Details

analyze1.3s (16.8%)

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
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.5s (19.7%)

Results

959.0ms	6993×	body	128	valid
163.0ms	352×	body	1024	valid
153.0ms	481×	body	512	valid
95.0ms	760×	body	128	invalid
86.0ms	384×	body	256	valid
22.0ms	46×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify141.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	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

13.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.6b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	19.2b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	2.8b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series64.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

43.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
21.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

simplify140.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
644×	`fma-neg_binary64`
523×	`cancel-sign-sub-inv_binary64`
397×	`sub-neg_binary64`
195×	`div-sub_binary64`

Counts

160 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4255
1	740	4157
2	2480	3550
3	4430	3531
4	5167	3531

prune118.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	6	139

Error

0.1b

Counts

139 → 6

Alt Table

Status	Error	Program
	13.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
	30.1b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.7b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
▶	13.6b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	37.1b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	17.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 3628 to 1210 computations (66.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
✓	4.0b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

series77.0ms (1%)

Counts

3 → 120

Calls

3 calls:

43.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
25.0ms	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
9.0ms	(/.f64 1 (-.f64 a t))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

11.0ms	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
4.0ms	(/.f64 1 (-.f64 a t))
0.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

simplify147.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

699×	`times-frac_binary64`
529×	`cancel-sign-sub-inv_binary64`
521×	`fma-neg_binary64`
400×	`sub-neg_binary64`
187×	`+-commutative_binary64`

Counts

225 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	304	5043
1	793	4777
2	2825	4721
3	4910	4720
4	5185	4720

prune162.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	230	6	236

Error

0.1b

Counts

236 → 6

Alt Table

Status	Error	Program
▶	13.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
	30.1b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.7b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	13.6b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	37.1b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	17.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 5834 to 2020 computations (65.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
✓	0.2b	(*.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
✓	2.8b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
✓	4.1b	(cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))

series866.0ms (11%)

Counts

4 → 168

Calls

4 calls:

551.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
230.0ms	(cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))
56.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
28.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))

rewrite128.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

303×	`*-un-lft-identity_binary64`
248×	`cbrt-prod_binary64`
247×	`add-sqr-sqrt_binary64`
205×	`times-frac_binary64`
96×	`distribute-lft-out--_binary64`

Counts

4 → 284

Calls

4 calls:

35.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
28.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))))
5.0ms	(cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))
0.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))

simplify282.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

657×	`*-commutative_binary64`
239×	`fma-def_binary64`
233×	`associate-+r+_binary64`
223×	`associate-r_binary64`
172×	`associate-/l*_binary64`

Counts

452 → 497

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1683	24862
1	5103	24862

prune864.0ms (11%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	711	0	711
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	711	6	717

Error

0.1b

Counts

717 → 6

Alt Table

Status	Error	Program
✓	13.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
	30.1b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	24.7b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	13.6b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	37.1b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
▶	17.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))

Compiler

Compiled 53091 to 22420 computations (57.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x)
✓	2.1b	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
✓	6.0b	(/.f64 (*.f64 y z) (-.f64 a t))
✓	10.7b	(/.f64 (*.f64 y t) (-.f64 a t))

series94.0ms (1.2%)

Counts

4 → 108

Calls

4 calls:

27.0ms	(/.f64 (*.f64 y z) (-.f64 a t))
25.0ms	(/.f64 (*.f64 y t) (-.f64 a t))
22.0ms	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
19.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x)

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
14×	`fma-def_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 103

Calls

4 calls:

8.0ms	(+.f64 y (+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x))
8.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a t)) x)
6.0ms	(/.f64 (*.f64 y t) (-.f64 a t))
5.0ms	(/.f64 (*.f64 y z) (-.f64 a t))

simplify118.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
337×	`fma-neg_binary64`
314×	`distribute-rgt-in_binary64`
234×	`cancel-sign-sub-inv_binary64`
227×	`distribute-lft-in_binary64`

Counts

211 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	3951
1	721	3855
2	2505	3245
3	4746	3245
4	5005	3245

prune159.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	203	8	211

Error

0.1b

Counts

211 → 8

Alt Table

Status	Error	Program
	17.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (.f64 (*.f64 y z) (/.f64 1 (-.f64 a t))))
	24.7b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	13.7b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (cbrt.f64 (/.f64 (-.f64 t z) (-.f64 a t)))) (+.f64 x y))
	15.1b	(-.f64 (+.f64 (+.f64 y (/.f64 (.f64 y t) (-.f64 a t))) x) (/.f64 (.f64 y z) (-.f64 a t)))
	13.7b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 z (cbrt.f64 (-.f64 a t)))))
	30.1b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
✓	13.6b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	37.1b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 5742 to 1354 computations (76.4% saved)

regimes1.4s (17.3%)

Accuracy

Total 6.7b remaining (99.3%)

Threshold costs 0b (0%)

Counts

114 → 3

Compiler

Compiled 14034 to 8178 computations (41.7% saved)

bsearch39.0ms (0.5%)

Steps

Iters	Range		Point
6	2.219516588209517e+80	1.405977608982601e+81	5.485833698658141e+80
5	-4.398184970783575e+162	-1.7385815158621938e+162	-2.874394328703431e+162

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	55
1	39	55
2	52	55
3	60	55
4	65	55
5	66	55
6	66	55

end115.0ms (1.5%)

Compiler: Compiled 288 to 155 computations (46.2% saved)

Details

analyze1.3s (16.8%)

sample1.5s (19.7%)

simplify141.0ms (1.8%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series64.0ms (0.8%)

rewrite11.0ms (0.1%)

simplify140.0ms (1.8%)

prune118.0ms (1.5%)

localize10.0ms (0.1%)

series77.0ms (1%)

rewrite22.0ms (0.3%)

simplify147.0ms (1.9%)

prune162.0ms (2.1%)

localize12.0ms (0.2%)

series866.0ms (11%)

rewrite128.0ms (1.6%)

simplify282.0ms (3.6%)

prune864.0ms (11%)

localize12.0ms (0.1%)

series94.0ms (1.2%)

rewrite32.0ms (0.4%)

simplify118.0ms (1.5%)

prune159.0ms (2%)

regimes1.4s (17.3%)

bsearch39.0ms (0.5%)

simplify4.0ms (0.1%)

end115.0ms (1.5%)

Profiling