Details

analyze16.0ms (0.7%)

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
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample1.1s (46.9%)

Results

932.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 38 computations (41.5% saved)

simplify113.0ms (4.9%)

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

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

34.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.5b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 76 to 42 computations (44.7% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 y (.f64 y 4)))
✓	5.4b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	33.9b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series30.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

15.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
7.0ms	(fma.f64 x x (.f64 y (.f64 y 4)))
7.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))

rewrite7.0ms (0.3%)

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:

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

simplify93.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
500×	`div-sub_binary64`
426×	`fma-neg_binary64`
356×	`cancel-sign-sub-inv_binary64`
223×	`distribute-rgt-in_binary64`

Counts

121 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	2496
1	221	2296
2	581	2284
3	2083	2266
4	4490	2230
5	5508	2230

prune68.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	107	5	112

Error

0.6b

Counts

112 → 5

Alt Table

Status	Error	Program
✓	34.5b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
▶	31.0b	-1
	35.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)))) (sqrt.f64 (fma.f64 x x (.f64 y (.f64 y 4))))) (/.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (sqrt.f64 (fma.f64 x x (.f64 y (.f64 y 4))))))
	36.3b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	33.0b	1

Compiler

Compiled 2999 to 1445 computations (51.8% saved)

localize0.0ms (0%)

prune4.0ms (0.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

0.6b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	34.5b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
✓	31.0b	-1
	35.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)))) (sqrt.f64 (fma.f64 x x (.f64 y (.f64 y 4))))) (/.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (sqrt.f64 (fma.f64 x x (.f64 y (.f64 y 4))))))
	36.3b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
▶	33.0b	1

Compiler

Compiled 154 to 90 computations (41.6% saved)

localize0.0ms (0%)

prune4.0ms (0.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Error

0.6b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	34.5b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
✓	31.0b	-1
▶	35.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)))) (sqrt.f64 (fma.f64 x x (.f64 y (.f64 y 4))))) (/.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (sqrt.f64 (fma.f64 x x (.f64 y (.f64 y 4))))))
	36.3b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	33.0b	1

Compiler

Compiled 151 to 87 computations (42.4% saved)

localize17.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.4b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	18.3b	(/.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)))) (sqrt.f64 (fma.f64 x x (.f64 y (*.f64 y 4)))))
✓	32.0b	(sqrt.f64 (fma.f64 x x (.f64 y (.f64 y 4))))
✓	33.2b	(cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)))

series89.0ms (3.9%)

Counts

3 → 72

Calls

3 calls:

50.0ms

(/.f64 (*.f64 (cbrt.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x))) (cbrt.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)))) (sqrt.f64 (fma.f64 x x (*.f64 y (*.f64 y 4)))))

29.0ms

(cbrt.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)))

9.0ms

(sqrt.f64 (fma.f64 x x (*.f64 y (*.f64 y 4))))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-exp-log_binary64`

Counts

3 → 57

Calls

3 calls:

5.0ms

(/.f64 (*.f64 (cbrt.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x))) (cbrt.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)))) (sqrt.f64 (fma.f64 x x (*.f64 y (*.f64 y 4)))))

1.0ms

(sqrt.f64 (fma.f64 x x (*.f64 y (*.f64 y 4))))

1.0ms

(cbrt.f64 (fma.f64 -4 (*.f64 y y) (*.f64 x x)))

simplify108.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
503×	`cancel-sign-sub-inv_binary64`
286×	`fma-neg_binary64`
209×	`sub-neg_binary64`
159×	`unswap-sqr_binary64`

Counts

129 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	4835
1	892	4493
2	2815	4311
3	5003	4311

prune408.0ms (17.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	413	1	414
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	414	5	419

Error

0.6b

Counts

419 → 5

Alt Table

Status	Error	Program
✓	34.5b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
✓	31.0b	-1
	36.3b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	33.0b	1
	36.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)))) (sqrt.f64 (fma.f64 x x (.f64 y (.f64 y 4))))) (/.f64 (cbrt.f64 (fma.f64 -4 (.f64 y y) (.f64 x x))) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x (.f64 y (.f64 y 4))))))))

Compiler

Compiled 24944 to 13851 computations (44.5% saved)

regimes159.0ms (6.9%)

Accuracy

Total 11.8b remaining (97.1%)

Threshold costs 0b (0%)

Counts

12 → 3

Compiler

Compiled 2288 to 1263 computations (44.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 5 to 3 computations (40% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

5×	`+-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	19	48
1	29	48
2	43	48
3	49	48
4	53	48
5	54	48
6	52	48

end80.0ms (3.5%)

Compiler: Compiled 160 to 94 computations (41.3% saved)

Details

analyze16.0ms (0.7%)

sample1.1s (46.9%)

simplify113.0ms (4.9%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

series30.0ms (1.3%)

rewrite7.0ms (0.3%)

simplify93.0ms (4.1%)

prune68.0ms (3%)

localize0.0ms (0%)

prune4.0ms (0.2%)

localize0.0ms (0%)

prune4.0ms (0.2%)

localize17.0ms (0.7%)

series89.0ms (3.9%)

rewrite10.0ms (0.4%)

simplify108.0ms (4.7%)

prune408.0ms (17.7%)

regimes159.0ms (6.9%)

bsearch1.0ms (0%)

simplify4.0ms (0.2%)

end80.0ms (3.5%)

Profiling