Details

analyze941.0ms (8%)

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)

sample1.5s (13.1%)

Results

948.0ms	8256×	body	128	valid
362.0ms	3115×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify63.0ms (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

5.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z z))
✓	4.9b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series36.0ms (0.3%)

Counts

2 → 72

Calls

2 calls:

31.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
5.0ms	(-.f64 t (*.f64 z z))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-neg_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(-.f64 t (*.f64 z z))
0.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

703×	`distribute-rgt-in_binary64`
653×	`distribute-lft-in_binary64`
495×	`fma-neg_binary64`
369×	`exp-prod_binary64`
193×	`fma-def_binary64`

Counts

103 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	1591
1	187	1301
2	431	1282
3	1535	1282
4	4588	1282
5	5085	1282

prune41.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	6	65

Error

4.6b

Counts

65 → 6

Alt Table

Status	Error	Program
✓	5.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
▶	6.4b	(.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))))
	41.8b	(pow.f64 x 2)
	24.7b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	17.3b	(fma.f64 x x (.f64 4 (.f64 y t)))
	37.0b	(.f64 4 (.f64 y t))

Compiler

Compiled 1243 to 495 computations (60.2% saved)

localize17.0ms (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))))
✓	0.6b	(.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))))
✓	1.4b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
	4.9b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series595.0ms (5%)

Counts

3 → 144

Calls

3 calls:

401.0ms

(*.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))))

161.0ms

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

33.0ms

(*.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))))

rewrite20.0ms (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)))

simplify518.0ms (4.4%)

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

prune910.0ms (7.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	567	2	569
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	568	7	575

Error

4.6b

Counts

575 → 7

Alt Table

Status	Error	Program
✓	5.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
✓	6.4b	(.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))))
	41.8b	(pow.f64 x 2)
	24.7b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	46.8b	(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) (.f64 4 (.f64 y (.f64 z z)))) 2)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))
	37.0b	(.f64 4 (.f64 y t))
▶	24.3b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))

Compiler

Compiled 51492 to 29880 computations (42% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
✓	0.5b	(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))) 3)
	1.4b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
	4.9b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series523.0ms (4.4%)

Counts

2 → 96

Calls

2 calls:

486.0ms

(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) 3)

38.0ms

(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) 3)) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64`
12×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

8.0ms

(*.f64 (*.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) 3)) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))

3.0ms

(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) 3)

simplify167.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

639×	`times-frac_binary64`
526×	`associate-/l*_binary64`
416×	`associate-/r*_binary64`
355×	`fma-def_binary64`
169×	`*-commutative_binary64`

Counts

161 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	512	9569
1	1720	8579
2	5433	8579

prune873.0ms (7.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	562	1	563
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	562	8	570

Error

4.6b

Counts

570 → 8

Alt Table

Status	Error	Program
✓	5.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
✓	6.4b	(.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))))
	41.8b	(pow.f64 x 2)
▶	24.5b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (.f64 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3)) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3))) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	24.7b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	46.8b	(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) (.f64 4 (.f64 y (.f64 z z)))) 2)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))
	37.0b	(.f64 4 (.f64 y t))
✓	24.3b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))

Compiler

Compiled 48992 to 28486 computations (41.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3)) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))) 3)))
	0.5b	(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))) 3)
	1.4b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
	4.9b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series169.0ms (1.4%)

Counts

1 → 48

Calls

1 calls:

169.0ms

(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) 3)) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) 3)))

rewrite97.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

364×	`cbrt-prod_binary64`
205×	`add-sqr-sqrt_binary64`
152×	`sqrt-prod_binary64`
116×	`cube-prod_binary64`
116×	`unpow-prod-down_binary64`

Counts

1 → 208

Calls

1 calls:

23.0ms

(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) 3)) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) 3)))

simplify291.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

415×	`associate-l_binary64`
412×	`times-frac_binary64`
349×	`fma-def_binary64`
320×	`associate-/r*_binary64`
290×	`associate-/l*_binary64`

Counts

256 → 217

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	558	17382
1	1677	16013
2	5395	16013

prune2.7s (22.5%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	1230	0	1230
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	1230	8	1238

Error

4.6b

Counts

1238 → 8

Alt Table

Status	Error	Program
✓	5.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
✓	6.4b	(.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))))
	41.8b	(pow.f64 x 2)
✓	24.5b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (.f64 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3)) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3))) (cbrt.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	24.7b	(fma.f64 y (.f64 4 (/.f64 (-.f64 (.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
	46.8b	(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 x x) (.f64 4 (.f64 y (.f64 z z)))) 2)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))))
	37.0b	(.f64 4 (.f64 y t))
✓	24.3b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) 3)) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))

Compiler

Compiled 154637 to 86722 computations (43.9% saved)

regimes2.1s (17.5%)

Accuracy

Total 0.8b remaining (12.9%)

Threshold costs 0.8b (12.9%)

Counts

148 → 1

Compiler

Compiled 76528 to 42509 computations (44.5% 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

end141.0ms (1.2%)

Compiler: Compiled 299 to 166 computations (44.5% saved)

Details

analyze941.0ms (8%)

sample1.5s (13.1%)

simplify63.0ms (0.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series36.0ms (0.3%)

rewrite4.0ms (0%)

simplify75.0ms (0.6%)

prune41.0ms (0.3%)

localize17.0ms (0.1%)

series595.0ms (5%)

rewrite20.0ms (0.2%)

simplify518.0ms (4.4%)

prune910.0ms (7.7%)

localize13.0ms (0.1%)

series523.0ms (4.4%)

rewrite17.0ms (0.1%)

simplify167.0ms (1.4%)

prune873.0ms (7.4%)

localize16.0ms (0.1%)

series169.0ms (1.4%)

rewrite97.0ms (0.8%)

simplify291.0ms (2.5%)

prune2.7s (22.5%)

regimes2.1s (17.5%)

simplify2.0ms (0%)

end141.0ms (1.2%)

Profiling