Details

analyze153.0ms (6.4%)

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
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample21.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify49.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
623×	`fma-def_binary64`
311×	`fma-neg_binary64`
283×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	60	21
3	159	21
4	518	17
5	1687	17
6	3597	17
7	5026	17

prune4.0ms (0.2%)

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

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 80 to 54 computations (32.5% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(hypot.f64 a b)
0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
0.0b	(pow.f64 (hypot.f64 a b) 4)

rewrite117.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`add-cube-cbrt_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64`

Counts

3 → 112

Calls

3 calls:

13.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
11.0ms	(pow.f64 (hypot.f64 a b) 4)
10.0ms	(hypot.f64 a b)

Compiler

Compiled 1757 to 1068 computations (39.2% saved)

series184.0ms (7.7%)

Error

0.0b

Counts

3 → 54

Calls

3 calls:

69.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
61.0ms	(pow.f64 (hypot.f64 a b) 4)
32.0ms	(hypot.f64 a b)

Compiler

Compiled 2033 to 1579 computations (22.3% saved)

simplify106.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-neg_binary64`
482×	`fma-def_binary64`
436×	`associate-l_binary64`
432×	`associate-r_binary64`
327×	`times-frac_binary64`

Counts

166 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	2251
1	333	2069
2	1026	1987
3	4723	1987
4	5069	1987

prune38.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	3	80

Error

Counts

80 → 3

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
	13.0b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 1007 to 606 computations (39.8% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite121.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-cube-cbrt_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
12×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`

Counts

3 → 117

Calls

3 calls:

19.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
16.0ms	(.f64 4 (.f64 b b))
14.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 2559 to 1127 computations (56% saved)

series133.0ms (5.6%)

Error

Counts

3 → 39

Calls

3 calls:

84.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
33.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
5.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1363 to 1072 computations (21.3% saved)

simplify116.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-def_binary64`
621×	`times-frac_binary64`
537×	`fma-neg_binary64`
159×	`distribute-rgt-in_binary64`
159×	`cancel-sign-sub-inv_binary64`

Counts

156 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	2293
1	307	2071
2	1048	1973
3	4339	1973
4	4978	1973
5	4833	1973

prune43.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	91	3	94

Error

Counts

94 → 3

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
▶	13.0b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 1272 to 614 computations (51.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
0.1b	(*.f64 b (fma.f64 b b 4))

rewrite113.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`pow1_binary64`
13×	`fma-udef_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
8×	`add-exp-log_binary64`

Counts

2 → 77

Calls

2 calls:

15.0ms	(*.f64 b (fma.f64 b b 4))
9.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

Compiler

Compiled 1035 to 626 computations (39.5% saved)

series34.0ms (1.4%)

Error

Counts

2 → 15

Calls

2 calls:

17.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
10.0ms	(*.f64 b (fma.f64 b b 4))

Compiler

Compiled 273 to 217 computations (20.5% saved)

simplify85.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
352×	`prod-exp_binary64`
311×	`fma-def_binary64`
284×	`distribute-rgt-neg-in_binary64`

Counts

92 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	997
1	245	890
2	805	876
3	2590	870
4	4781	870
5	4952	870

prune30.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	53	3	56

Error

Counts

56 → 3

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
	13.0b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 597 to 421 computations (29.5% saved)

regimes251.0ms (10.6%)

Accuracy

Total 0.0b remaining (63%)

Threshold costs 0.0b (63%)

Compiler

Compiled 3505 to 2609 computations (25.6% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	15	19
2	15	19

end1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample750.0ms (31.5%)

Algorithm

1×

intervals

Results

441.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 81 to 55 computations (32.1% saved)

Details

analyze153.0ms (6.4%)

sample21.0ms (0.9%)

simplify49.0ms (2.1%)

prune4.0ms (0.2%)

localize9.0ms (0.4%)

rewrite117.0ms (4.9%)

series184.0ms (7.7%)

simplify106.0ms (4.5%)

prune38.0ms (1.6%)

localize10.0ms (0.4%)

rewrite121.0ms (5.1%)

series133.0ms (5.6%)

simplify116.0ms (4.9%)

prune43.0ms (1.8%)

localize5.0ms (0.2%)

rewrite113.0ms (4.7%)

series34.0ms (1.4%)

simplify85.0ms (3.6%)

prune30.0ms (1.3%)

regimes251.0ms (10.6%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample750.0ms (31.5%)

Profiling