Details

analyze408.0ms (3.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.5%	34.3%	0.1%	8
65.5%	34.3%	0.1%	9
76.5%	23.4%	0.1%	10
81.9%	17.9%	0.1%	11
81.9%	17.9%	0.1%	12
87.8%	12.1%	0.1%	13
90.7%	9.2%	0.1%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample1.5s (13.4%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 47 to 26 computations (44.7% saved)

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
505×	`times-frac_binary64`
497×	`div-sub_binary64`
469×	`neg-mul-1_binary64`
463×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	30	18
2	83	18
3	193	18
4	334	18
5	435	18
6	600	18
7	871	18
8	1369	16
9	3594	16
10	4298	16
11	4856	16

prune7.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	18.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

Compiler

Compiled 84 to 47 computations (44% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 v (+.f64 t1 u))
✓	0.0b	(-.f64 -1 (/.f64 u t1))
✓	1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series176.0ms (1.6%)

Counts

3 → 84

Calls

3 calls:

140.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
30.0ms	(/.f64 v (+.f64 t1 u))
6.0ms	(-.f64 -1 (/.f64 u t1))

rewrite127.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

260×	`times-frac_binary64`
229×	`add-sqr-sqrt_binary64`
219×	`*-un-lft-identity_binary64`
129×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`

Counts

3 → 257

Calls

3 calls:

26.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
14.0ms	(-.f64 -1 (/.f64 u t1))
8.0ms	(/.f64 v (+.f64 t1 u))

simplify410.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-def_binary64`
310×	`associate-/l/_binary64`
233×	`associate-/l*_binary64`
223×	`div-sub_binary64`
212×	`fma-neg_binary64`

Counts

341 → 304

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	465	9966
1	1202	8417
2	3569	8323
3	4946	8323
4	5008	8323

prune426.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	300	4	304
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	300	6	306

Error

0.0b

Counts

306 → 6

Alt Table

Status	Error	Program
▶	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	18.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
	2.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	8.1b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
	13.6b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 (.f64 -1 -1) (*.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))

Compiler

Compiled 8191 to 2937 computations (64.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	0.3b	(/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))
✓	0.5b	(/.f64 1 (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	7.4b	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))

series2.1s (18.5%)

Counts

4 → 120

Calls

4 calls:

1.6s	(/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))
283.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
126.0ms	(/.f64 1 (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
72.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))

rewrite478.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Rules

624×	`times-frac_binary64`
469×	`add-sqr-sqrt_binary64`
431×	`*-un-lft-identity_binary64`
236×	`add-cube-cbrt_binary64`
234×	`cbrt-prod_binary64`

Counts

4 → 513

Calls

4 calls:

116.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
44.0ms	(cbrt.f64 (-.f64 -1 (/.f64 u t1)))
27.0ms	(/.f64 1 (*.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
24.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))

simplify1.1s (9.7%)

Algorithm

1×	egg-herbie

Rules

580×	`fma-def_binary64`
552×	`times-frac_binary64`
469×	`associate-/l/_binary64`
268×	`*-commutative_binary64`
182×	`associate-*r/_binary64`

Counts

633 → 823

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	849	26624
1	2499	24027
2	4803	23996
3	5153	23996

prune1.9s (16.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	933	0	933
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	933	6	939

Error

0.0b

Counts

939 → 6

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	18.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
▶	2.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	8.1b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
	13.6b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 (.f64 -1 -1) (*.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))

Compiler

Compiled 42893 to 22201 computations (48.2% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1))
✓	2.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))

series174.0ms (1.5%)

Counts

2 → 60

Calls

2 calls:

162.0ms	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
12.0ms	(fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
12×	`distribute-lft-neg-in_binary64`

Counts

2 → 69

Calls

2 calls:

7.0ms	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
1.0ms	(fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1))

simplify180.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

855×	`times-frac_binary64`
573×	`associate-/l*_binary64`
435×	`associate-/r*_binary64`
285×	`fma-neg_binary64`
239×	`associate-/r/_binary64`

Counts

129 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	3276
1	348	3056
2	1153	2932
3	4910	2932
4	5078	2932

prune218.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	146	6	152

Error

0.0b

Counts

152 → 6

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	18.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	2.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
▶	8.1b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
	13.6b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 (.f64 -1 -1) (*.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))

Compiler

Compiled 3322 to 1474 computations (55.6% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 -1 (neg.f64 (*.f64 (/.f64 1 t1) u)))
✓	0.2b	(*.f64 (/.f64 1 t1) u)
✓	1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
✓	55.1b	(fma.f64 (neg.f64 (/.f64 1 t1)) u (*.f64 (/.f64 1 t1) u))

series374.0ms (3.3%)

Counts

4 → 108

Calls

4 calls:

312.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
39.0ms	(fma.f64 (neg.f64 (/.f64 1 t1)) u (*.f64 (/.f64 1 t1) u))
12.0ms	(*.f64 (/.f64 1 t1) u)
11.0ms	(fma.f64 1 -1 (neg.f64 (*.f64 (/.f64 1 t1) u)))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`times-frac_binary64`
140×	`*-un-lft-identity_binary64`
78×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
34×	`distribute-lft-out_binary64`

Counts

4 → 170

Calls

4 calls:

11.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))))
5.0ms	(*.f64 (/.f64 1 t1) u)
1.0ms	(fma.f64 (neg.f64 (/.f64 1 t1)) u (*.f64 (/.f64 1 t1) u))
0.0ms	(fma.f64 1 -1 (neg.f64 (*.f64 (/.f64 1 t1) u)))

simplify387.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

488×	`associate-/l/_binary64`
448×	`fma-def_binary64`
390×	`div-sub_binary64`
356×	`distribute-rgt-in_binary64`
308×	`distribute-lft-in_binary64`

Counts

278 → 273

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	8039
1	761	6651
2	2280	5016
3	4254	5016
4	5058	5016

prune586.0ms (5.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	331	1	332
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	332	6	338

Error

0.0b

Counts

338 → 6

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 -1 (/.f64 u t1))) (cbrt.f64 (-.f64 -1 (/.f64 u t1))))) (/.f64 (/.f64 v (+.f64 t1 u)) (cbrt.f64 (-.f64 -1 (/.f64 u t1)))))
✓	1.0b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))
	18.6b	(/.f64 (.f64 (neg.f64 t1) v) (.f64 (+.f64 t1 u) (+.f64 t1 u)))
✓	2.9b	(/.f64 (neg.f64 v) (fma.f64 u (/.f64 u t1) (fma.f64 u 2 t1)))
	42.3b	(/.f64 (/.f64 v (+.f64 (pow.f64 t1 3) (pow.f64 u 3))) (/.f64 (+.f64 (fma.f64 1 -1 (neg.f64 (.f64 (/.f64 1 t1) u))) (fma.f64 (neg.f64 (/.f64 1 t1)) u (.f64 (/.f64 1 t1) u))) (+.f64 (.f64 t1 t1) (-.f64 (.f64 u u) (*.f64 t1 u)))))
	13.6b	(.f64 (/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 (.f64 -1 -1) (*.f64 (/.f64 u t1) (/.f64 u t1)))) (+.f64 -1 (/.f64 u t1)))

Compiler

Compiled 11804 to 6531 computations (44.7% saved)

regimes421.0ms (3.7%)

Accuracy

Total 1.1b remaining (83.4%)

Threshold costs 0b (0%)

Counts

72 → 1

Compiler

Compiled 6286 to 4014 computations (36.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	13	16
2	19	16
3	23	16
4	26	16
5	27	16
6	27	16

end111.0ms (1%)

Compiler: Compiled 175 to 110 computations (37.1% saved)

Details

analyze408.0ms (3.6%)

sample1.5s (13.4%)

simplify114.0ms (1%)

prune7.0ms (0.1%)

localize14.0ms (0.1%)

series176.0ms (1.6%)

rewrite127.0ms (1.1%)

simplify410.0ms (3.6%)

prune426.0ms (3.8%)

localize20.0ms (0.2%)

series2.1s (18.5%)

rewrite478.0ms (4.2%)

simplify1.1s (9.7%)

prune1.9s (16.4%)

localize18.0ms (0.2%)

series174.0ms (1.5%)

rewrite18.0ms (0.2%)

simplify180.0ms (1.6%)

prune218.0ms (1.9%)

localize31.0ms (0.3%)

series374.0ms (3.3%)

rewrite46.0ms (0.4%)

simplify387.0ms (3.4%)

prune586.0ms (5.2%)

regimes421.0ms (3.7%)

simplify3.0ms (0%)

end111.0ms (1%)

Profiling