Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 10 to 7 computations (30% saved)

sample531.0ms (28%)

Results

484.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify17.0ms (0.9%)

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 (0.1%)

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 (0.2%)

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)))

series11.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

7.0ms	(.f64 x (-.f64 1 (.f64 x y)))
3.0ms	(-.f64 1 (*.f64 x y))

rewrite9.0ms (0.5%)

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))

simplify89.0ms (4.7%)

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

prune68.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	6	82

Error

0.0b

Counts

82 → 6

Alt Table

Status	Error	Program
	6.9b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))
	30.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	5.7b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	13.0b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
	22.4b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))
▶	0.1b	(.f64 x (+.f64 1 (neg.f64 (.f64 x y))))

Compiler

Compiled 1253 to 590 computations (52.9% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series11.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

7.0ms	(.f64 x (+.f64 1 (neg.f64 (.f64 x y))))
3.0ms	(+.f64 1 (neg.f64 (*.f64 x y)))

rewrite9.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64`
5×	`add-cube-cbrt_binary64`
4×	`associate-r_binary64`

Counts

2 → 45

Calls

2 calls:

5.0ms	(.f64 x (+.f64 1 (neg.f64 (.f64 x y))))
3.0ms	(+.f64 1 (neg.f64 (*.f64 x y)))

simplify72.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

483×	`associate-+r+_binary64`
416×	`neg-mul-1_binary64`
393×	`fma-def_binary64`
376×	`unsub-neg_binary64`
328×	`distribute-rgt-neg-out_binary64`

Counts

93 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	907
1	194	840
2	680	834
3	1875	831
4	4504	831
5	4988	831

prune51.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	78	6	84

Error

0.0b

Counts

84 → 6

Alt Table

Status	Error	Program
	6.9b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))
	30.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
▶	5.7b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	13.0b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
	22.4b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))
✓	0.1b	(.f64 x (+.f64 1 (neg.f64 (.f64 x y))))

Compiler

Compiled 1226 to 573 computations (53.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	7.8b	(*.f64 y (pow.f64 x 2))

series17.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

9.0ms	(-.f64 x (*.f64 y (pow.f64 x 2)))
8.0ms	(*.f64 y (pow.f64 x 2))

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64`

Counts

2 → 49

Calls

2 calls:

4.0ms	(*.f64 y (pow.f64 x 2))
2.0ms	(-.f64 x (*.f64 y (pow.f64 x 2)))

simplify88.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

518×	`fma-neg_binary64`
448×	`associate-l_binary64`
412×	`unswap-sqr_binary64`
398×	`associate-r_binary64`
375×	`distribute-rgt-neg-in_binary64`

Counts

55 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	730
1	176	586
2	495	558
3	2159	558
4	4134	558
5	4989	558
6	4819	558

prune63.0ms (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	82	6	88

Error

0.0b

Counts

88 → 6

Alt Table

Status	Error	Program
▶	6.9b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))
	30.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
✓	5.7b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	13.0b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
	22.4b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))
✓	0.1b	(.f64 x (+.f64 1 (neg.f64 (.f64 x y))))

Compiler

Compiled 1231 to 636 computations (48.3% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 1 (*.f64 x y))
✓	0.1b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))
✓	0.1b	(pow.f64 (-.f64 1 (*.f64 x y)) 3)
✓	14.4b	(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x y)) 3))

series21.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

10.0ms	(pow.f64 (-.f64 1 (*.f64 x y)) 3)
6.0ms	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))
5.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x y)) 3))

rewrite18.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 90

Calls

3 calls:

8.0ms	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))
3.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x y)) 3))
3.0ms	(pow.f64 (-.f64 1 (*.f64 x y)) 3)

simplify106.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
572×	`cancel-sign-sub-inv_binary64`
380×	`fma-def_binary64`
301×	`unswap-sqr_binary64`
283×	`*-commutative_binary64`

Counts

162 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	2218
1	296	2037
2	1063	1987
3	2869	1963
4	4822	1963
5	5048	1963

prune160.0ms (8.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	176	7	183

Error

Counts

183 → 7

Alt Table

Status	Error	Program
✓	6.9b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 x y)) 3)))
	30.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	4.2b	(.f64 x (.f64 (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y x)) 2)) (cbrt.f64 (-.f64 1 (.f64 y x)))))
✓	5.7b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	22.4b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))
	4.2b	(.f64 (.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y x)) 2))) (cbrt.f64 (-.f64 1 (.f64 x y))))
✓	0.1b	(.f64 x (+.f64 1 (neg.f64 (.f64 x y))))

Compiler

Compiled 3032 to 1821 computations (39.9% saved)

regimes406.0ms (21.4%)

Accuracy

Total 0.1b remaining (80.4%)

Threshold costs 0.1b (80.4%)

Counts

82 → 1

Compiler

Compiled 3932 to 2588 computations (34.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	13	10
2	28	10
3	36	10
4	42	10
5	44	10
6	44	10

end113.0ms (6%)

Compiler: Compiled 129 to 84 computations (34.9% 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

analyze1.0ms (0.1%)

sample531.0ms (28%)

simplify17.0ms (0.9%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series11.0ms (0.6%)

rewrite9.0ms (0.5%)

simplify89.0ms (4.7%)

prune68.0ms (3.6%)

localize5.0ms (0.3%)

series11.0ms (0.6%)

rewrite9.0ms (0.5%)

simplify72.0ms (3.8%)

prune51.0ms (2.7%)

localize4.0ms (0.2%)

series17.0ms (0.9%)

rewrite8.0ms (0.4%)

simplify88.0ms (4.6%)

prune63.0ms (3.3%)

localize7.0ms (0.4%)

series21.0ms (1.1%)

rewrite18.0ms (1%)

simplify106.0ms (5.6%)

prune160.0ms (8.4%)

regimes406.0ms (21.4%)

simplify3.0ms (0.1%)

end113.0ms (6%)

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