Details

analyze692.0ms (9.2%)

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)

sample1.1s (14%)

Results

968.0ms	8256×	body	128	valid
61.0ms	489×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	18	18
2	22	18
3	22	18

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

26.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.7b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 c c (*.f64 d d))
✓	0.2b	(fma.f64 a c (*.f64 b d))
✓	26.3b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series95.0ms (1.3%)

Counts

3 → 120

Calls

3 calls:

80.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
8.0ms	(fma.f64 a c (*.f64 b d))
6.0ms	(fma.f64 c c (*.f64 d d))

rewrite5.0ms (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 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
0.0ms	(fma.f64 c c (*.f64 d d))
0.0ms	(fma.f64 a c (*.f64 b d))

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary64`
410×	`associate-/l/_binary64`
377×	`fma-neg_binary64`
252×	`distribute-rgt-neg-in_binary64`
251×	`distribute-lft-neg-in_binary64`

Counts

169 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	2836
1	205	2674
2	611	2590
3	2163	2542
4	5054	2542

prune94.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Error

2.1b

Counts

118 → 10

Alt Table

Status	Error	Program
▶	18.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	37.4b	(-.f64 (fma.f64 a (/.f64 c (.f64 d d)) (/.f64 b d)) (.f64 (/.f64 (*.f64 c c) (pow.f64 d 3)) (+.f64 b (/.f64 a (/.f64 d c)))))
	19.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	26.0b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	38.5b	(/.f64 a c)
	34.0b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	37.4b	(/.f64 b d)
	26.6b	(/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (.f64 d d))))
	27.1b	(/.f64 (.f64 (cbrt.f64 (fma.f64 a c (.f64 b d))) (cbrt.f64 (fma.f64 a c (.f64 b d)))) (/.f64 (fma.f64 c c (.f64 d d)) (cbrt.f64 (fma.f64 a c (*.f64 b d)))))
	26.9b	(.f64 (fma.f64 a c (.f64 b d)) (/.f64 1 (fma.f64 c c (*.f64 d d))))

Compiler

Compiled 2769 to 610 computations (78% saved)

localize9.0ms (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 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	0.5b	(fma.f64 d b (*.f64 c a))
✓	17.8b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series225.0ms (3%)

Counts

4 → 168

Calls

4 calls:

101.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
97.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
19.0ms	(/.f64 1 (hypot.f64 d c))
9.0ms	(fma.f64 d b (*.f64 c a))

rewrite22.0ms (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 → 130

Calls

4 calls:

8.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
2.0ms	(/.f64 1 (hypot.f64 d c))
2.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
0.0ms	(fma.f64 d b (*.f64 c a))

simplify155.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

845×	`times-frac_binary64`
428×	`fma-neg_binary64`
410×	`fma-def_binary64`
335×	`cancel-sign-sub-inv_binary64`
274×	`distribute-rgt-in_binary64`

Counts

298 → 286

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	233	6205
1	631	5720
2	2125	5547
3	4841	5539
4	5079	5539

prune203.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	279	7	286
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	287	9	296

Error

0.0b

Counts

296 → 9

Alt Table

Status	Error	Program
	38.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (sqrt.f64 (fma.f64 a c (.f64 d b))) (/.f64 (sqrt.f64 (fma.f64 a c (.f64 d b))) (hypot.f64 d c))))
	24.9b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
▶	19.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))))
	31.2b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	19.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	26.0b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	31.9b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 7471 to 2241 computations (70% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))))
	0.5b	(fma.f64 d b (*.f64 c a))
	17.8b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series312.0ms (4.1%)

Counts

2 → 80

Calls

2 calls:

205.0ms

(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))

106.0ms

(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
32×	`sqrt-prod_binary64`
32×	`associate-l_binary64`
27×	`*-un-lft-identity_binary64`

Counts

2 → 97

Calls

2 calls:

11.0ms

(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))))

10.0ms

(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))

simplify139.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

709×	`times-frac_binary64`
310×	`fma-def_binary64`
306×	`cancel-sign-sub-inv_binary64`
228×	`distribute-rgt-in_binary64`
223×	`associate-r_binary64`

Counts

177 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	5443
1	522	4883
2	1865	4772
3	4625	4772
4	4984	4772

prune264.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	306	9	315

Error

0.0b

Counts

315 → 9

Alt Table

Status	Error	Program
	38.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (sqrt.f64 (fma.f64 a c (.f64 d b))) (/.f64 (sqrt.f64 (fma.f64 a c (.f64 d b))) (hypot.f64 d c))))
	24.9b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
✓	19.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))))
	31.2b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
▶	19.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	26.0b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	31.9b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 10132 to 3902 computations (61.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a))))
	0.5b	(fma.f64 d b (*.f64 c a))
✓	5.8b	(/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a)))) (hypot.f64 d c))
✓	18.3b	(cbrt.f64 (fma.f64 d b (*.f64 c a)))

series349.0ms (4.6%)

Counts

3 → 144

Calls

3 calls:

159.0ms

(/.f64 (*.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a)))) (hypot.f64 d c))

115.0ms

(*.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a))))

74.0ms

(cbrt.f64 (fma.f64 d b (*.f64 c a)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms

(/.f64 (*.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a)))) (hypot.f64 d c))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a))))

1.0ms

(cbrt.f64 (fma.f64 d b (*.f64 c a)))

simplify193.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

919×	`associate-/l*_binary64`
460×	`fma-def_binary64`
341×	`*-commutative_binary64`
286×	`cancel-sign-sub-inv_binary64`
181×	`sub-neg_binary64`

Counts

222 → 342

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	841	14036
1	2935	12685
2	5787	12685

prune546.0ms (7.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	588	0	588
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	588	9	597

Error

0.0b

Counts

597 → 9

Alt Table

Status	Error	Program
	38.9b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (sqrt.f64 (fma.f64 a c (.f64 d b))) (/.f64 (sqrt.f64 (fma.f64 a c (.f64 d b))) (hypot.f64 d c))))
	24.9b	(fma.f64 (/.f64 c (fma.f64 d d (.f64 c c))) a (/.f64 (.f64 d b) (fma.f64 d d (*.f64 c c))))
	44.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
✓	19.1b	(.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 d c))) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))))
	31.2b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
✓	19.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (fma.f64 d b (.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
	26.0b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	31.9b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))

Compiler

Compiled 35987 to 14871 computations (58.7% saved)

regimes2.8s (36.7%)

Accuracy

Total 10.0b remaining (98.6%)

Threshold costs 0b (0%)

Counts

187 → 5

Compiler

Compiled 20343 to 11244 computations (44.7% saved)

bsearch95.0ms (1.3%)

Steps

Iters	Range		Point
9	7.060439802304055e+93	7.718541126311962e+98	5.388057696506973e+98
7	1.2640662547794736e-100	1.6017282220243597e-98	1.544901258368836e-100
10	-1.7678441460080387e-125	-1.5461171796053897e-136	-1.0098211784491114e-135
9	-6.481809507013464e+133	-6.924095184360179e+127	-2.558733259505715e+128

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	114
1	51	114
2	58	112
3	66	112
4	69	112
5	70	112
6	68	112

end143.0ms (1.9%)

Compiler: Compiled 365 to 176 computations (51.8% saved)

Details

analyze692.0ms (9.2%)

sample1.1s (14%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series95.0ms (1.3%)

rewrite5.0ms (0.1%)

simplify85.0ms (1.1%)

prune94.0ms (1.2%)

localize9.0ms (0.1%)

series225.0ms (3%)

rewrite22.0ms (0.3%)

simplify155.0ms (2.1%)

prune203.0ms (2.7%)

localize14.0ms (0.2%)

series312.0ms (4.1%)

rewrite33.0ms (0.4%)

simplify139.0ms (1.8%)

prune264.0ms (3.5%)

localize11.0ms (0.1%)

series349.0ms (4.6%)

rewrite16.0ms (0.2%)

simplify193.0ms (2.6%)

prune546.0ms (7.2%)

regimes2.8s (36.7%)

bsearch95.0ms (1.3%)

simplify5.0ms (0.1%)

end143.0ms (1.9%)

Profiling