Details

analyze1.9s (26.8%)

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
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
3.7%	96.1%	0.2%	13
4.2%	94.5%	1.3%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.5s (21.1%)

Results

1.1s	8256×	body	128	valid
339.0ms	2418×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify101.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
614×	`times-frac_binary64`
480×	`neg-mul-1_binary64`
416×	`div-sub_binary64`
394×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	28	23
2	55	23
3	101	21
4	220	21
5	423	21
6	834	20
7	1845	19
8	3893	19
9	4281	19
10	4633	19
11	4956	19
12	4804	19

prune4.0ms (0.1%)

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
	11.4b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series52.0ms (0.7%)

Counts

3 → 96

Calls

3 calls:

32.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
12.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
8.0ms	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

rewrite192.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

179×	`*-un-lft-identity_binary64`
121×	`add-sqr-sqrt_binary64`
118×	`times-frac_binary64`
116×	`add-cube-cbrt_binary64`
96×	`prod-diff_binary64`

Counts

3 → 215

Calls

3 calls:

138.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
10.0ms	(-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))
5.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

simplify184.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
501×	`distribute-rgt-in_binary64`
470×	`distribute-lft-in_binary64`
329×	`fma-neg_binary64`
178×	`cancel-sign-sub-inv_binary64`

Counts

311 → 270

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	8725
1	750	5951
2	1752	4992
3	4889	4992
4	4828	4992

prune346.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	263	7	270
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	264	8	272

Error

Counts

272 → 8

Alt Table

Status	Error	Program
	46.8b	(log1p.f64 (expm1.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	30.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	11.8b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))
	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
	30.9b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (+.f64 -2 (/.f64 -2 z)) (sqrt.f64 t)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	48.8b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) (/.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))

Compiler

Compiled 10219 to 7173 computations (29.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z))))))
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
✓	0.0b	(+.f64 (/.f64 2 t) (/.f64 2 (*.f64 t z)))
✓	0.7b	(/.f64 2 (*.f64 t z))

series59.0ms (0.9%)

Counts

4 → 96

Calls

4 calls:

31.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
11.0ms	(+.f64 (/.f64 2 t) (/.f64 2 (*.f64 t z)))
9.0ms	(-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z))))))
8.0ms	(/.f64 2 (*.f64 t z))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
26×	`fma-def_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`

Counts

4 → 112

Calls

4 calls:

9.0ms	(+.f64 (/.f64 2 t) (/.f64 2 (*.f64 t z)))
7.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
3.0ms	(/.f64 2 (*.f64 t z))
2.0ms	(-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z))))))

simplify111.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
616×	`distribute-rgt-in_binary64`
563×	`distribute-lft-in_binary64`
299×	`fma-neg_binary64`
133×	`cancel-sign-sub-inv_binary64`

Counts

208 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	3372
1	451	3214
2	1391	3162
3	4827	3162
4	4872	3162

prune219.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	180	4	184
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	186	6	192

Error

Counts

192 → 6

Alt Table

Status	Error	Program
	46.8b	(log1p.f64 (expm1.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (.f64 t z) (sqrt.f64 2))))))))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (.f64 (/.f64 (sqrt.f64 2) t) (/.f64 (sqrt.f64 2) z)))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (fma.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 2) t) (/.f64 2 (.f64 t z)))))))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))

Compiler

Compiled 5052 to 3260 computations (35.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z)))))
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
✓	0.0b	(+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))
✓	0.3b	(/.f64 (/.f64 2 t) z)

series61.0ms (0.9%)

Counts

4 → 120

Calls

4 calls:

30.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
11.0ms	(/.f64 (/.f64 2 t) z)
10.0ms	(-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z)))))
10.0ms	(+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`times-frac_binary64`
74×	`*-un-lft-identity_binary64`
63×	`add-sqr-sqrt_binary64`
63×	`add-cube-cbrt_binary64`
26×	`fma-def_binary64`

Counts

4 → 161

Calls

4 calls:

22.0ms	(+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))
7.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
4.0ms	(/.f64 (/.f64 2 t) z)
2.0ms	(-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z)))))

simplify132.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

657×	`fma-def_binary64`
599×	`times-frac_binary64`
579×	`distribute-rgt-in_binary64`
367×	`fma-neg_binary64`
147×	`associate-/l/_binary64`

Counts

281 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	4528
1	655	4371
2	1845	4316
3	4856	4316
4	4970	4316

prune262.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	245	6	251

Error

Counts

251 → 6

Alt Table

Status	Error	Program
	46.8b	(log1p.f64 (expm1.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
▶	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (.f64 t z) (sqrt.f64 2))))))))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (.f64 (/.f64 (sqrt.f64 2) t) (/.f64 (sqrt.f64 2) z)))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (fma.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 2) t) (/.f64 2 (.f64 t z)))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))

Compiler

Compiled 6807 to 4528 computations (33.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (.f64 t z) (sqrt.f64 2))))))))
✓	0.0b	(+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (*.f64 t z) (sqrt.f64 2))))
✓	0.4b	(/.f64 (*.f64 t z) (sqrt.f64 2))
✓	0.8b	(/.f64 (sqrt.f64 2) (/.f64 (*.f64 t z) (sqrt.f64 2)))

series107.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

46.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (.f64 t z) (sqrt.f64 2))))))))
24.0ms	(/.f64 (sqrt.f64 2) (/.f64 (*.f64 t z) (sqrt.f64 2)))
21.0ms	(+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (*.f64 t z) (sqrt.f64 2))))
14.0ms	(/.f64 (*.f64 t z) (sqrt.f64 2))

rewrite69.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`times-frac_binary64`
76×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
60×	`sqrt-prod_binary64`

Counts

4 → 190

Calls

4 calls:

32.0ms	(+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (*.f64 t z) (sqrt.f64 2))))
9.0ms	(/.f64 (sqrt.f64 2) (/.f64 (*.f64 t z) (sqrt.f64 2)))
7.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (.f64 t z) (sqrt.f64 2))))))))
4.0ms	(/.f64 (*.f64 t z) (sqrt.f64 2))

simplify156.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

511×	`distribute-rgt-in_binary64`
468×	`distribute-lft-in_binary64`
468×	`fma-def_binary64`
173×	`fma-neg_binary64`
142×	`associate-/r/_binary64`

Counts

286 → 261

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	5467
1	666	4786
2	2076	4642
3	4668	4442
4	4948	4442

prune323.0ms (4.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	261	6	267

Error

Counts

267 → 6

Alt Table

Status	Error	Program
	46.8b	(log1p.f64 (expm1.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (.f64 t (/.f64 z (sqrt.f64 2)))))))))
✓	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (.f64 t z) (sqrt.f64 2))))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (fma.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (sqrt.f64 2) t) (/.f64 2 (.f64 t z)))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))

Compiler

Compiled 8006 to 5767 computations (28% saved)

regimes1.0s (14.6%)

Accuracy

Total 0.1b remaining (82.9%)

Threshold costs 0.1b (82.9%)

Counts

128 → 1

Compiler

Compiled 19763 to 15418 computations (22% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`cancel-sign-sub-inv_binary64`
15×	`distribute-rgt-neg-in_binary64`
10×	`distribute-lft-neg-in_binary64`
9×	`sub-neg_binary64`
9×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	38	25
2	59	25
3	82	25
4	97	25
5	106	25
6	108	25
7	102	25

end105.0ms (1.5%)

Compiler: Compiled 179 to 141 computations (21.2% saved)

Details

analyze1.9s (26.8%)

sample1.5s (21.1%)

simplify101.0ms (1.5%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series52.0ms (0.7%)

rewrite192.0ms (2.8%)

simplify184.0ms (2.6%)

prune346.0ms (5%)

localize11.0ms (0.2%)

series59.0ms (0.9%)

rewrite26.0ms (0.4%)

simplify111.0ms (1.6%)

prune219.0ms (3.1%)

localize10.0ms (0.1%)

series61.0ms (0.9%)

rewrite47.0ms (0.7%)

simplify132.0ms (1.9%)

prune262.0ms (3.8%)

localize17.0ms (0.2%)

series107.0ms (1.5%)

rewrite69.0ms (1%)

simplify156.0ms (2.2%)

prune323.0ms (4.6%)

regimes1.0s (14.6%)

simplify4.0ms (0.1%)

end105.0ms (1.5%)

Profiling