Details

analyze1.2s (20.4%)

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
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
26.2%	73.5%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample29.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	255×	body	128	valid
1.0ms	22×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify126.0ms (2.2%)

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

1 alts after pruning (1 fresh and 0 done)

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

Error

1.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 56 to 29 computations (48.2% 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))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

rewrite12.0ms (0.2%)

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:

7.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series96.0ms (1.6%)

Counts

2 → 96

Calls

2 calls:

70.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
26.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify135.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 260

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune116.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	256	4	260
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	257	4	261

Error

0.0b

Counts

261 → 4

Alt Table

Status	Error	Program
	2.5b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	32.2b	(fma.f64 y (.f64 (/.f64 (sqrt.f64 (-.f64 z t)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (sqrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t)))) x)
▶	1.3b	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)

Compiler

Compiled 3378 to 1123 computations (66.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))
✓	0.0b	(/.f64 z (-.f64 a t))
✓	0.0b	(/.f64 t (-.f64 a t))
✓	1.3b	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)

rewrite129.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

728×	`*-un-lft-identity_binary64`
718×	`add-sqr-sqrt_binary64`
708×	`times-frac_binary64`
441×	`prod-diff_binary64`
422×	`add-cube-cbrt_binary64`

Counts

4 → 601

Calls

4 calls:

34.0ms	(-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))
5.0ms	(/.f64 z (-.f64 a t))
4.0ms	(/.f64 t (-.f64 a t))
0.0ms	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)

series187.0ms (3.2%)

Counts

4 → 135

Calls

4 calls:

92.0ms	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)
52.0ms	(/.f64 z (-.f64 a t))
34.0ms	(-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t)))
8.0ms	(/.f64 t (-.f64 a t))

simplify730.0ms (12.5%)

Algorithm

1×	egg-herbie

Rules

307×	`fma-udef_binary64`
266×	`fma-neg_binary64`
263×	`unsub-neg_binary64`
259×	`associate-+r-_binary64`
196×	`associate-/l*_binary64`

Counts

736 → 1347

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	723	47230
1	1744	27687
2	4481	26877
3	5090	26877

prune476.0ms (8.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1347	0	1347
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	1347	4	1351

Error

0.0b

Counts

1351 → 4

Alt Table

Status	Error	Program
▶	2.5b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	32.2b	(fma.f64 y (.f64 (/.f64 (sqrt.f64 (-.f64 z t)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (sqrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t)))) x)
✓	1.3b	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)

Compiler

Compiled 31985 to 5849 computations (81.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	10.9b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
31×	`times-frac_binary64`
21×	`associate-l_binary64`

Counts

2 → 113

Calls

2 calls:

11.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
5.0ms	(/.f64 y (-.f64 a t))

series81.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

56.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
25.0ms	(/.f64 y (-.f64 a t))

simplify176.0ms (3%)

Algorithm

1×	egg-herbie

Rules

766×	`cancel-sign-sub-inv_binary64`
366×	`fma-neg_binary64`
238×	`sub-neg_binary64`
178×	`times-frac_binary64`
174×	`associate-/l*_binary64`

Counts

185 → 321

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	340	4235
1	810	4049
2	3050	3971
3	4777	3970
4	4973	3970
5	4980	3970

prune142.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	320	5	325

Error

Counts

325 → 5

Alt Table

Status	Error	Program
✓	2.5b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
▶	0.7b	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 a t))) (-.f64 z t))))
	32.2b	(fma.f64 y (.f64 (/.f64 (sqrt.f64 (-.f64 z t)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (sqrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t)))) x)
	9.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	1.3b	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)

Compiler

Compiled 5188 to 1501 computations (71.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 y)
	0.6b	(cbrt.f64 y)
✓	0.6b	(cbrt.f64 y)
✓	2.1b	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 a t))) (-.f64 z t)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-exp-log_binary64`
52×	`distribute-lft-in_binary64`
52×	`distribute-rgt-in_binary64`
37×	`cbrt-unprod_binary64`
37×	`add-cbrt-cube_binary64`

Counts

2 → 132

Calls

2 calls:

26.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 a t))) (-.f64 z t)))
1.0ms	(cbrt.f64 y)

series304.0ms (5.2%)

Counts

2 → 60

Calls

2 calls:

211.0ms	(cbrt.f64 y)
93.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 a t))) (-.f64 z t)))

simplify169.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

909×	`fma-def_binary64`
457×	`associate-l_binary64`
440×	`associate-r_binary64`
430×	`times-frac_binary64`
329×	`associate-/l*_binary64`

Counts

192 → 360

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	431	8220
1	1036	4332
2	4473	4220
3	5337	4220

prune182.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	480	0	480
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	480	5	485

Error

Counts

485 → 5

Alt Table

Status	Error	Program
✓	2.5b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	0.7b	(+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (-.f64 a t))) (-.f64 z t))))
	32.2b	(fma.f64 y (.f64 (/.f64 (sqrt.f64 (-.f64 z t)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (sqrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t)))) x)
	9.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
✓	1.3b	(fma.f64 y (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) x)

Compiler

Compiled 11072 to 2030 computations (81.7% saved)

regimes647.0ms (11%)

Accuracy

Total 1.0b remaining (98.4%)

Threshold costs 1.0b (98.4%)

Compiler

Compiled 13354 to 8056 computations (39.7% saved)

simplify4.0ms (0.1%)

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	46
1	23	46
2	29	46
3	31	46
4	32	46
5	32	46

end1.0ms (0%)

Compiler: Compiled 34 to 16 computations (52.9% saved)

sample816.0ms (13.9%)

Algorithm

1×

intervals

Results

369.0ms	7998×	body	128	valid
33.0ms	762×	body	128	invalid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 173 to 92 computations (46.8% saved)

Details

analyze1.2s (20.4%)

sample29.0ms (0.5%)

simplify126.0ms (2.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite12.0ms (0.2%)

series96.0ms (1.6%)

simplify135.0ms (2.3%)

prune116.0ms (2%)

localize8.0ms (0.1%)

rewrite129.0ms (2.2%)

series187.0ms (3.2%)

simplify730.0ms (12.5%)

prune476.0ms (8.1%)

localize7.0ms (0.1%)

rewrite22.0ms (0.4%)

series81.0ms (1.4%)

simplify176.0ms (3%)

prune142.0ms (2.4%)

localize15.0ms (0.3%)

rewrite43.0ms (0.7%)

series304.0ms (5.2%)

simplify169.0ms (2.9%)

prune182.0ms (3.1%)

regimes647.0ms (11%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample816.0ms (13.9%)

Profiling