Details

analyze2.8s (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample1.1s (0.2%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 19 to 9 computations (52.6% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-lft-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	15	4
3	18	4

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)

series6.0ms (0%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(hypot.f64 x x)

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(hypot.f64 x x)

simplify149.0ms (0%)

Algorithm

1×	egg-herbie

Rules

590×	`sqr-pow_binary64`
362×	`unswap-sqr_binary64`
308×	`*-commutative_binary64`
297×	`pow-sqr_binary64`
230×	`cube-prod_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	159
1	29	150
2	50	150
3	62	150
4	74	150
5	102	150
6	213	150
7	331	150
8	763	150
9	1595	150
10	1753	150
11	1953	150
12	2278	150
13	2724	150
14	3378	150
15	3840	150
16	4391	150

prune16.0ms (0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	11	4	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	5	16

Error

0.0b

Counts

16 → 5

Alt Table

Status	Error	Program
	42.7b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	30.3b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	32.6b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
▶	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

Compiler

Compiled 161 to 81 computations (49.7% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
	0.1b	(hypot.f64 x x)
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

series26.0ms (0%)

Counts

2 → 12

Calls

2 calls:

18.0ms	(sqrt.f64 (hypot.f64 x x))
7.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

9.0ms	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
1.0ms	(sqrt.f64 (hypot.f64 x x))

simplify717.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

694×	`unswap-sqr_binary64`
385×	`associate-/l*_binary64`
226×	`*-commutative_binary64`
220×	`associate-l_binary64`
219×	`associate-/r/_binary64`

Counts

80 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	643
1	91	602
2	235	589
3	793	554
4	1303	554
5	3499	554

prune84.0ms (0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	9	129

Error

0.0b

Counts

129 → 9

Alt Table

Status	Error	Program
▶	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.1b	(hypot.f64 x x)
	42.7b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	30.3b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	32.6b	(*.f64 (sqrt.f64 2) x)
	1.0b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
	2.0b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	1.5b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 4) (cbrt.f64 (hypot.f64 x x)))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

Compiler

Compiled 1797 to 457 computations (74.6% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.1b	(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))
✓	0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

series874.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

527.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))

336.0ms

(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

10.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`sqrt-pow1_binary64`
51×	`pow1_binary64`
47×	`sqrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
36×	`pow-prod-up_binary64`

Counts

3 → 121

Calls

3 calls:

19.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))

13.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))

2.0ms

(sqrt.f64 (sqrt.f64 (hypot.f64 x x)))

simplify1.4s (0.2%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-def_binary64`
432×	`associate-r_binary64`
397×	`associate-l_binary64`
273×	`exp-sum_binary64`
212×	`*-commutative_binary64`

Counts

157 → 153

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	140	1915
1	292	1702
2	684	1614
3	1423	1530
4	3412	1476

prune174.0ms (0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	4	2	6
Picked	0	1	1
Done	0	2	2
Total	226	8	234

Error

0.0b

Counts

234 → 8

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (sqrt.f64 (hypot.f64 x x))))
	30.3b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	0.7b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
✓	0.1b	(hypot.f64 x x)
	0.9b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x)))))
	32.6b	(*.f64 (sqrt.f64 2) x)
	1.4b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))

Compiler

Compiled 4585 to 1104 computations (75.9% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (sqrt.f64 (hypot.f64 x x)))
✓	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (sqrt.f64 (hypot.f64 x x))))
✓	0.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	0.7b	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)

series1.2s (0.2%)

Counts

4 → 48

Calls

4 calls:

470.0ms	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (sqrt.f64 (hypot.f64 x x)))
380.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)
358.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
6.0ms	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (sqrt.f64 (hypot.f64 x x))))

rewrite55.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`sqrt-prod_binary64`
65×	`add-sqr-sqrt_binary64`
64×	`cbrt-prod_binary64`
36×	`associate-l_binary64`
33×	`cube-prod_binary64`

Counts

4 → 167

Calls

4 calls:

16.0ms	(*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (sqrt.f64 (hypot.f64 x x)))
13.0ms	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)) (sqrt.f64 (hypot.f64 x x))))
4.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
4.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) 3)

simplify9.9min (98.5%)

Algorithm

1×	egg-herbie

Rules

513×	`*-commutative_binary64`
347×	`fma-def_binary64`
257×	`exp-prod_binary64`
223×	`associate-r_binary64`
219×	`sqr-pow_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	3153
1	447	3072
2	1472	2738
3	3331	2523

Details

analyze2.8s (0.5%)

sample1.1s (0.2%)

simplify14.0ms (0%)

prune6.0ms (0%)

localize2.0ms (0%)

series6.0ms (0%)

rewrite3.0ms (0%)

simplify149.0ms (0%)

prune16.0ms (0%)

localize7.0ms (0%)

series26.0ms (0%)

rewrite18.0ms (0%)

simplify717.0ms (0.1%)

prune84.0ms (0%)

localize8.0ms (0%)

series874.0ms (0.1%)

rewrite48.0ms (0%)

simplify1.4s (0.2%)

prune174.0ms (0%)

localize11.0ms (0%)

series1.2s (0.2%)

rewrite55.0ms (0%)

simplify9.9min (98.5%)

Profiling