Details

analyze1.3s (17.2%)

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
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
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (15.6%)

Results

1.0s	8250×	body	128	valid
85.0ms	725×	body	128	invalid
1.0ms	3×	body	512	valid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify119.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1627×	`fma-def_binary64`
927×	`div-sub_binary64`
619×	`times-frac_binary64`
541×	`fma-neg_binary64`
386×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	40	14
3	78	14
4	161	14
5	302	14
6	659	14
7	1591	14
8	3045	14
9	3070	14
10	3380	14
11	3469	14
12	3480	14
13	4892	14
14	5124	14

prune3.0ms (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

1.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	1.6b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

Compiler

Compiled 88 to 49 computations (44.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	2.7b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

series93.0ms (1.3%)

Counts

3 → 144

Calls

3 calls:

42.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
31.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
19.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite29.0ms (0.4%)

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:

11.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
6.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
2.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

simplify163.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

568×	`sub-neg_binary64`
307×	`fma-neg_binary64`
290×	`associate--l+_binary64`
228×	`+-commutative_binary64`
216×	`associate--r+_binary64`

Counts

266 → 248

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	6563
1	1064	6071
2	4018	6005
3	4934	6005
4	4983	6005

prune186.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	241	7	248
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	242	8	250

Error

0.0b

Counts

250 → 8

Alt Table

Status	Error	Program
	32.4b	(+.f64 x (*.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t))) (sqrt.f64 (-.f64 a t)))))
	18.1b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))
▶	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	9.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
	7.3b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))))
	1.6b	(+.f64 x (*.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))))
	34.1b	(+.f64 x (.f64 (sqrt.f64 (/.f64 (.f64 (-.f64 z t) y) (-.f64 a t))) (sqrt.f64 (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))))
	33.3b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))

Compiler

Compiled 6607 to 1989 computations (69.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.5b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series40.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

40.0ms

(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-def_binary64`
506×	`times-frac_binary64`
476×	`cancel-sign-sub-inv_binary64`
453×	`associate-/l*_binary64`
373×	`fma-neg_binary64`

Counts

70 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	2025
1	375	1996
2	1299	1448
3	4541	1448
4	4981	1448
5	4975	1448

prune121.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	137	7	144

Error

0.0b

Counts

144 → 7

Alt Table

Status	Error	Program
	30.4b	(+.f64 (fma.f64 (/.f64 y a) z x) (*.f64 (/.f64 y a) (-.f64 (/.f64 z (/.f64 a t)) t)))
▶	7.3b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))))
	32.4b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t))) (sqrt.f64 (-.f64 a t))) x)
	18.1b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))
✓	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	27.1b	(-.f64 (+.f64 x (fma.f64 (/.f64 a t) y y)) (*.f64 (/.f64 y t) (+.f64 z (/.f64 z (/.f64 t a)))))
	33.3b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))

Compiler

Compiled 3522 to 1151 computations (67.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
✓	0.6b	(cbrt.f64 (-.f64 z t))
✓	7.6b	(.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t)))

series174.0ms (2.4%)

Counts

4 → 132

Calls

4 calls:

64.0ms	(/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))
46.0ms	(.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t)))
35.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
29.0ms	(cbrt.f64 (-.f64 z t))

rewrite65.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64`
125×	`*-un-lft-identity_binary64`
88×	`cbrt-prod_binary64`
80×	`times-frac_binary64`
54×	`associate-r_binary64`

Counts

4 → 235

Calls

4 calls:

21.0ms	(.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t)))
8.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
7.0ms	(/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))
2.0ms	(cbrt.f64 (-.f64 z t))

simplify227.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

403×	`fma-def_binary64`
382×	`associate-/l*_binary64`
255×	`times-frac_binary64`
250×	`*-commutative_binary64`
172×	`associate-/r*_binary64`

Counts

367 → 444

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	717	11308
1	2069	10257
2	4988	10257
3	5005	10257

prune430.0ms (5.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	547	1	548
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	547	8	555

Error

Counts

555 → 8

Alt Table

Status	Error	Program
	20.4b	(+.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (cbrt.f64 (.f64 (*.f64 (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t)) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))))))
✓	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	30.4b	(+.f64 (fma.f64 (/.f64 y a) z x) (*.f64 (/.f64 y a) (-.f64 (/.f64 z (/.f64 a t)) t)))
✓	7.3b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))))
	32.4b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t))) (sqrt.f64 (-.f64 a t))) x)
▶	18.1b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))
	27.1b	(-.f64 (+.f64 x (fma.f64 (/.f64 a t) y y)) (*.f64 (/.f64 y t) (+.f64 z (/.f64 z (/.f64 t a)))))
	33.3b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))

Compiler

Compiled 21127 to 7386 computations (65% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	0.1b	(*.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
✓	0.1b	(.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
✓	3.2b	(sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

series609.0ms (8.2%)

Counts

3 → 92

Calls

3 calls:

231.0ms	(sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))
221.0ms	(*.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
156.0ms	(.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64`
99×	`*-un-lft-identity_binary64`
95×	`sqrt-prod_binary64`
77×	`times-frac_binary64`
68×	`associate-r_binary64`

Counts

3 → 153

Calls

3 calls:

19.0ms	(.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
12.0ms	(*.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))
6.0ms	(sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))

simplify135.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

732×	`times-frac_binary64`
554×	`associate-/l*_binary64`
503×	`associate-/r*_binary64`
456×	`fma-def_binary64`
219×	`*-commutative_binary64`

Counts

245 → 268

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	670	8564
1	2066	8295
2	5495	8295

prune635.0ms (8.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	507	1	508
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	509	7	516

Error

Counts

516 → 7

Alt Table

Status	Error	Program
	30.4b	(+.f64 (fma.f64 (/.f64 y a) z x) (*.f64 (/.f64 y a) (-.f64 (/.f64 z (/.f64 a t)) t)))
✓	7.3b	(+.f64 x (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))))
	32.4b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t))) (sqrt.f64 (-.f64 a t))) x)
	18.1b	(+.f64 x (.f64 (.f64 (*.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))))))
✓	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	27.1b	(-.f64 (+.f64 x (fma.f64 (/.f64 a t) y y)) (*.f64 (/.f64 y t) (+.f64 z (/.f64 z (/.f64 t a)))))
	33.3b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))

Compiler

Compiled 21568 to 6978 computations (67.6% saved)

regimes1.7s (22.4%)

Accuracy

Total 0.5b remaining (93.9%)

Threshold costs 0.5b (93.9%)

Counts

176 → 1

Compiler

Compiled 35452 to 19554 computations (44.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	23	52
2	29	52
3	31	52
4	32	52
5	32	52

end96.0ms (1.3%)

Compiler: Compiled 246 to 117 computations (52.4% saved)

Details

analyze1.3s (17.2%)

sample1.2s (15.6%)

simplify119.0ms (1.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series93.0ms (1.3%)

rewrite29.0ms (0.4%)

simplify163.0ms (2.2%)

prune186.0ms (2.5%)

localize7.0ms (0.1%)

series40.0ms (0.5%)

rewrite1.0ms (0%)

simplify87.0ms (1.2%)

prune121.0ms (1.6%)

localize11.0ms (0.2%)

series174.0ms (2.4%)

rewrite65.0ms (0.9%)

simplify227.0ms (3.1%)

prune430.0ms (5.8%)

localize10.0ms (0.1%)

series609.0ms (8.2%)

rewrite56.0ms (0.8%)

simplify135.0ms (1.8%)

prune635.0ms (8.6%)

regimes1.7s (22.4%)

simplify3.0ms (0%)

end96.0ms (1.3%)

Profiling