Details

analyze1.9s (25.3%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
7.8%	92%	0.2%	11
11.7%	88.1%	0.2%	12
17.9%	81.8%	0.2%	13
22.6%	77.2%	0.2%	14

Compiler

Compiled 19 to 14 computations (26.3% saved)

sample1.3s (16.7%)

Results

1.0s	8113×	body	128	valid
90.0ms	704×	body	128	invalid
28.0ms	35×	body	2048	valid
20.0ms	57×	body	1024	valid
10.0ms	31×	body	512	valid
3.0ms	15×	body	256	valid
3.0ms	5×	body	4096	valid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify110.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1714×	`fma-neg_binary64`
791×	`div-sub_binary64`
702×	`fma-def_binary64`
633×	`distribute-rgt-in_binary64`
427×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	23	17
2	46	17
3	90	17
4	173	17
5	320	17
6	671	17
7	1532	17
8	2980	17
9	3024	17
10	3167	17
11	3232	17
12	3299	17
13	3318	17
14	5334	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

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 60 (-.f64 x y))
✓	0.0b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
✓	0.7b	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

series79.0ms (1%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
34.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
3.0ms	(*.f64 60 (-.f64 x y))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 91

Calls

3 calls:

9.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
5.0ms	(*.f64 60 (-.f64 x y))
0.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

simplify116.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

742×	`cancel-sign-sub-inv_binary64`
331×	`sub-neg_binary64`
233×	`fma-neg_binary64`
229×	`fma-def_binary64`
197×	`associate-/l*_binary64`

Counts

223 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	319	4894
1	845	4557
2	3320	4449
3	5001	4449

prune154.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	5	164

Error

Counts

164 → 5

Alt Table

Status	Error	Program
	34.7b	(fma.f64 a 120 (*.f64 (/.f64 60 (sqrt.f64 (-.f64 z t))) (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 z t)))))
▶	0.1b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
	37.5b	(+.f64 (fma.f64 60 (/.f64 (.f64 y z) (.f64 t t)) (fma.f64 60 (+.f64 (/.f64 y t) (/.f64 (.f64 y (.f64 z z)) (pow.f64 t 3))) (.f64 120 a))) (.f64 -60 (+.f64 (/.f64 (.f64 z x) (.f64 t t)) (+.f64 (/.f64 x t) (/.f64 (.f64 z (.f64 z x)) (pow.f64 t 3))))))
	0.2b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))

Compiler

Compiled 4473 to 2148 computations (52% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t))))
✓	0.0b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
✓	0.2b	(*.f64 60 (/.f64 y (-.f64 z t)))
✓	0.3b	(*.f64 60 (/.f64 x (-.f64 z t)))

series113.0ms (1.5%)

Counts

4 → 138

Calls

4 calls:

44.0ms	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
36.0ms	(-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t))))
16.0ms	(*.f64 60 (/.f64 x (-.f64 z t)))
16.0ms	(*.f64 60 (/.f64 y (-.f64 z t)))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
42×	`associate-r_binary64`
36×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 113

Calls

4 calls:

9.0ms	(-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t))))
7.0ms	(*.f64 60 (/.f64 x (-.f64 z t)))
7.0ms	(*.f64 60 (/.f64 y (-.f64 z t)))
0.0ms	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

870×	`times-frac_binary64`
342×	`sub-neg_binary64`
322×	`fma-neg_binary64`
240×	`fma-def_binary64`
167×	`associate-/l*_binary64`

Counts

251 → 224

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	6505
1	980	6245
2	3374	6236
3	5084	6236

prune194.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	224	5	229

Error

Counts

229 → 5

Alt Table

Status	Error	Program
	34.7b	(fma.f64 a 120 (*.f64 (/.f64 60 (sqrt.f64 (-.f64 z t))) (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 z t)))))
	0.3b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 (.f64 (cbrt.f64 60) (cbrt.f64 60)) (.f64 (cbrt.f64 60) (/.f64 y (-.f64 z t))))))
✓	0.1b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
▶	0.2b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))

Compiler

Compiled 6722 to 3076 computations (54.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 x y))
✓	0.3b	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

series88.0ms (1.2%)

Counts

3 → 156

Calls

3 calls:

34.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
31.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))
23.0ms	(/.f64 (-.f64 z t) (-.f64 x y))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 208

Calls

3 calls:

8.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))
6.0ms	(/.f64 (-.f64 z t) (-.f64 x y))
0.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))

simplify201.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

273×	`fma-neg_binary64`
253×	`associate-/r/_binary64`
228×	`fma-def_binary64`
220×	`*-commutative_binary64`
191×	`+-commutative_binary64`

Counts

364 → 308

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	477	10058
1	1305	9703
2	4771	9703
3	5001	9703

prune234.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	308	0	308
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	308	5	313

Error

Counts

313 → 5

Alt Table

Status	Error	Program
	34.7b	(fma.f64 a 120 (*.f64 (/.f64 60 (sqrt.f64 (-.f64 z t))) (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 z t)))))
▶	0.3b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 (.f64 (cbrt.f64 60) (cbrt.f64 60)) (.f64 (cbrt.f64 60) (/.f64 y (-.f64 z t))))))
✓	0.1b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
✓	0.2b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))

Compiler

Compiled 8383 to 3436 computations (59% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 60) (/.f64 y (-.f64 z t)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 60) (cbrt.f64 60)) (*.f64 (cbrt.f64 60) (/.f64 y (-.f64 z t))))
	0.3b	(*.f64 60 (/.f64 x (-.f64 z t)))
✓	1.0b	(*.f64 (cbrt.f64 60) (cbrt.f64 60))

series55.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

30.0ms	(.f64 (.f64 (cbrt.f64 60) (cbrt.f64 60)) (*.f64 (cbrt.f64 60) (/.f64 y (-.f64 z t))))
25.0ms	(*.f64 (cbrt.f64 60) (/.f64 y (-.f64 z t)))
0.0ms	(*.f64 (cbrt.f64 60) (cbrt.f64 60))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
31×	`add-exp-log_binary64`
28×	`associate-r_binary64`
28×	`*-un-lft-identity_binary64`
24×	`pow1_binary64`

Counts

3 → 118

Calls

3 calls:

11.0ms	(*.f64 (cbrt.f64 60) (/.f64 y (-.f64 z t)))
10.0ms	(.f64 (.f64 (cbrt.f64 60) (cbrt.f64 60)) (*.f64 (cbrt.f64 60) (/.f64 y (-.f64 z t))))
4.0ms	(*.f64 (cbrt.f64 60) (cbrt.f64 60))

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

530×	`associate-/r*_binary64`
495×	`fma-def_binary64`
250×	`associate-/r/_binary64`
221×	`associate-l_binary64`
216×	`associate-r_binary64`

Counts

190 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	230	3624
1	571	3304
2	2240	3023
3	4958	3023

prune227.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	239	5	244

Error

Counts

244 → 5

Alt Table

Status	Error	Program
	34.7b	(fma.f64 a 120 (*.f64 (/.f64 60 (sqrt.f64 (-.f64 z t))) (/.f64 (-.f64 x y) (sqrt.f64 (-.f64 z t)))))
✓	0.3b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 (.f64 (cbrt.f64 60) (cbrt.f64 60)) (.f64 (cbrt.f64 60) (/.f64 y (-.f64 z t))))))
✓	0.1b	(fma.f64 a 120 (-.f64 (.f64 60 (/.f64 x (-.f64 z t))) (.f64 60 (/.f64 y (-.f64 z t)))))
✓	0.2b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.7b	(fma.f64 a 120 (.f64 (.f64 60 (-.f64 x y)) (/.f64 1 (-.f64 z t))))

Compiler

Compiled 7934 to 4534 computations (42.9% saved)

regimes2.3s (30.9%)

Accuracy

Total 0.1b remaining (86%)

Threshold costs 0.1b (86%)

Counts

175 → 1

Compiler

Compiled 47623 to 33015 computations (30.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	19	23
2	29	23
3	35	23
4	39	23
5	40	23
6	40	23

end82.0ms (1.1%)

Compiler: Compiled 154 to 103 computations (33.1% saved)

Details

analyze1.9s (25.3%)

sample1.3s (16.7%)

simplify110.0ms (1.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series79.0ms (1%)

rewrite19.0ms (0.3%)

simplify116.0ms (1.5%)

prune154.0ms (2%)

localize10.0ms (0.1%)

series113.0ms (1.5%)

rewrite29.0ms (0.4%)

simplify137.0ms (1.8%)

prune194.0ms (2.6%)

localize8.0ms (0.1%)

series88.0ms (1.2%)

rewrite36.0ms (0.5%)

simplify201.0ms (2.7%)

prune234.0ms (3.1%)

localize13.0ms (0.2%)

series55.0ms (0.7%)

rewrite32.0ms (0.4%)

simplify86.0ms (1.1%)

prune227.0ms (3%)

regimes2.3s (30.9%)

simplify3.0ms (0%)

end82.0ms (1.1%)

Profiling