Details

analyze894.0ms (7.4%)

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
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.6s (12.9%)

Results

960.0ms	8256×	body	128	valid
364.0ms	3165×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

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

5.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series32.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

32.0ms

(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-l_binary64`
618×	`exp-prod_binary64`
546×	`associate-r_binary64`
433×	`distribute-rgt-in_binary64`
424×	`distribute-lft-in_binary64`

Counts

58 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	1181
1	101	928
2	231	928
3	721	928
4	3522	928
5	4742	928
6	4963	928
7	4910	928

prune24.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	29	4	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	5	34

Error

5.4b

Counts

34 → 5

Alt Table

Status	Error	Program
	43.0b	(pow.f64 x 2)
▶	7.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	40.6b	(cbrt.f64 (pow.f64 (fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
✓	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	35.8b	(.f64 4 (.f64 y t))

Compiler

Compiled 674 to 296 computations (56.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
✓	1.8b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
	5.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series624.0ms (5.2%)

Counts

3 → 144

Calls

3 calls:

412.0ms

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

177.0ms

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

34.0ms

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

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

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

4.0ms

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

1.0ms

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

simplify255.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

478×	`*-commutative_binary64`
220×	`+-commutative_binary64`
212×	`cancel-sign-sub-inv_binary64`
207×	`fma-def_binary64`
195×	`sub-neg_binary64`

Counts

237 → 282

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1128	19837
1	3968	19315
2	5082	19315

prune1.2s (10.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	568	1	569
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	568	6	574

Error

5.4b

Counts

574 → 6

Alt Table

Status	Error	Program
▶	7.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))))
✓	7.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	43.0b	(pow.f64 x 2)
	40.6b	(cbrt.f64 (pow.f64 (fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
✓	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	35.8b	(.f64 4 (.f64 y t))

Compiler

Compiled 51474 to 29858 computations (42% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	1.8b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
	5.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series178.0ms (1.5%)

Counts

1 → 48

Calls

1 calls:

178.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 16

Calls

1 calls:

1.0ms

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

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

443×	`times-frac_binary64`
344×	`fma-def_binary64`
339×	`associate-l_binary64`
339×	`associate-/r*_binary64`
334×	`associate-/l*_binary64`

Counts

64 → 97

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	456	6237
1	1563	6001
2	5180	6001

prune2.2s (18.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	1050	2	1052
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1050	8	1058

Error

5.4b

Counts

1058 → 8

Alt Table

Status	Error	Program
▶	21.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))))
	43.0b	(pow.f64 x 2)
✓	7.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))))
✓	7.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	21.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))) (expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))))))
	40.6b	(cbrt.f64 (pow.f64 (fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
✓	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	35.8b	(.f64 4 (.f64 y t))

Compiler

Compiled 132951 to 72627 computations (45.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
✓	1.4b	(expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))))
	1.8b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
	5.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series198.0ms (1.6%)

Counts

1 → 48

Calls

1 calls:

198.0ms

(expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))))

simplify160.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

443×	`times-frac_binary64`
344×	`fma-def_binary64`
339×	`associate-/r*_binary64`
337×	`associate-l_binary64`
334×	`associate-/l*_binary64`

Counts

59 → 97

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	449	6038
1	1555	5754
2	5166	5754

prune2.1s (17.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	1023	0	1023
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	1023	8	1031

Error

5.4b

Counts

1031 → 8

Alt Table

Status	Error	Program
✓	21.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))))
	43.0b	(pow.f64 x 2)
✓	7.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))))
✓	7.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	21.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))) (expm1.f64 (log1p.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))))))
	40.6b	(cbrt.f64 (pow.f64 (fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
✓	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	35.8b	(.f64 4 (.f64 y t))

Compiler

Compiled 127106 to 69642 computations (45.2% saved)

regimes2.1s (17.5%)

Accuracy

Total 0.9b remaining (14.8%)

Threshold costs 0.9b (14.8%)

Counts

146 → 1

Compiler

Compiled 86324 to 44079 computations (48.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	17	17
2	24	17
3	28	17
4	30	17
5	30	17

end142.0ms (1.2%)

Compiler: Compiled 360 to 183 computations (49.2% saved)

Details

analyze894.0ms (7.4%)

sample1.6s (12.9%)

simplify62.0ms (0.5%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series32.0ms (0.3%)

rewrite1.0ms (0%)

simplify100.0ms (0.8%)

prune24.0ms (0.2%)

localize13.0ms (0.1%)

series624.0ms (5.2%)

rewrite23.0ms (0.2%)

simplify255.0ms (2.1%)

prune1.2s (10.1%)

localize15.0ms (0.1%)

series178.0ms (1.5%)

rewrite2.0ms (0%)

simplify100.0ms (0.8%)

prune2.2s (18.1%)

localize17.0ms (0.1%)

series198.0ms (1.6%)

rewrite1.0ms (0%)

simplify160.0ms (1.3%)

prune2.1s (17.7%)

regimes2.1s (17.5%)

simplify2.0ms (0%)

end142.0ms (1.2%)

Profiling