Details

analyze796.0ms (10.7%)

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.3s (17.2%)

Results

1.1s	8256×	body	128	valid
62.0ms	471×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1070×	`fma-neg_binary64`
881×	`fma-def_binary64`
768×	`times-frac_binary64`
551×	`cancel-sign-sub-inv_binary64`
514×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	25	20
2	47	20
3	78	20
4	149	20
5	228	20
6	324	20
7	500	20
8	694	20
9	867	20
10	999	20
11	2422	20
12	3920	20
13	4950	20

prune3.0ms (0%)

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

22.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	22.2b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

Compiler

Compiled 69 to 33 computations (52.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 b c) (.f64 a d))
✓	21.8b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series112.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

102.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
10.0ms	(-.f64 (.f64 b c) (.f64 a d))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 48

Calls

2 calls:

4.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
3.0ms	(-.f64 (.f64 b c) (.f64 a d))

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

491×	`fma-neg_binary64`
380×	`associate-l_binary64`
348×	`fma-def_binary64`
315×	`associate-r_binary64`
247×	`associate-/l*_binary64`

Counts

144 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2762
1	323	2614
2	1084	2567
3	4430	2567
4	4952	2567

prune88.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	100	9	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	9	110

Error

2.6b

Counts

110 → 9

Alt Table

Status	Error	Program
	22.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (-.f64 (.f64 b c) (*.f64 a d))))
	36.3b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	14.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (hypot.f64 d c)))
	40.7b	(neg.f64 (/.f64 a d))
▶	13.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	22.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 c c (.f64 d d))) (cbrt.f64 (fma.f64 c c (.f64 d d))))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (cbrt.f64 (fma.f64 c c (*.f64 d d)))))
	35.8b	(/.f64 b c)
	40.4b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	22.7b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d)))) (/.f64 (cbrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (fma.f64 d d (*.f64 c c))))

Compiler

Compiled 2917 to 641 computations (78% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 c b) (.f64 a d))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
✓	12.9b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series242.0ms (3.3%)

Counts

3 → 108

Calls

3 calls:

116.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
112.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
13.0ms	(-.f64 (.f64 c b) (.f64 a d))

rewrite61.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 106

Calls

3 calls:

13.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
4.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
3.0ms	(-.f64 (.f64 c b) (.f64 a d))

simplify226.0ms (3%)

Algorithm

1×	egg-herbie

Rules

741×	`times-frac_binary64`
476×	`fma-neg_binary64`
402×	`fma-def_binary64`
251×	`cancel-sign-sub-inv_binary64`
230×	`distribute-rgt-in_binary64`

Counts

214 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	216	5451
1	603	4941
2	2097	4885
3	4752	4884
4	5041	4884

prune208.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	201	6	207
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	205	11	216

Error

2.6b

Counts

216 → 11

Alt Table

Status	Error	Program
	22.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (-.f64 (.f64 b c) (*.f64 a d))))
	36.3b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	42.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (/.f64 (.f64 a d) c) b))
	16.0b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))))
	45.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 a (/.f64 (.f64 c b) d)))
	40.4b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	46.9b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 a))
	22.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 c c (.f64 d d))) (cbrt.f64 (fma.f64 c c (.f64 d d))))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (cbrt.f64 (fma.f64 c c (*.f64 d d)))))
	44.2b	(*.f64 (/.f64 1 (hypot.f64 d c)) b)
▶	13.6b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	40.7b	(neg.f64 (/.f64 a d))

Compiler

Compiled 5824 to 1625 computations (72.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 c b) (.f64 a d))
✓	0.1b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	12.9b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series140.0ms (1.9%)

Counts

1 → 48

Calls

1 calls:

140.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 73

Calls

1 calls:

6.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))

simplify121.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

562×	`times-frac_binary64`
475×	`associate-/l/_binary64`
466×	`associate-/l*_binary64`
465×	`fma-neg_binary64`
359×	`div-sub_binary64`

Counts

121 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	4368
1	439	4066
2	1089	3872
3	4050	3805
4	5223	3805

prune156.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	226	5	231
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	233	9	242

Error

2.6b

Counts

242 → 9

Alt Table

Status	Error	Program
▶	13.8b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))
	22.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (-.f64 (.f64 b c) (*.f64 a d))))
	36.3b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	42.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (/.f64 (.f64 a d) c) b))
	40.4b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	47.1b	(/.f64 (-.f64 (/.f64 (*.f64 c b) d) a) (hypot.f64 d c))
	42.3b	(/.f64 (-.f64 b (/.f64 (*.f64 a d) c)) (hypot.f64 d c))
	14.3b	(/.f64 1 (/.f64 (hypot.f64 d c) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))))
	45.1b	(/.f64 (-.f64 a (/.f64 (*.f64 c b) d)) (hypot.f64 d c))

Compiler

Compiled 6327 to 1341 computations (78.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 c b) (.f64 a d))
✓	0.1b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))
✓	4.2b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
✓	8.7b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (sqrt.f64 (hypot.f64 d c)))

series372.0ms (5%)

Counts

3 → 128

Calls

3 calls:

153.0ms

(/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c)))

115.0ms

(/.f64 (/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))

104.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))

rewrite328.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

1644×	`times-frac_binary64`
784×	`*-un-lft-identity_binary64`
784×	`add-sqr-sqrt_binary64`
784×	`add-cube-cbrt_binary64`
624×	`sqrt-prod_binary64`

Counts

3 → 789

Calls

3 calls:

76.0ms

(/.f64 (/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))

11.0ms

(/.f64 (/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))

5.0ms

(/.f64 (-.f64 (*.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c)))

simplify873.0ms (11.7%)

Algorithm

1×	egg-herbie

Rules

538×	`fma-def_binary64`
517×	`associate-/r*_binary64`
466×	`div-sub_binary64`
445×	`associate-/l/_binary64`
273×	`associate-/l*_binary64`

Counts

917 → 959

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	799	47433
1	1863	44983
2	4015	42572
3	5427	42572

prune553.0ms (7.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	981	2	983
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	981	11	992

Error

2.5b

Counts

992 → 11

Alt Table

Status	Error	Program
✓	13.8b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))
	22.3b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (-.f64 (.f64 b c) (*.f64 a d))))
	36.3b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	48.2b	(/.f64 (/.f64 (*.f64 (sqrt.f64 c) b) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))
	45.1b	(/.f64 (-.f64 a (/.f64 (*.f64 c b) d)) (hypot.f64 d c))
	42.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (-.f64 (/.f64 (.f64 a d) c) b))
	40.4b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	47.1b	(/.f64 (-.f64 (/.f64 (*.f64 c b) d) a) (hypot.f64 d c))
	42.3b	(/.f64 (-.f64 b (/.f64 (*.f64 a d) c)) (hypot.f64 d c))
	51.0b	(/.f64 (/.f64 (neg.f64 (*.f64 a (sqrt.f64 d))) (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c))
	14.3b	(/.f64 1 (/.f64 (hypot.f64 d c) (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))))

Compiler

Compiled 41138 to 5293 computations (87.1% saved)

regimes1.4s (18.9%)

Accuracy

Total 12.1b remaining (85.3%)

Threshold costs 0b (0%)

Counts

178 → 5

Compiler

Compiled 18998 to 10844 computations (42.9% saved)

bsearch106.0ms (1.4%)

Steps

Iters	Range		Point
9	1.2062456310266416e+30	3.152343568014545e+36	3.0970906241597073e+36
7	-1.4070828750648742e-192	-7.862765862347215e-195	-9.658402922807776e-195
10	-4.167357273759762e-132	-4.963514388699338e-144	-1.9738142544677371e-143
10	-1.5928261157303677e+235	-4.3180897455970947e+223	-5.124136587792355e+226

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	129
1	58	129
2	76	129
3	86	129
4	92	129
5	93	129
6	92	129

end153.0ms (2.1%)

Compiler: Compiled 395 to 199 computations (49.6% saved)

Details

analyze796.0ms (10.7%)

sample1.3s (17.2%)

simplify66.0ms (0.9%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series112.0ms (1.5%)

rewrite12.0ms (0.2%)

simplify86.0ms (1.2%)

prune88.0ms (1.2%)

localize11.0ms (0.1%)

series242.0ms (3.3%)

rewrite61.0ms (0.8%)

simplify226.0ms (3%)

prune208.0ms (2.8%)

localize10.0ms (0.1%)

series140.0ms (1.9%)

rewrite16.0ms (0.2%)

simplify121.0ms (1.6%)

prune156.0ms (2.1%)

localize12.0ms (0.2%)

series372.0ms (5%)

rewrite328.0ms (4.4%)

simplify873.0ms (11.7%)

prune553.0ms (7.4%)

regimes1.4s (18.9%)

bsearch106.0ms (1.4%)

simplify6.0ms (0.1%)

end153.0ms (2.1%)

Profiling