Details

analyze1.8s (19.8%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.4s (15.4%)

Results

1.1s	8256×	body	128	valid
185.0ms	250×	body	8192	exit
31.0ms	243×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify67.0ms (0.7%)

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

24.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.7b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 c c (*.f64 d d))
✓	0.5b	(-.f64 (.f64 b c) (.f64 a d))
✓	24.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))

series102.0ms (1.1%)

Counts

3 → 120

Calls

3 calls:

86.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
9.0ms	(-.f64 (.f64 b c) (.f64 a d))
6.0ms	(fma.f64 c c (*.f64 d d))

rewrite11.0ms (0.1%)

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`
5×	`add-cbrt-cube_binary64`

Counts

3 → 58

Calls

3 calls:

5.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (fma.f64 c c (*.f64 d d)))
3.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(fma.f64 c c (*.f64 d d))

simplify113.0ms (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

178 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	3054
1	326	2877
2	1091	2830
3	4396	2830
4	4994	2830
5	4942	2830

prune105.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	122	10	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Error

1.6b

Counts

133 → 10

Alt Table

Status	Error	Program
▶	16.7b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
	38.7b	(/.f64 b c)
	25.2b	(.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)))))
	38.6b	(/.f64 (/.f64 (.f64 (-.f64 (.f64 c b) (.f64 a d)) (fma.f64 a d (.f64 c b))) (fma.f64 a d (.f64 c b))) (fma.f64 c c (.f64 d d)))
	38.0b	(-.f64 (/.f64 b c) (fma.f64 (/.f64 a c) (/.f64 d c) (/.f64 (.f64 (.f64 d d) b) (pow.f64 c 3))))
	24.7b	(-.f64 (/.f64 (.f64 b c) (fma.f64 c c (.f64 d d))) (/.f64 (.f64 a d) (fma.f64 c c (.f64 d d))))
	17.3b	(.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)))
	37.6b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	25.2b	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (.f64 (cbrt.f64 (fma.f64 c c (.f64 d d))) (cbrt.f64 (fma.f64 c c (.f64 d d))))) (cbrt.f64 (fma.f64 c c (.f64 d d))))
	37.3b	(neg.f64 (/.f64 a d))

Compiler

Compiled 3381 to 725 computations (78.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 d c))
✓	0.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
✓	0.5b	(-.f64 (.f64 c b) (.f64 a d))
✓	15.7b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series247.0ms (2.7%)

Counts

4 → 132

Calls

4 calls:

110.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (hypot.f64 d c)))
107.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))
20.0ms	(/.f64 1 (hypot.f64 d c))
9.0ms	(-.f64 (.f64 c b) (.f64 a d))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 139

Calls

4 calls:

9.0ms	(.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))
2.0ms	(/.f64 1 (hypot.f64 d c))

simplify131.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

874×	`times-frac_binary64`
537×	`fma-def_binary64`
368×	`cancel-sign-sub-inv_binary64`
196×	`fma-neg_binary64`
181×	`sub-neg_binary64`

Counts

271 → 271

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	6415
1	744	5877
2	2552	5818
3	5061	5818

prune204.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	264	7	271
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	271	10	281

Error

1.6b

Counts

281 → 10

Alt Table

Status	Error	Program
	24.7b	(.f64 1 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (.f64 (hypot.f64 d c) (hypot.f64 d c))))
	48.4b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 b))
	16.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
	42.7b	(*.f64 (/.f64 1 (hypot.f64 d c)) b)
▶	16.6b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	37.6b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	38.7b	(.f64 (.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (sqrt.f64 (-.f64 (.f64 c b) (.f64 a d))) 1)) (/.f64 (sqrt.f64 (-.f64 (.f64 c b) (.f64 a d))) (hypot.f64 d c)))
	37.3b	(neg.f64 (/.f64 a d))
	44.6b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 a))
	38.7b	(/.f64 b c)

Compiler

Compiled 7445 to 2228 computations (70.1% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
	15.7b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series103.0ms (1.1%)

Counts

1 → 48

Calls

1 calls:

103.0ms

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

rewrite17.0ms (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:

8.0ms

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

simplify117.0ms (1.3%)

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

prune143.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	227	4	231
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	232	9	241

Error

1.6b

Counts

241 → 9

Alt Table

Status	Error	Program
✓	16.6b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	37.6b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	42.4b	(/.f64 (-.f64 b (/.f64 (*.f64 a d) c)) (hypot.f64 d c))
	37.3b	(neg.f64 (/.f64 a d))
	48.4b	(/.f64 (neg.f64 b) (hypot.f64 d c))
	16.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (/.f64 (-.f64 (.f64 c b) (*.f64 a d)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c))))
▶	16.8b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	44.6b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 a))
	42.6b	(/.f64 b (hypot.f64 d c))

Compiler

Compiled 6256 to 1302 computations (79.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c)))
✓	0.3b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	0.5b	(-.f64 (.f64 c b) (.f64 a d))
	15.7b	(/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c))

series332.0ms (3.7%)

Counts

2 → 80

Calls

2 calls:

220.0ms

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

112.0ms

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

rewrite261.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

1557×	`times-frac_binary64`
728×	`*-un-lft-identity_binary64`
728×	`add-sqr-sqrt_binary64`
728×	`add-cube-cbrt_binary64`
564×	`sqrt-prod_binary64`

Counts

2 → 715

Calls

2 calls:

21.0ms

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

7.0ms

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

simplify937.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

746×	`div-sub_binary64`
452×	`associate-/l/_binary64`
349×	`fma-def_binary64`
318×	`associate-/r*_binary64`
265×	`cancel-sign-sub-inv_binary64`

Counts

795 → 847

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	745	46940
1	1631	43437
2	3059	40615
3	4460	39864
4	5744	39864

prune477.0ms (5.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	937	4	941
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	940	10	950

Error

1.6b

Counts

950 → 10

Alt Table

Status	Error	Program
	48.4b	(/.f64 (neg.f64 b) (hypot.f64 d c))
	44.6b	(/.f64 (/.f64 (neg.f64 a) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
✓	16.6b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (hypot.f64 d c))
	37.6b	(-.f64 (fma.f64 (/.f64 c d) (/.f64 b d) (/.f64 (.f64 a (.f64 c c)) (pow.f64 d 3))) (/.f64 a d))
	42.7b	(/.f64 (/.f64 b (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	48.5b	(/.f64 (/.f64 (neg.f64 b) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
✓	16.8b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 a d)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))) (sqrt.f64 (hypot.f64 d c)))
	24.3b	(.f64 (-.f64 (.f64 c b) (*.f64 a d)) (/.f64 (/.f64 1 (hypot.f64 d c)) (hypot.f64 d c)))
	42.6b	(/.f64 b (hypot.f64 d c))
	37.3b	(neg.f64 (/.f64 a d))

Compiler

Compiled 39376 to 5264 computations (86.6% saved)

regimes2.2s (24.7%)

Accuracy

Total 10.5b remaining (84.3%)

Threshold costs 0b (0%)

Counts

216 → 5

Compiler

Compiled 24053 to 13679 computations (43.1% saved)

bsearch74.0ms (0.8%)

Steps

Iters	Range		Point
4	2.1632354542689256e+70	3.4779604366576765e+70	3.4182045595690496e+70
7	1.1136234348634036e-116	1.9856969308334364e-114	2.532329616296603e-115
9	-2.0285685508430287e-67	-3.209187298588941e-73	-5.175827438536771e-73
8	-6.638769396851526e+187	-6.272179725595773e+183	-7.275365746467164e+183

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	106
1	49	106
2	64	106
3	72	106
4	76	106
5	76	106

end115.0ms (1.3%)

Compiler: Compiled 315 to 157 computations (50.2% saved)

Details

analyze1.8s (19.8%)

sample1.4s (15.4%)

simplify67.0ms (0.7%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series102.0ms (1.1%)

rewrite11.0ms (0.1%)

simplify113.0ms (1.2%)

prune105.0ms (1.2%)

localize11.0ms (0.1%)

series247.0ms (2.7%)

rewrite31.0ms (0.3%)

simplify131.0ms (1.4%)

prune204.0ms (2.3%)

localize11.0ms (0.1%)

series103.0ms (1.1%)

rewrite17.0ms (0.2%)

simplify117.0ms (1.3%)

prune143.0ms (1.6%)

localize11.0ms (0.1%)

series332.0ms (3.7%)

rewrite261.0ms (2.9%)

simplify937.0ms (10.3%)

prune477.0ms (5.3%)

regimes2.2s (24.7%)

bsearch74.0ms (0.8%)

simplify5.0ms (0.1%)

end115.0ms (1.3%)

Profiling