Details

analyze1.7s (24.6%)

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)

sample51.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
5.0ms	75×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify88.0ms (1.2%)

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

prune6.0ms (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
	8.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	5.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z x))
✓	5.1b	(/.f64 (*.f64 y (-.f64 z x)) t)

series49.0ms (0.7%)

Counts

2 → 56

Calls

2 calls:

37.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
12.0ms	(*.f64 y (-.f64 z x))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 75

Calls

2 calls:

15.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
10.0ms	(*.f64 y (-.f64 z x))

simplify142.0ms (2%)

Algorithm

1×	egg-herbie

Rules

666×	`associate-/l*_binary64`
500×	`times-frac_binary64`
338×	`fma-def_binary64`
273×	`distribute-rgt-in_binary64`
259×	`distribute-lft-in_binary64`

Counts

131 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	1462
1	333	1331
2	1232	1277
3	4764	1277
4	5111	1277

prune169.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	97	8	105
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Error

0.0b

Counts

107 → 9

Alt Table

Status	Error	Program
▶	5.1b	(+.f64 x (/.f64 (-.f64 (.f64 y z) (.f64 y x)) t))
	7.5b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	5.1b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	5.1b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
	35.1b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 t)) (/.f64 (-.f64 z x) (sqrt.f64 t))))
	31.4b	(+.f64 x (.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 z x) t) y)) (sqrt.f64 (*.f64 (/.f64 (-.f64 z x) t) y))))
	33.7b	(+.f64 x (/.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x))) t))
	8.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	36.3b	(+.f64 x (/.f64 (+.f64 (.f64 z y) (.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)) y)) t))

Compiler

Compiled 2118 to 702 computations (66.9% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(-.f64 (.f64 y z) (.f64 y x))
✓	5.1b	(/.f64 (-.f64 (.f64 y z) (.f64 y x)) t)

series64.0ms (0.9%)

Counts

2 → 58

Calls

2 calls:

47.0ms	(/.f64 (-.f64 (.f64 y z) (.f64 y x)) t)
16.0ms	(-.f64 (.f64 y z) (.f64 y x))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out--_binary64`

Counts

2 → 53

Calls

2 calls:

9.0ms	(/.f64 (-.f64 (.f64 y z) (.f64 y x)) t)
5.0ms	(-.f64 (.f64 y z) (.f64 y x))

simplify184.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

442×	`div-sub_binary64`
384×	`fma-neg_binary64`
367×	`associate-l_binary64`
289×	`associate-r_binary64`
273×	`associate-*l/_binary64`

Counts

111 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1355
1	273	1293
2	898	1285
3	3423	1285
4	4939	1285
5	5105	1285

prune136.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	97	9	106

Error

0.0b

Counts

106 → 9

Alt Table

Status	Error	Program
	27.4b	(+.f64 x (/.f64 (-.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 (.f64 y x) (.f64 y x))) (.f64 t (+.f64 (.f64 y z) (*.f64 y x)))))
✓	5.1b	(+.f64 x (/.f64 (-.f64 (.f64 y z) (.f64 y x)) t))
	7.5b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
▶	5.1b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	35.1b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 t)) (/.f64 (-.f64 z x) (sqrt.f64 t))))
	31.4b	(+.f64 x (.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 z x) t) y)) (sqrt.f64 (*.f64 (/.f64 (-.f64 z x) t) y))))
	33.7b	(+.f64 x (/.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x))) t))
	8.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	36.3b	(+.f64 x (/.f64 (+.f64 (.f64 z y) (.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)) y)) t))

Compiler

Compiled 2033 to 572 computations (71.9% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z x))
✓	5.1b	(.f64 (.f64 y (-.f64 z x)) (/.f64 1 t))

series48.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

48.0ms

(*.f64 (*.f64 y (-.f64 z x)) (/.f64 1 t))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`add-cbrt-cube_binary64`
12×	`prod-exp_binary64`
9×	`times-frac_binary64`

Counts

1 → 44

Calls

1 calls:

15.0ms

(*.f64 (*.f64 y (-.f64 z x)) (/.f64 1 t))

simplify99.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

807×	`times-frac_binary64`
669×	`fma-def_binary64`
384×	`distribute-rgt-in_binary64`
380×	`distribute-lft-in_binary64`
242×	`*-commutative_binary64`

Counts

92 → 69

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	101	1120
1	265	1012
2	902	1012
3	2995	1012
4	4975	1012
5	4991	1012

prune198.0ms (2.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	128	9	137

Error

0.0b

Counts

137 → 9

Alt Table

Status	Error	Program
	27.4b	(+.f64 x (/.f64 (-.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 (.f64 y x) (.f64 y x))) (.f64 t (+.f64 (.f64 y z) (*.f64 y x)))))
✓	5.1b	(+.f64 x (/.f64 (-.f64 (.f64 y z) (.f64 y x)) t))
▶	7.5b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
✓	5.1b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	35.1b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 t)) (/.f64 (-.f64 z x) (sqrt.f64 t))))
	31.4b	(+.f64 x (.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 z x) t) y)) (sqrt.f64 (*.f64 (/.f64 (-.f64 z x) t) y))))
	33.7b	(+.f64 x (/.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x))) t))
	8.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	36.3b	(+.f64 x (/.f64 (+.f64 (.f64 z y) (.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)) y)) t))

Compiler

Compiled 2766 to 1082 computations (60.9% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z x))
✓	8.3b	(/.f64 y (/.f64 t (-.f64 z x)))

series71.0ms (1%)

Counts

2 → 72

Calls

2 calls:

38.0ms	(/.f64 y (/.f64 t (-.f64 z x)))
33.0ms	(/.f64 t (-.f64 z x))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
102×	`*-un-lft-identity_binary64`
102×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

2 → 143

Calls

2 calls:

15.0ms	(/.f64 y (/.f64 t (-.f64 z x)))
8.0ms	(/.f64 t (-.f64 z x))

simplify246.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

557×	`associate-/l*_binary64`
552×	`associate-/r/_binary64`
501×	`times-frac_binary64`
333×	`fma-def_binary64`
287×	`distribute-rgt-in_binary64`

Counts

215 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	4051
1	599	3937
2	2116	3812
3	5005	3812

prune269.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	210	3	213
Fresh	4	2	6
Picked	1	0	1
Done	1	1	2
Total	216	6	222

Error

Counts

222 → 6

Alt Table

Status	Error	Program
	27.4b	(+.f64 x (/.f64 (-.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 (.f64 y x) (.f64 y x))) (.f64 t (+.f64 (.f64 y z) (*.f64 y x)))))
✓	5.1b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	2.9b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z x)))
	7.5b	(+.f64 x (/.f64 1 (/.f64 (/.f64 t (-.f64 z x)) y)))
	8.0b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	2.9b	(+.f64 x (/.f64 (/.f64 y t) (/.f64 1 (-.f64 z x))))

Compiler

Compiled 4164 to 1078 computations (74.1% saved)

regimes1.5s (21.1%)

Accuracy

Total 1.4b remaining (99.3%)

Threshold costs 0b (0%)

Counts

92 → 3

Compiler

Compiled 9721 to 5538 computations (43% saved)

bsearch66.0ms (0.9%)

Steps

Iters	Range		Point
9	7.383312883357167e-187	2.6848585434855182e-179	1.3006984664826421e-183
7	-1.601259580662426e-28	-4.0562958854110046e-30	-7.933019809099192e-29

Compiler

Compiled 5 to 4 computations (20% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	85
1	35	85
2	40	85
3	42	85
4	43	85
5	43	85

end2.0ms (0%)

Compiler: Compiled 59 to 26 computations (55.9% saved)

sample1.7s (24.6%)

Algorithm

1×

intervals

Results

614.0ms	8000×	body	128	valid
169.0ms	2103×	body	128	invalid

Compiler

Compiled 178 to 97 computations (45.5% saved)

Details

analyze1.7s (24.6%)

sample51.0ms (0.7%)

simplify88.0ms (1.2%)

prune6.0ms (0.1%)

localize16.0ms (0.2%)

series49.0ms (0.7%)

rewrite35.0ms (0.5%)

simplify142.0ms (2%)

prune169.0ms (2.4%)

localize14.0ms (0.2%)

series64.0ms (0.9%)

rewrite19.0ms (0.3%)

simplify184.0ms (2.6%)

prune136.0ms (1.9%)

localize15.0ms (0.2%)

series48.0ms (0.7%)

rewrite26.0ms (0.4%)

simplify99.0ms (1.4%)

prune198.0ms (2.8%)

localize12.0ms (0.2%)

series71.0ms (1%)

rewrite55.0ms (0.8%)

simplify246.0ms (3.5%)

prune269.0ms (3.8%)

regimes1.5s (21.1%)

bsearch66.0ms (0.9%)

simplify10.0ms (0.1%)

end2.0ms (0%)

sample1.7s (24.6%)

Profiling