Details

analyze1.3s (13.8%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
16.4%	83.4%	0.2%	11
19.9%	79.9%	0.2%	12
21.6%	77.2%	1.2%	13
24.8%	73.7%	1.4%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (14.8%)

Symmetry

(sort x y)

(sort z t)

Results

961.0ms	8256×	body	128	valid
373.0ms	3093×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify43.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
389×	`fma-neg_binary64`
130×	`cancel-sign-sub-inv_binary64`
113×	`distribute-rgt-in_binary64`
103×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	42	13
3	73	13
4	144	13
5	223	13
6	319	13
7	495	13
8	678	13
9	833	13
10	889	13
11	976	13
12	982	13
13	987	13
14	914	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

7.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.2b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(-.f64 (.f64 x y) (.f64 z t))
✓	6.8b	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)

series32.0ms (0.3%)

Counts

2 → 108

Calls

2 calls:

23.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
9.0ms	(-.f64 (.f64 x y) (.f64 z t))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 48

Calls

2 calls:

4.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)
2.0ms	(-.f64 (.f64 x y) (.f64 z t))

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

644×	`distribute-rgt-in_binary64`
301×	`fma-neg_binary64`
270×	`associate-l_binary64`
223×	`fma-def_binary64`
213×	`associate-r_binary64`

Counts

156 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	2115
1	251	2035
2	743	2029
3	2355	2029
4	4590	2029
5	4996	2029
6	4923	2029

prune80.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	12	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	12	94

Error

6.9b

Counts

94 → 12

Alt Table

Status	Error	Program
	8.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (.f64 x y) (.f64 z t)) (cbrt.f64 a)))
	32.0b	(/.f64 (*.f64 y x) a)
	7.3b	(.f64 (-.f64 (.f64 x y) (*.f64 z t)) (/.f64 1 a))
	8.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a))) (cbrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)))
	35.8b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) (sqrt.f64 a)))
▶	7.2b	(-.f64 (/.f64 (.f64 y x) a) (/.f64 (.f64 t z) a))
	32.4b	(neg.f64 (/.f64 (*.f64 t z) a))
	8.1b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (/.f64 a (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z t)))))
	30.4b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z t) (.f64 z t))) (.f64 a (fma.f64 t z (.f64 y x))))
	32.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) a)))
	42.8b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (.f64 a (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t))))))
	7.6b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))

Compiler

Compiled 2150 to 573 computations (73.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 y x) a) (/.f64 (.f64 t z) a))
✓	3.9b	(/.f64 (*.f64 t z) a)
✓	6.1b	(/.f64 (*.f64 y x) a)

series49.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

26.0ms	(-.f64 (/.f64 (.f64 y x) a) (/.f64 (.f64 t z) a))
12.0ms	(/.f64 (*.f64 y x) a)
11.0ms	(/.f64 (*.f64 t z) a)

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64`
49×	`prod-diff_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`

Counts

3 → 127

Calls

3 calls:

7.0ms	(-.f64 (/.f64 (.f64 y x) a) (/.f64 (.f64 t z) a))
5.0ms	(/.f64 (*.f64 t z) a)
3.0ms	(/.f64 (*.f64 y x) a)

simplify140.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

943×	`times-frac_binary64`
526×	`fma-def_binary64`
355×	`fma-neg_binary64`
145×	`cancel-sign-sub-inv_binary64`
145×	`exp-prod_binary64`

Counts

151 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	3243
1	483	2673
2	1675	2230
3	4200	2230
4	4900	2230
5	4999	2230
6	4854	2230

prune216.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	158	4	162
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	166	8	174

Error

0.0b

Counts

174 → 8

Alt Table

Status	Error	Program
	32.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) a)))
	9.1b	(-.f64 (/.f64 (*.f64 y x) a) (/.f64 t (/.f64 a z)))
	7.7b	(-.f64 (/.f64 y (/.f64 a x)) (/.f64 (*.f64 t z) a))
	36.2b	(-.f64 (.f64 (/.f64 y (sqrt.f64 a)) (/.f64 x (sqrt.f64 a))) (/.f64 (.f64 t z) a))
	30.4b	(/.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z t) (.f64 z t))) (.f64 a (fma.f64 t z (.f64 y x))))
	8.3b	(+.f64 (fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (.f64 (/.f64 z a) (/.f64 t 1)))) (fma.f64 (neg.f64 (/.f64 z a)) (/.f64 t 1) (.f64 (/.f64 z a) (/.f64 t 1))))
	42.8b	(/.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 z t) 3)) (.f64 a (+.f64 (.f64 (.f64 x y) (.f64 x y)) (+.f64 (.f64 (.f64 z t) (.f64 z t)) (.f64 (.f64 x y) (.f64 z t))))))
▶	7.6b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))

Compiler

Compiled 4565 to 932 computations (79.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(-.f64 (.f64 x y) (.f64 z t))
✓	0.5b	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
✓	6.8b	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))

series99.0ms (1%)

Counts

2 → 120

Calls

2 calls:

58.0ms	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))
41.0ms	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

2 → 117

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))
4.0ms	(/.f64 a (-.f64 (.f64 x y) (.f64 z t)))

simplify178.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
372×	`fma-neg_binary64`
341×	`times-frac_binary64`
322×	`associate-/l/_binary64`
189×	`cancel-sign-sub-inv_binary64`

Counts

237 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	5987
1	558	5614
2	2374	5371
3	4849	5371
4	5107	5371

prune227.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	234	3	237
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	237	8	245

Error

0.0b

Counts

245 → 8

Alt Table

Status	Error	Program
	33.9b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (-.f64 (.f64 x y) (.f64 z t)))) (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))))
▶	7.4b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (.f64 x y) (.f64 z t))))
	32.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) a)))
	9.1b	(-.f64 (/.f64 (*.f64 y x) a) (/.f64 t (/.f64 a z)))
	7.7b	(-.f64 (/.f64 y (/.f64 a x)) (/.f64 (*.f64 t z) a))
	36.2b	(-.f64 (.f64 (/.f64 y (sqrt.f64 a)) (/.f64 x (sqrt.f64 a))) (/.f64 (.f64 t z) a))
	7.7b	(/.f64 1 (.f64 a (/.f64 1 (-.f64 (.f64 x y) (*.f64 z t)))))
	8.3b	(+.f64 (fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (.f64 (/.f64 z a) (/.f64 t 1)))) (fma.f64 (neg.f64 (/.f64 z a)) (/.f64 t 1) (.f64 (/.f64 z a) (/.f64 t 1))))

Compiler

Compiled 5809 to 1718 computations (70.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (-.f64 (.f64 x y) (.f64 z t)))
	0.4b	(-.f64 (.f64 x y) (.f64 z t))
✓	6.7b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (.f64 x y) (.f64 z t))))

series62.0ms (0.6%)

Counts

2 → 108

Calls

2 calls:

35.0ms	(/.f64 1 (-.f64 (.f64 x y) (.f64 z t)))
27.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (.f64 x y) (.f64 z t))))

rewrite60.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

474×	`times-frac_binary64`
220×	`*-un-lft-identity_binary64`
220×	`add-sqr-sqrt_binary64`
220×	`add-cube-cbrt_binary64`
46×	`add-exp-log_binary64`

Counts

2 → 292

Calls

2 calls:

10.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (.f64 x y) (.f64 z t))))
6.0ms	(/.f64 1 (-.f64 (.f64 x y) (.f64 z t)))

simplify268.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
283×	`fma-neg_binary64`
217×	`distribute-rgt-in_binary64`
199×	`distribute-lft-in_binary64`
197×	`cancel-sign-sub-inv_binary64`

Counts

400 → 369

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	12199
1	635	11258
2	2385	11054
3	4689	11054
4	4967	11054

prune294.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	400	1	401
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	401	8	409

Error

0.0b

Counts

409 → 8

Alt Table

Status	Error	Program
	32.2b	(.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (.f64 z t)) a)) (sqrt.f64 (/.f64 (-.f64 (.f64 x y) (*.f64 z t)) a)))
	9.1b	(-.f64 (/.f64 (*.f64 y x) a) (/.f64 t (/.f64 a z)))
	35.0b	(/.f64 (/.f64 1 a) (cbrt.f64 (pow.f64 (/.f64 1 (-.f64 (.f64 y x) (.f64 t z))) 3)))
	7.7b	(-.f64 (/.f64 y (/.f64 a x)) (/.f64 (*.f64 t z) a))
	33.9b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.f64 (.f64 (/.f64 a (-.f64 (.f64 x y) (.f64 z t))) (/.f64 a (-.f64 (.f64 x y) (.f64 z t)))) (/.f64 a (-.f64 (.f64 x y) (.f64 z t))))))
	36.2b	(-.f64 (.f64 (/.f64 y (sqrt.f64 a)) (/.f64 x (sqrt.f64 a))) (/.f64 (.f64 t z) a))
	7.7b	(/.f64 1 (.f64 a (/.f64 1 (-.f64 (.f64 x y) (*.f64 z t)))))
	8.3b	(+.f64 (fma.f64 (/.f64 y 1) (/.f64 x a) (neg.f64 (.f64 (/.f64 z a) (/.f64 t 1)))) (fma.f64 (neg.f64 (/.f64 z a)) (/.f64 t 1) (.f64 (/.f64 z a) (/.f64 t 1))))

Compiler

Compiled 11641 to 4787 computations (58.9% saved)

regimes4.2s (43.5%)

Accuracy

Total 0.6b remaining (95.1%)

Threshold costs 0.6b (95.1%)

Counts

214 → 3

Compiler

Compiled 51266 to 31279 computations (39% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`distribute-rgt-neg-in_binary64`
18×	`cancel-sign-sub-inv_binary64`
17×	`distribute-lft-neg-in_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	86
1	64	84
2	87	84
3	116	84
4	134	84
5	146	84
6	158	84
7	162	84
8	158	84

end715.0ms (7.4%)

Compiler: Compiled 560 to 274 computations (51.1% saved)

Iter	Nodes	Cost
0	10	13
1	21	13
2	42	13
3	73	13
4	144	13
5	223	13
6	319	13
7	495	13
8	678	13
9	833	13
10	889	13
11	976	13
12	982	13
13	987	13
14	914	13

Iter	Nodes	Cost
0	10	13
1	21	13
2	42	13
3	73	13
4	144	13
5	223	13
6	319	13
7	495	13
8	678	13
9	833	13
10	889	13
11	976	13
12	982	13
13	987	13
14	914	13

Details

analyze1.3s (13.8%)

sample1.4s (14.8%)

simplify43.0ms (0.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series32.0ms (0.3%)

rewrite9.0ms (0.1%)

simplify110.0ms (1.1%)

prune80.0ms (0.8%)

localize7.0ms (0.1%)

series49.0ms (0.5%)

rewrite24.0ms (0.2%)

simplify140.0ms (1.5%)

prune216.0ms (2.3%)

localize8.0ms (0.1%)

series99.0ms (1%)

rewrite22.0ms (0.2%)

simplify178.0ms (1.9%)

prune227.0ms (2.4%)

localize9.0ms (0.1%)

series62.0ms (0.6%)

rewrite60.0ms (0.6%)

simplify268.0ms (2.8%)

prune294.0ms (3.1%)

regimes4.2s (43.5%)

bsearch7.0ms (0.1%)

simplify9.0ms (0.1%)

end715.0ms (7.4%)

Profiling

Iter	Nodes	Cost
0	10	13
1	21	13
2	42	13
3	73	13
4	144	13
5	223	13
6	319	13
7	495	13
8	678	13
9	833	13
10	889	13
11	976	13
12	982	13
13	987	13
14	914	13