Details

analyze1.9s (23.2%)

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 (15.7%)

Results

1.1s	8124×	body	128	valid
97.0ms	687×	body	128	invalid
16.0ms	47×	body	1024	valid
14.0ms	34×	body	2048	valid
13.0ms	32×	body	512	valid
4.0ms	18×	body	256	valid
0.0ms	1×	body	4096	valid

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify112.0ms (1.4%)

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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(+.f64 (/.f64 (.f64 60 (-.f64 x y)) (-.f64 z t)) (.f64 a 120))
▶	0.1b	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

Compiler

Compiled 100 to 68 computations (32% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series88.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))
40.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
7.0ms	(*.f64 60 (-.f64 x y))

rewrite21.0ms (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:

8.0ms	(/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))
7.0ms	(*.f64 60 (-.f64 x y))
0.0ms	(fma.f64 a 120 (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)))

simplify114.0ms (1.4%)

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

prune158.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	160	5	165

Error

Counts

165 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 a 120 (*.f64 60 (/.f64 (-.f64 x y) (-.f64 z t))))
	0.3b	(fma.f64 a 120 (/.f64 (+.f64 (.f64 x 60) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) 60)) (-.f64 z t)))
	0.5b	(fma.f64 a 120 (/.f64 (.f64 (.f64 (cbrt.f64 60) (cbrt.f64 60)) (*.f64 (cbrt.f64 60) (-.f64 x y))) (-.f64 z t)))
	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
	0.2b	(fma.f64 a 120 (/.f64 1 (/.f64 (-.f64 z t) (*.f64 60 (-.f64 x y)))))

Compiler

Compiled 4405 to 2122 computations (51.8% 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 x y) (-.f64 z t))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z t))
✓	0.3b	(*.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)))

series107.0ms (1.3%)

Counts

3 → 156

Calls

3 calls:

41.0ms	(fma.f64 a 120 (*.f64 60 (/.f64 (-.f64 x y) (-.f64 z t))))
39.0ms	(*.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)))
26.0ms	(/.f64 (-.f64 x y) (-.f64 z t))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`

Counts

3 → 116

Calls

3 calls:

10.0ms	(*.f64 60 (/.f64 (-.f64 x y) (-.f64 z t)))
7.0ms	(/.f64 (-.f64 x y) (-.f64 z t))
0.0ms	(fma.f64 a 120 (*.f64 60 (/.f64 (-.f64 x y) (-.f64 z t))))

simplify185.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

788×	`times-frac_binary64`
500×	`fma-neg_binary64`
426×	`sub-neg_binary64`
211×	`fma-def_binary64`
175×	`+-commutative_binary64`

Counts

272 → 181

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	318	6872
1	952	6595
2	3252	6595
3	4972	6595
4	5208	6595

prune138.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	181	5	186

Error

Counts

186 → 5

Alt Table

Status	Error	Program
	0.4b	(fma.f64 a 120 (.f64 (.f64 (cbrt.f64 60) (cbrt.f64 60)) (*.f64 (cbrt.f64 60) (/.f64 (-.f64 x y) (-.f64 z t)))))
▶	0.1b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.1b	(fma.f64 a 120 (*.f64 60 (/.f64 (-.f64 x y) (-.f64 z t))))
	0.3b	(fma.f64 a 120 (/.f64 (+.f64 (.f64 x 60) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) 60)) (-.f64 z t)))
	0.2b	(fma.f64 a 120 (/.f64 1 (/.f64 (-.f64 z t) (*.f64 60 (-.f64 x y)))))

Compiler

Compiled 5027 to 2185 computations (56.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 x y))
✓	0.0b	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
✓	0.9b	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))

series104.0ms (1.3%)

Counts

3 → 156

Calls

3 calls:

43.0ms	(fma.f64 a 120 (/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y))))
35.0ms	(/.f64 60 (/.f64 (-.f64 z t) (-.f64 x y)))
26.0ms	(/.f64 (-.f64 z t) (-.f64 x y))

rewrite40.0ms (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:

10.0ms	(/.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))))

simplify204.0ms (2.5%)

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

prune238.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	309	4	313

Error

Counts

313 → 4

Alt Table

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

Compiler

Compiled 8333 to 3405 computations (59.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 120 (*.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y)))))
✓	0.2b	(/.f64 (sqrt.f64 60) (-.f64 z t))
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y))))
✓	0.4b	(/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y)))

series193.0ms (2.3%)

Counts

4 → 156

Calls

4 calls:

94.0ms	(fma.f64 a 120 (*.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y)))))
80.0ms	(*.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y))))
12.0ms	(/.f64 (sqrt.f64 60) (-.f64 z t))
6.0ms	(/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y)))

rewrite152.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

551×	`times-frac_binary64`
428×	`add-sqr-sqrt_binary64`
354×	`*-un-lft-identity_binary64`
244×	`add-cube-cbrt_binary64`
178×	`sqrt-prod_binary64`

Counts

4 → 457

Calls

4 calls:

72.0ms	(*.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y))))
9.0ms	(/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y)))
5.0ms	(/.f64 (sqrt.f64 60) (-.f64 z t))
0.0ms	(fma.f64 a 120 (*.f64 (/.f64 (sqrt.f64 60) (-.f64 z t)) (/.f64 (sqrt.f64 60) (/.f64 1 (-.f64 x y)))))

simplify328.0ms (4%)

Algorithm

1×	egg-herbie

Rules

310×	`associate-/l*_binary64`
299×	`*-commutative_binary64`
277×	`associate-*l/_binary64`
275×	`associate-*r/_binary64`
269×	`sub-neg_binary64`

Counts

613 → 578

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	459	15723
1	1266	14906
2	4437	14534
3	5074	14534

prune555.0ms (6.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	578	0	578
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	578	4	582

Error

Counts

582 → 4

Alt Table

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

Compiler

Compiled 17880 to 11064 computations (38.1% saved)

regimes2.1s (26.1%)

Accuracy

Total 0.1b remaining (86.6%)

Threshold costs 0.1b (86.6%)

Counts

154 → 1

Compiler

Compiled 37119 to 26953 computations (27.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	18	17
2	26	17
3	30	17
4	32	17
5	32	17

end77.0ms (0.9%)

Compiler: Compiled 118 to 84 computations (28.8% saved)

Details

analyze1.9s (23.2%)

sample1.3s (15.7%)

simplify112.0ms (1.4%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series88.0ms (1.1%)

rewrite21.0ms (0.3%)

simplify114.0ms (1.4%)

prune158.0ms (1.9%)

localize8.0ms (0.1%)

series107.0ms (1.3%)

rewrite26.0ms (0.3%)

simplify185.0ms (2.2%)

prune138.0ms (1.7%)

localize9.0ms (0.1%)

series104.0ms (1.3%)

rewrite40.0ms (0.5%)

simplify204.0ms (2.5%)

prune238.0ms (2.9%)

localize12.0ms (0.1%)

series193.0ms (2.3%)

rewrite152.0ms (1.8%)

simplify328.0ms (4%)

prune555.0ms (6.7%)

regimes2.1s (26.1%)

simplify2.0ms (0%)

end77.0ms (0.9%)

Profiling