Details

analyze734.0ms (10.6%)

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
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 (16.2%)

Results

1.0s	8256×	body	128	valid
62.0ms	490×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify11.0ms (0.2%)

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

28.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.0b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 66 to 32 computations (51.5% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 c c (*.f64 d d))
✓	27.5b	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))

series97.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

90.0ms	(/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))
6.0ms	(fma.f64 c c (*.f64 d d))

rewrite5.0ms (0.1%)

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 → 39

Calls

2 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))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

111 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	2376
1	200	2231
2	589	2147
3	2131	2099
4	5022	2099

prune70.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	87	8	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	8	96

Error

1.0b

Counts

96 → 8

Alt Table

Status	Error	Program
	36.8b	(/.f64 b d)
	28.1b	(/.f64 1 (/.f64 (fma.f64 c c (.f64 d d)) (fma.f64 a c (.f64 b d))))
	27.3b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
▶	17.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
	36.7b	(/.f64 a c)
	28.0b	(/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (.f64 d d))))
	35.6b	(fma.f64 a (/.f64 c (*.f64 d d)) (/.f64 b d))
	41.5b	(.f64 (sqrt.f64 (/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (.f64 d d)))) (sqrt.f64 (/.f64 (fma.f64 a c (.f64 b d)) (fma.f64 c c (*.f64 d d)))))

Compiler

Compiled 2264 to 498 computations (78% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 d c)
✓	0.2b	(fma.f64 d b (*.f64 c a))
✓	0.3b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	16.1b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series246.0ms (3.6%)

Counts

4 → 168

Calls

4 calls:

117.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
106.0ms	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
14.0ms	(hypot.f64 d c)
9.0ms	(fma.f64 d b (*.f64 c a))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

9.0ms	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (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))
0.0ms	(hypot.f64 d c)

simplify147.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

843×	`times-frac_binary64`
425×	`fma-neg_binary64`
389×	`fma-def_binary64`
310×	`cancel-sign-sub-inv_binary64`
283×	`distribute-rgt-in_binary64`

Counts

275 → 264

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	5683
1	623	5331
2	2083	5152
3	4804	5152
4	5030	5152

prune198.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	300	6	306
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	305	9	314

Error

0.2b

Counts

314 → 9

Alt Table

Status	Error	Program
✓	17.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
▶	17.8b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))) (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))))
	45.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	31.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	33.2b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	27.3b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
	17.9b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 a c (.f64 d b))) (cbrt.f64 (fma.f64 a c (.f64 d b)))) (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (hypot.f64 d c))))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
	28.0b	(/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (.f64 d d))))

Compiler

Compiled 8020 to 2489 computations (69% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))) (cbrt.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))))
✓	0.5b	(.f64 (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (cbrt.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))))
✓	0.6b	(cbrt.f64 (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))
	16.1b	(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series385.0ms (5.6%)

Counts

3 → 144

Calls

3 calls:

156.0ms

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

127.0ms

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

102.0ms

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

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`cbrt-prod_binary64`
78×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 160

Calls

3 calls:

15.0ms

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

11.0ms

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

2.0ms

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

simplify283.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-def_binary64`
567×	`times-frac_binary64`
390×	`associate-/l*_binary64`
251×	`*-commutative_binary64`
183×	`cancel-sign-sub-inv_binary64`

Counts

304 → 434

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	666	15228
1	2118	14447
2	4929	14399
3	5182	14399

prune740.0ms (10.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	943	0	943
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	943	9	952

Error

0.2b

Counts

952 → 9

Alt Table

Status	Error	Program
✓	17.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	17.8b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))) (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))))
	45.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	31.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	33.2b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	27.3b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
▶	17.9b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 a c (.f64 d b))) (cbrt.f64 (fma.f64 a c (.f64 d b)))) (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (hypot.f64 d c))))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
	28.0b	(/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (.f64 d d))))

Compiler

Compiled 58512 to 17586 computations (69.9% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (hypot.f64 d c))
✓	5.5b	(/.f64 (.f64 (cbrt.f64 (fma.f64 a c (.f64 d b))) (cbrt.f64 (fma.f64 a c (.f64 d b)))) (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c))))
✓	16.6b	(cbrt.f64 (fma.f64 a c (*.f64 d b)))
✓	16.6b	(cbrt.f64 (fma.f64 d b (*.f64 c a)))

series344.0ms (5%)

Counts

4 → 168

Calls

4 calls:

149.0ms	(/.f64 (.f64 (cbrt.f64 (fma.f64 a c (.f64 d b))) (cbrt.f64 (fma.f64 a c (.f64 d b)))) (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c))))
79.0ms	(cbrt.f64 (fma.f64 d b (*.f64 c a)))
72.0ms	(cbrt.f64 (fma.f64 a c (*.f64 d b)))
44.0ms	(cbrt.f64 (hypot.f64 d c))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
9×	`cbrt-prod_binary64`
8×	`add-cbrt-cube_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`

Counts

4 → 62

Calls

4 calls:

9.0ms	(/.f64 (.f64 (cbrt.f64 (fma.f64 a c (.f64 d b))) (cbrt.f64 (fma.f64 a c (.f64 d b)))) (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c))))
1.0ms	(cbrt.f64 (fma.f64 d b (*.f64 c a)))
1.0ms	(cbrt.f64 (hypot.f64 d c))
1.0ms	(cbrt.f64 (fma.f64 a c (*.f64 d b)))

simplify181.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
591×	`associate-/l*_binary64`
299×	`fma-def_binary64`
224×	`*-commutative_binary64`
208×	`cancel-sign-sub-inv_binary64`

Counts

230 → 258

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	647	12808
1	2189	11885
2	5472	11885

prune315.0ms (4.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	373	0	373
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	373	9	382

Error

0.2b

Counts

382 → 9

Alt Table

Status	Error	Program
✓	17.2b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))
✓	17.8b	(.f64 (/.f64 1 (hypot.f64 d c)) (.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c))) (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))) (cbrt.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)))))
	45.3b	(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 c d) a b)))
	31.7b	(fma.f64 (/.f64 a d) (/.f64 c d) (/.f64 b d))
	33.2b	(fma.f64 (/.f64 b c) (/.f64 d c) (/.f64 a c))
	27.3b	(fma.f64 b (/.f64 d (fma.f64 d d (.f64 c c))) (/.f64 (.f64 c a) (fma.f64 d d (*.f64 c c))))
✓	17.9b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 a c (.f64 d b))) (cbrt.f64 (fma.f64 a c (.f64 d b)))) (.f64 (cbrt.f64 (hypot.f64 d c)) (cbrt.f64 (hypot.f64 d c)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (.f64 c a))) (cbrt.f64 (hypot.f64 d c))))
	45.1b	(*.f64 (/.f64 1 (hypot.f64 d c)) (fma.f64 (/.f64 d c) b a))
	28.0b	(/.f64 (/.f64 (fma.f64 d b (.f64 c a)) (hypot.f64 d c)) (sqrt.f64 (fma.f64 c c (.f64 d d))))

Compiler

Compiled 23924 to 7438 computations (68.9% saved)

regimes1.6s (22.6%)

Accuracy

Total 9.5b remaining (98.4%)

Threshold costs 0b (0%)

Counts

129 → 5

Compiler

Compiled 15783 to 8044 computations (49% saved)

bsearch122.0ms (1.8%)

Steps

Iters	Range		Point
6	3.0699538592237883e+125	2.1844518315752034e+126	9.252763405738269e+125
9	1.9939569543929294e-215	1.3129904177370859e-207	8.257594576029714e-210
10	-2.441238558004582e-136	-1.8691431763602715e-146	-3.2778058876870277e-146
10	-7.246277711792929e+140	-1.0831246780352106e+130	-2.9753592065970103e+133

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	106
1	32	106
2	32	106

end131.0ms (1.9%)

Compiler: Compiled 374 to 160 computations (57.2% saved)

Details

analyze734.0ms (10.6%)

sample1.1s (16.2%)

simplify11.0ms (0.2%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series97.0ms (1.4%)

rewrite5.0ms (0.1%)

simplify73.0ms (1.1%)

prune70.0ms (1%)

localize10.0ms (0.1%)

series246.0ms (3.6%)

rewrite20.0ms (0.3%)

simplify147.0ms (2.1%)

prune198.0ms (2.9%)

localize16.0ms (0.2%)

series385.0ms (5.6%)

rewrite51.0ms (0.7%)

simplify283.0ms (4.1%)

prune740.0ms (10.7%)

localize20.0ms (0.3%)

series344.0ms (5%)

rewrite14.0ms (0.2%)

simplify181.0ms (2.6%)

prune315.0ms (4.6%)

regimes1.6s (22.6%)

bsearch122.0ms (1.8%)

simplify4.0ms (0.1%)

end131.0ms (1.9%)

Profiling