Details

analyze82.0ms (2.5%)

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
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
50%	37.5%	12.6%	7
56.2%	25%	18.8%	8
62.4%	18.7%	18.8%	9
65.6%	12.5%	22%	10
68.7%	9.4%	22%	11
70.2%	6.2%	23.5%	12
71.8%	4.7%	23.5%	13
72.6%	3.1%	24.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample960.0ms (29.7%)

Results

909.0ms	8256×	body	128	valid
7.0ms	92×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify18.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

265×	`fma-def_binary64`
84×	`fma-neg_binary64`
35×	`distribute-rgt-in_binary64`
26×	`unsub-neg_binary64`
25×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 x y))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

series9.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

6.0ms	(.f64 x (-.f64 1 (.f64 x y)))
3.0ms	(-.f64 1 (*.f64 x y))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
5×	`distribute-lft-in_binary64`

Counts

2 → 52

Calls

2 calls:

5.0ms	(.f64 x (-.f64 1 (.f64 x y)))
2.0ms	(-.f64 1 (*.f64 x y))

simplify87.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1016×	`fma-def_binary64`
587×	`unsub-neg_binary64`
328×	`associate-l_binary64`
293×	`unswap-sqr_binary64`
278×	`*-commutative_binary64`

Counts

100 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	1128
1	162	1037
2	490	982
3	1467	953
4	3061	953
5	4899	953
6	4821	953

prune73.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Error

Counts

82 → 8

Alt Table

Status	Error	Program
	14.3b	(.f64 x (/.f64 (-.f64 1 (.f64 y (.f64 y (.f64 x x)))) (fma.f64 x y 1)))
	37.0b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (.f64 x y)))) (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x y)))))
	0.5b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
	42.5b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	7.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
▶	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	7.6b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))

Compiler

Compiled 1355 to 650 computations (52% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 1 (neg.f64 (*.f64 y x)))
✓	0.1b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
✓	51.4b	(fma.f64 (neg.f64 y) x (*.f64 y x))

series19.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

7.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))
6.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
6.0ms	(fma.f64 1 1 (neg.f64 (*.f64 y x)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

2.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
0.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))
0.0ms	(fma.f64 1 1 (neg.f64 (*.f64 y x)))

simplify95.0ms (3%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
640×	`distribute-rgt-in_binary64`
588×	`distribute-lft-in_binary64`
390×	`distribute-neg-out_binary64`
241×	`associate-l_binary64`

Counts

112 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	907
1	108	825
2	295	777
3	922	777
4	3226	777
5	4767	777
6	4999	777
7	4815	777

prune75.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Error

Counts

88 → 8

Alt Table

Status	Error	Program
	14.3b	(.f64 x (/.f64 (-.f64 1 (.f64 y (.f64 y (.f64 x x)))) (fma.f64 x y 1)))
	37.0b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (.f64 x y)))) (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x y)))))
▶	0.5b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
	42.5b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	7.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	7.6b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))

Compiler

Compiled 2081 to 773 computations (62.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
✓	0.1b	(.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
✓	0.2b	(cbrt.f64 (-.f64 1 (*.f64 x y)))
✓	0.2b	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))

series50.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

23.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
17.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))
6.0ms	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
4.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (*.f64 x y))))

rewrite59.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`cbrt-div_binary64`
61×	`flip--_binary64`
61×	`flip3--_binary64`
60×	`frac-times_binary64`
44×	`associate-*r/_binary64`

Counts

4 → 178

Calls

4 calls:

14.0ms	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
12.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
7.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
2.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))

simplify163.0ms (5%)

Algorithm

1×	egg-herbie

Rules

727×	`cancel-sign-sub-inv_binary64`
288×	`associate-/r*_binary64`
280×	`distribute-neg-frac_binary64`
275×	`associate-r_binary64`
254×	`associate-l_binary64`

Counts

274 → 340

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	348	7780
1	860	7171
2	3009	6801
3	5205	6801

prune512.0ms (15.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	470	0	470
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	470	8	478

Error

Counts

478 → 8

Alt Table

Status	Error	Program
	14.3b	(.f64 x (/.f64 (-.f64 1 (.f64 y (.f64 y (.f64 x x)))) (fma.f64 x y 1)))
	37.0b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (.f64 x y)))) (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x y)))))
✓	0.5b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
	42.5b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
▶	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	7.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	7.6b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))

Compiler

Compiled 18752 to 10630 computations (43.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)

series148.0ms (4.6%)

Counts

4 → 72

Calls

4 calls:

63.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
35.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
33.0ms	(cbrt.f64 x)
16.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`

Counts

4 → 137

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
5.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify137.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

500×	`exp-prod_binary64`
419×	`fma-neg_binary64`
398×	`fma-def_binary64`
345×	`associate-l_binary64`
291×	`distribute-rgt-in_binary64`

Counts

209 → 195

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	2627
1	348	2339
2	1356	2193
3	3351	2063
4	4202	1965
5	4737	1965
6	4598	1965

prune105.0ms (3.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	231	8	239

Error

Counts

239 → 8

Alt Table

Status	Error	Program
	14.3b	(.f64 x (/.f64 (-.f64 1 (.f64 y (.f64 y (.f64 x x)))) (fma.f64 x y 1)))
	37.0b	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (.f64 x y)))) (.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 1 (*.f64 x y)))))
✓	0.5b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
	42.5b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
✓	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	7.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	7.6b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))

Compiler

Compiled 4763 to 1727 computations (63.7% saved)

regimes364.0ms (11.3%)

Accuracy

Total 0.1b remaining (65.6%)

Threshold costs 0.1b (65.6%)

Counts

130 → 1

Compiler

Compiled 6100 to 3973 computations (34.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	28	25
2	36	25
3	40	25
4	41	25
5	40	25

end197.0ms (6.1%)

Compiler: Compiled 183 to 109 computations (40.4% saved)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Details

analyze82.0ms (2.5%)

sample960.0ms (29.7%)

simplify18.0ms (0.5%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite9.0ms (0.3%)

simplify87.0ms (2.7%)

prune73.0ms (2.2%)

localize12.0ms (0.4%)

series19.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify95.0ms (3%)

prune75.0ms (2.3%)

localize8.0ms (0.2%)

series50.0ms (1.6%)

rewrite59.0ms (1.8%)

simplify163.0ms (5%)

prune512.0ms (15.9%)

localize8.0ms (0.2%)

series148.0ms (4.6%)

rewrite28.0ms (0.9%)

simplify137.0ms (4.2%)

prune105.0ms (3.3%)

regimes364.0ms (11.3%)

simplify2.0ms (0.1%)

end197.0ms (6.1%)

Profiling

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10