Details

analyze1.8s (40.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample1.2s (26.8%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 43 to 25 computations (41.9% saved)

simplify104.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

27.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	27.3b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

Compiler

Compiled 80 to 44 computations (45% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.5b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
✓	26.7b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

series32.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
10.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

rewrite13.0ms (0.3%)

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 → 50

Calls

2 calls:

7.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
3.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

simplify94.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-l_binary64`
433×	`fma-def_binary64`
328×	`times-frac_binary64`
299×	`associate-/l*_binary64`
248×	`associate-/r*_binary64`

Counts

98 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	2360
1	338	2193
2	1191	2164
3	4702	2164
4	4914	2164

prune80.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	4	110

Error

0.4b

Counts

110 → 4

Alt Table

Status	Error	Program
	33.7b	-1
▶	27.3b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))
	30.0b	1
	27.3b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4))) 3))

Compiler

Compiled 3293 to 1730 computations (47.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 y y) -4)
✓	0.0b	(.f64 (.f64 y y) 4)
✓	1.0b	(fma.f64 x x (.f64 (.f64 y y) -4))
✓	26.7b	(/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4)))

series37.0ms (0.8%)

Counts

4 → 72

Calls

4 calls:

21.0ms	(/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4)))
9.0ms	(fma.f64 x x (.f64 (.f64 y y) -4))
5.0ms	(.f64 (.f64 y y) -4)
2.0ms	(.f64 (.f64 y y) 4)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 81

Calls

4 calls:

4.0ms	(.f64 (.f64 y y) 4)
4.0ms	(.f64 (.f64 y y) -4)
2.0ms	(/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4)))
0.0ms	(fma.f64 x x (.f64 (.f64 y y) -4))

simplify110.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-neg_binary64`
335×	`distribute-rgt-neg-in_binary64`
334×	`times-frac_binary64`
300×	`distribute-lft-neg-in_binary64`
267×	`cancel-sign-sub-inv_binary64`

Counts

153 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	2638
1	341	2451
2	1015	2427
3	2852	2421
4	4668	2421
5	4934	2421

prune74.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	109	4	113

Error

0.4b

Counts

113 → 4

Alt Table

Status	Error	Program
	33.7b	-1
✓	27.3b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))
	30.0b	1
▶	27.3b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4))) 3))

Compiler

Compiled 2878 to 1562 computations (45.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 (.f64 y y) 4)
✓	0.0b	(pow.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4))) 3)
	1.0b	(fma.f64 x x (.f64 (.f64 y y) -4))
✓	26.7b	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))

series51.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(pow.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4))) 3)
18.0ms	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
13×	`cube-prod_binary64`

Counts

2 → 77

Calls

2 calls:

3.0ms	(pow.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4))) 3)
2.0ms	(/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4)))

simplify119.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

956×	`times-frac_binary64`
649×	`log-prod_binary64`
437×	`fma-def_binary64`
357×	`unswap-sqr_binary64`
180×	`fma-neg_binary64`

Counts

125 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	4224
1	454	3941
2	1476	3837
3	4280	3813
4	5692	3813

prune112.0ms (2.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	142	4	146

Error

0.4b

Counts

146 → 4

Alt Table

Status	Error	Program
	33.7b	-1
✓	27.3b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))
▶	30.0b	1
✓	27.3b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4))) 3))

Compiler

Compiled 4237 to 2366 computations (44.2% saved)

localize0.0ms (0%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.4b

Counts

4 → 4

Alt Table

Status	Error	Program
	33.7b	-1
✓	27.3b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 (.f64 y y) 4)) (fma.f64 x x (.f64 (.f64 y y) -4))))
✓	30.0b	1
✓	27.3b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x x (.f64 (.f64 y y) -4)) (fma.f64 x x (.f64 (.f64 y y) 4))) 3))

Compiler

Compiled 49 to 31 computations (36.7% saved)

regimes305.0ms (7%)

Accuracy

Total 13.3b remaining (97.1%)

Threshold costs 0b (0%)

Counts

21 → 7

Compiler

Compiled 2733 to 1693 computations (38.1% saved)

bsearch129.0ms (2.9%)

Steps

Iters	Range		Point
8	9.65102767281371e+25	6.7856512678118345e+28	6.7124149431424e+28
8	2.0750627768133943e-221	4.943764724251152e-218	4.844477666462499e-218
7	-2.8830167639287285e-140	-6.465584682643109e-142	-3.889732912922227e-141
10	-1.2199095626484389e-85	-2.634966245111764e-95	-3.9297601949890104e-88
6	-3.9418310152414216e-53	-6.314368334689589e-54	-1.8134981297322904e-53
9	-4.646624349279353e+159	-2.7635964405258236e+152	-2.329334044066695e+153

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`
3×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	208
1	52	208
2	66	208
3	72	208
4	76	208
5	77	208
6	75	208

end103.0ms (2.4%)

Compiler: Compiled 335 to 197 computations (41.2% saved)

Details

analyze1.8s (40.3%)

sample1.2s (26.8%)

simplify104.0ms (2.4%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series32.0ms (0.7%)

rewrite13.0ms (0.3%)

simplify94.0ms (2.1%)

prune80.0ms (1.8%)

localize12.0ms (0.3%)

series37.0ms (0.8%)

rewrite15.0ms (0.3%)

simplify110.0ms (2.5%)

prune74.0ms (1.7%)

localize13.0ms (0.3%)

series51.0ms (1.2%)

rewrite13.0ms (0.3%)

simplify119.0ms (2.7%)

prune112.0ms (2.6%)

localize0.0ms (0%)

prune2.0ms (0.1%)

regimes305.0ms (7%)

bsearch129.0ms (2.9%)

simplify9.0ms (0.2%)

end103.0ms (2.4%)

Profiling