Details

analyze1.5s (24.8%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.4s (22.4%)

Results

1.2s	8255×	body	128	valid
117.0ms	789×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify111.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

1.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.9b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

Compiler

Compiled 58 to 31 computations (46.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	3.1b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

series101.0ms (1.7%)

Counts

3 → 144

Calls

3 calls:

48.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
32.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
20.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
28×	`add-cube-cbrt_binary64`

Counts

3 → 122

Calls

3 calls:

12.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
6.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
2.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

simplify130.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

766×	`cancel-sign-sub-inv_binary64`
498×	`sub-neg_binary64`
213×	`associate--l+_binary64`
201×	`fma-neg_binary64`
200×	`+-commutative_binary64`

Counts

266 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	6584
1	983	6188
2	3712	6122
3	5248	6122

prune185.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	236	6	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	236	7	243

Error

Counts

243 → 7

Alt Table

Status	Error	Program
	7.7b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))))
✓	1.9b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
▶	2.0b	(+.f64 x (*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))))
	47.9b	(+.f64 x (.f64 (.f64 y (/.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 t)) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a))))) (/.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 t)) (cbrt.f64 (-.f64 z a)))))
	32.1b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a)))))
	29.8b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z t))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 z a))))
	9.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 6431 to 1943 computations (69.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))))
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	3.1b	(*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))))

series123.0ms (2%)

Counts

4 → 180

Calls

4 calls:

47.0ms	(+.f64 x (*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))))
32.0ms	(*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))))
22.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
21.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite93.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

392×	`times-frac_binary64`
337×	`add-sqr-sqrt_binary64`
325×	`*-un-lft-identity_binary64`
159×	`add-cube-cbrt_binary64`
98×	`associate-r_binary64`

Counts

4 → 349

Calls

4 calls:

24.0ms	(*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))))
10.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
6.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
3.0ms	(+.f64 x (*.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))))

simplify251.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

295×	`fma-neg_binary64`
284×	`associate--l+_binary64`
262×	`associate--r+_binary64`
241×	`associate-/l*_binary64`
202×	`sub-neg_binary64`

Counts

529 → 556

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	490	12377
1	1312	11592
2	4811	11592
3	5074	11592

prune431.0ms (7.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	555	1	556
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	557	6	563

Error

Counts

563 → 6

Alt Table

Status	Error	Program
	7.7b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 z a))))
✓	1.9b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
▶	1.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	47.9b	(+.f64 x (.f64 (.f64 y (/.f64 (+.f64 (sqrt.f64 z) (sqrt.f64 t)) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a))))) (/.f64 (-.f64 (sqrt.f64 z) (sqrt.f64 t)) (cbrt.f64 (-.f64 z a)))))
	32.1b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a)))))
	9.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 15171 to 5009 computations (67% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 z a))
✓	9.8b	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

series97.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

47.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
33.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))
17.0ms	(/.f64 y (-.f64 z a))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
31×	`times-frac_binary64`

Counts

3 → 155

Calls

3 calls:

10.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))
4.0ms	(/.f64 y (-.f64 z a))
4.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))

simplify160.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

630×	`cancel-sign-sub-inv_binary64`
319×	`sub-neg_binary64`
276×	`fma-neg_binary64`
202×	`associate-r_binary64`
197×	`associate-l_binary64`

Counts

287 → 303

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	413	6877
1	970	6238
2	3548	6142
3	4957	6141
4	4988	6141

prune211.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	301	2	303
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	303	6	309

Error

Counts

309 → 6

Alt Table

Status	Error	Program
	32.1b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a)))))
	13.4b	(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 z a)) 3)) (-.f64 z t)))
✓	1.9b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	1.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	34.3b	(+.f64 x (.f64 (/.f64 1 (sqrt.f64 (-.f64 z a))) (.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (-.f64 z t))))
▶	9.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 8008 to 2071 computations (74.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
✓	0.0b	(*.f64 (-.f64 z t) y)
✓	9.9b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))

series87.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

46.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
34.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))
6.0ms	(*.f64 (-.f64 z t) y)

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
6.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))
4.0ms	(*.f64 (-.f64 z t) y)

simplify113.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

900×	`fma-def_binary64`
563×	`cancel-sign-sub-inv_binary64`
333×	`sub-neg_binary64`
196×	`div-sub_binary64`
166×	`fma-neg_binary64`

Counts

192 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	258	4561
1	727	4147
2	2695	3786
3	4896	3783
4	4975	3783

prune126.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	189	5	194

Error

Counts

194 → 5

Alt Table

Status	Error	Program
✓	1.9b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	1.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	1.1b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 z a) y)))
	13.4b	(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 z a)) 3)) (-.f64 z t)))
✓	9.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 4517 to 1326 computations (70.6% saved)

regimes794.0ms (13%)

Accuracy

Total 3.0b remaining (99.6%)

Threshold costs 0b (0%)

Counts

102 → 1

Compiler

Compiled 15351 to 9621 computations (37.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-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	11	16
1	17	16
2	25	16
3	29	16
4	31	16
5	31	16

end73.0ms (1.2%)

Compiler: Compiled 115 to 73 computations (36.5% saved)

Details

analyze1.5s (24.8%)

sample1.4s (22.4%)

simplify111.0ms (1.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series101.0ms (1.7%)

rewrite32.0ms (0.5%)

simplify130.0ms (2.1%)

prune185.0ms (3%)

localize10.0ms (0.2%)

series123.0ms (2%)

rewrite93.0ms (1.5%)

simplify251.0ms (4.1%)

prune431.0ms (7.1%)

localize8.0ms (0.1%)

series97.0ms (1.6%)

rewrite32.0ms (0.5%)

simplify160.0ms (2.6%)

prune211.0ms (3.5%)

localize8.0ms (0.1%)

series87.0ms (1.4%)

rewrite22.0ms (0.4%)

simplify113.0ms (1.9%)

prune126.0ms (2.1%)

regimes794.0ms (13%)

simplify2.0ms (0%)

end73.0ms (1.2%)

Profiling