (/.f64 t (*.f64 y (-.f64 z x))))
✓	6.5b	(/.f64 t (*.f64 y (-.f64 z x)))

series160.0ms (3.3%)

Counts

3 → 128

Calls

3 calls:

101.0ms	(/.f64 1 (/.f64 t (*.f64 y (-.f64 z x))))
35.0ms	(/.f64 t (*.f64 y (-.f64 z x)))
23.0ms	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64`
29×	`add-exp-log_binary64`
27×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 109

Calls

3 calls:

8.0ms	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
7.0ms	(/.f64 1 (/.f64 t (*.f64 y (-.f64 z x))))
5.0ms	(/.f64 t (*.f64 y (-.f64 z x)))

simplify127.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-def_binary64`
458×	`distribute-rgt-in_binary64`
423×	`distribute-lft-in_binary64`
269×	`associate-/l/_binary64`
178×	`fma-neg_binary64`

Counts

237 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	4017
1	500	3446
2	1832	3256
3	4772	3256
4	5027	3256

prune161.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	237	5	242

Error

0.0b

Counts

242 → 5

Alt Table

Status	Error	Program
▶	2.6b	(+.f64 x (/.f64 1 (/.f64 (/.f64 t y) (-.f64 z x))))
	7.3b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	7.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	2.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	5.7b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))

Compiler

Compiled 4569 to 1653 computations (63.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 (/.f64 t y) (-.f64 z x))))
✓	0.4b	(/.f64 1 (/.f64 (/.f64 t y) (-.f64 z x)))
✓	7.5b	(/.f64 (/.f64 t y) (-.f64 z x))

series88.0ms (1.8%)

Counts

3 → 144

Calls

3 calls:

40.0ms	(/.f64 (/.f64 t y) (-.f64 z x))
24.0ms	(/.f64 1 (/.f64 (/.f64 t y) (-.f64 z x)))
23.0ms	(+.f64 x (/.f64 1 (/.f64 (/.f64 t y) (-.f64 z x))))

rewrite168.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

772×	`times-frac_binary64`
463×	`*-un-lft-identity_binary64`
460×	`add-sqr-sqrt_binary64`
328×	`add-cube-cbrt_binary64`
76×	`associate-/r*_binary64`

Counts

3 → 434

Calls

3 calls:

71.0ms	(+.f64 x (/.f64 1 (/.f64 (/.f64 t y) (-.f64 z x))))
16.0ms	(/.f64 1 (/.f64 (/.f64 t y) (-.f64 z x)))
12.0ms	(/.f64 (/.f64 t y) (-.f64 z x))

simplify451.0ms (9.3%)

Algorithm

1×	egg-herbie

Rules

518×	`fma-def_binary64`
427×	`distribute-rgt-in_binary64`
369×	`associate-/r/_binary64`
270×	`associate-/l/_binary64`
186×	`fma-neg_binary64`

Counts

578 → 556

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	13398
1	989	11976
2	3092	11727
3	4828	11727
4	4990	11727
5	5000	11727
6	4967	11727

prune299.0ms (6.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	555	1	556
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	555	6	561

Error

Counts

561 → 6

Alt Table

Status	Error	Program
✓	2.6b	(+.f64 x (/.f64 1 (/.f64 (/.f64 t y) (-.f64 z x))))
	7.3b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	7.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	2.3b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	5.7b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
	5.7b	(+.f64 x (.f64 (/.f64 1 (/.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) 1)) (/.f64 1 (/.f64 (/.f64 t (cbrt.f64 y)) (-.f64 z x)))))

Compiler

Compiled 13247 to 3927 computations (70.4% saved)

regimes731.0ms (15.1%)

Accuracy

Total 2.3b remaining (99.5%)

Threshold costs 0b (0%)

Counts

54 → 3

Compiler

Compiled 4315 to 2777 computations (35.6% saved)

bsearch64.0ms (1.3%)

Steps

Iters	Range		Point
11	7.392715445914405e+130	4.326610689056248e+153	2.050710958518032e+142
9	-7.384426320371462e-249	-3.794694724003662e-256	-2.2786730843016057e-249

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`/-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	71
1	36	71
2	40	71
3	42	71
4	43	71
5	42	71

end1.0ms (0%)

Compiler: Compiled 52 to 29 computations (44.2% saved)

sample878.0ms (18.2%)

Algorithm

1×

intervals

Results

330.0ms	8000×	body	128	valid
91.0ms	2073×	body	128	invalid

Compiler

Compiled 165 to 103 computations (37.6% saved)

Details

analyze935.0ms (19.3%)

sample227.0ms (4.7%)

simplify83.0ms (1.7%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series64.0ms (1.3%)

rewrite24.0ms (0.5%)

simplify106.0ms (2.2%)

prune94.0ms (2%)

localize6.0ms (0.1%)

series19.0ms (0.4%)

rewrite1.0ms (0%)

simplify70.0ms (1.5%)

prune17.0ms (0.4%)

localize8.0ms (0.2%)

series160.0ms (3.3%)

rewrite27.0ms (0.5%)

simplify127.0ms (2.6%)

prune161.0ms (3.3%)

localize10.0ms (0.2%)

series88.0ms (1.8%)

rewrite168.0ms (3.5%)

simplify451.0ms (9.3%)

prune299.0ms (6.2%)

regimes731.0ms (15.1%)

bsearch64.0ms (1.3%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample878.0ms (18.2%)

Profiling