Details

analyze336.0ms (10.9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	60.8%	3.3%	9
44.1%	48%	7.9%	10
54.8%	36.9%	8.3%	11
57.6%	31.5%	10.9%	12
61.9%	24%	14.1%	13
67.2%	18.6%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample186.0ms (6%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
1.0ms	29×	body	128	invalid

Compiler

Compiled 28 to 22 computations (21.4% saved)

simplify43.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
164×	`distribute-lft-in_binary64`
139×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	47	11
3	132	11
4	334	11
5	640	11
6	965	11
7	1254	11
8	1262	11
9	1262	11
10	1191	11

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

3.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 44 to 31 computations (29.5% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 y) z)
✓	2.9b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

series15.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
4.0ms	(*.f64 (-.f64 1 y) z)

rewrite35.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
9×	`associate-l_binary64`
8×	`add-cube-cbrt_binary64`
6×	`associate-r_binary64`

Counts

2 → 57

Calls

2 calls:

28.0ms	(*.f64 (-.f64 1 y) z)
5.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

simplify133.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

394×	`unsub-neg_binary64`
329×	`neg-mul-1_binary64`
328×	`sub-neg_binary64`
320×	`neg-sub0_binary64`
310×	`*-commutative_binary64`

Counts

105 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1393
1	253	1203
2	751	1133
3	2083	1115
4	3435	1115
5	4698	1115
6	4919	1115

prune84.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Error

0.0b

Counts

102 → 5

Alt Table

Status	Error	Program
▶	1.1b	(+.f64 x (.f64 (.f64 z x) (-.f64 y 1)))
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
	35.4b	(.f64 (sqrt.f64 (.f64 (-.f64 (fma.f64 y z 1) z) x)) (sqrt.f64 (*.f64 (-.f64 (fma.f64 y z 1) z) x)))
	17.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 1 (*.f64 (-.f64 1 y) z))))
	3.7b	(.f64 x (-.f64 1 (.f64 (.f64 (-.f64 1 y) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))

Compiler

Compiled 1719 to 1091 computations (36.5% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.7b	(.f64 (.f64 z x) (-.f64 y 1))

series12.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

12.0ms

(*.f64 (*.f64 z x) (-.f64 y 1))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`prod-diff_binary64`
16×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 52

Calls

1 calls:

6.0ms

(*.f64 (*.f64 z x) (-.f64 y 1))

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

397×	`fma-def_binary64`
356×	`*-commutative_binary64`
229×	`distribute-rgt-neg-in_binary64`
227×	`times-frac_binary64`
212×	`distribute-lft-neg-in_binary64`

Counts

88 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	87	1123
1	216	952
2	613	946
3	1447	946
4	2384	946
5	4543	946
6	5076	946

prune77.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	73	6	79

Error

0.0b

Counts

79 → 6

Alt Table

Status	Error	Program
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
	17.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 1 (*.f64 (-.f64 1 y) z))))
	34.0b	(+.f64 x (.f64 (.f64 x (fma.f64 z (sqrt.f64 y) z)) (-.f64 (sqrt.f64 y) 1)))
	29.0b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 z x) (-.f64 y 1))) (sqrt.f64 (.f64 (*.f64 z x) (-.f64 y 1)))))
	3.7b	(.f64 x (-.f64 1 (.f64 (.f64 (-.f64 1 y) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
▶	3.1b	(+.f64 x (.f64 z (.f64 (-.f64 y 1) x)))

Compiler

Compiled 1628 to 935 computations (42.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.9b	(.f64 z (.f64 (-.f64 y 1) x))

series10.0ms (0.3%)

Counts

1 → 28

Calls

1 calls:

10.0ms

(*.f64 z (*.f64 (-.f64 y 1) x))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 22

Calls

1 calls:

6.0ms

(*.f64 z (*.f64 (-.f64 y 1) x))

simplify66.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

546×	`associate-l_binary64`
470×	`fma-def_binary64`
373×	`associate-r_binary64`
276×	`distribute-rgt-neg-in_binary64`
266×	`distribute-lft-neg-in_binary64`

Counts

50 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	591
1	158	528
2	472	528
3	1881	528
4	2869	528
5	4787	528
6	4982	528

prune33.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	40	6	46

Error

0.0b

Counts

46 → 6

Alt Table

Status	Error	Program
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
	17.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 1 (*.f64 (-.f64 1 y) z))))
	34.0b	(+.f64 x (.f64 (.f64 x (fma.f64 z (sqrt.f64 y) z)) (-.f64 (sqrt.f64 y) 1)))
	29.0b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 z x) (-.f64 y 1))) (sqrt.f64 (.f64 (*.f64 z x) (-.f64 y 1)))))
▶	3.7b	(.f64 x (-.f64 1 (.f64 (.f64 (-.f64 1 y) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
✓	3.1b	(+.f64 x (.f64 z (.f64 (-.f64 y 1) x)))

Compiler

Compiled 746 to 392 computations (47.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (-.f64 1 y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
✓	0.6b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	2.9b	(.f64 x (-.f64 1 (.f64 (.f64 (-.f64 1 y) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))

series116.0ms (3.8%)

Counts

4 → 84

Calls

4 calls:

36.0ms	(cbrt.f64 z)
35.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
27.0ms	(.f64 x (-.f64 1 (.f64 (.f64 (-.f64 1 y) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
18.0ms	(.f64 (.f64 (-.f64 1 y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
22×	`pow1_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`

Counts

4 → 115

Calls

4 calls:

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

simplify118.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

464×	`fma-neg_binary64`
422×	`fma-def_binary64`
408×	`distribute-rgt-in_binary64`
384×	`distribute-lft-in_binary64`
293×	`associate-l_binary64`

Counts

199 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	2255
1	387	1953
2	1468	1808
3	3985	1785
4	4860	1785
5	4982	1785

prune146.0ms (4.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	216	7	223

Error

Counts

223 → 7

Alt Table

Status	Error	Program
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
	3.7b	(.f64 x (-.f64 1 (.f64 (.f64 (-.f64 1 y) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z))))))
	17.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 1 (*.f64 (-.f64 1 y) z))))
	34.0b	(+.f64 x (.f64 (.f64 x (fma.f64 z (sqrt.f64 y) z)) (-.f64 (sqrt.f64 y) 1)))
	29.0b	(+.f64 x (.f64 (sqrt.f64 (.f64 (.f64 z x) (-.f64 y 1))) (sqrt.f64 (.f64 (*.f64 z x) (-.f64 y 1)))))
✓	3.7b	(.f64 x (-.f64 1 (.f64 (.f64 (-.f64 1 y) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
✓	3.1b	(+.f64 x (.f64 z (.f64 (-.f64 y 1) x)))

Compiler

Compiled 4711 to 2289 computations (51.4% saved)

regimes819.0ms (26.6%)

Accuracy

Total 0.4b remaining (94.6%)

Threshold costs 0.4b (94.6%)

Counts

72 → 3

Compiler

Compiled 10100 to 6846 computations (32.2% saved)

bsearch31.0ms (1%)

Steps

Iters	Range		Point
2	2.1353890343694827e+64	4.030606122212929e+79	1.4089650473537223e+68
11	-8.725093439394517e+117	-6.315889867143053e+94	-1.49884295671476e+112

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
12×	`+-commutative_binary64`
11×	`distribute-rgt-neg-in_binary64`
11×	`sub-neg_binary64`
11×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	47	40
2	67	40
3	86	40
4	100	40
5	110	40
6	116	40
7	119	40
8	120	40
9	116	40

end2.0ms (0.1%)

Compiler: Compiled 30 to 20 computations (33.3% saved)

sample654.0ms (21.2%)

Algorithm

1×

intervals

Results

284.0ms	8000×	body	128	valid
22.0ms	662×	body	128	invalid

Compiler

Compiled 175 to 115 computations (34.3% saved)

Details

analyze336.0ms (10.9%)

sample186.0ms (6%)

simplify43.0ms (1.4%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series15.0ms (0.5%)

rewrite35.0ms (1.1%)

simplify133.0ms (4.3%)

prune84.0ms (2.7%)

localize5.0ms (0.2%)

series12.0ms (0.4%)

rewrite10.0ms (0.3%)

simplify82.0ms (2.7%)

prune77.0ms (2.5%)

localize5.0ms (0.2%)

series10.0ms (0.3%)

rewrite7.0ms (0.2%)

simplify66.0ms (2.1%)

prune33.0ms (1.1%)

localize9.0ms (0.3%)

series116.0ms (3.8%)

rewrite28.0ms (0.9%)

simplify118.0ms (3.8%)

prune146.0ms (4.7%)

regimes819.0ms (26.6%)

bsearch31.0ms (1%)

simplify5.0ms (0.2%)

end2.0ms (0.1%)

sample654.0ms (21.2%)

Profiling