Details

analyze55.0ms (2.2%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
56.2%	43.7%	0.1%	6
65.6%	34.3%	0.1%	7
76.5%	23.4%	0.1%	8
82%	18%	0.1%	9
87.8%	12.1%	0.1%	10
90.7%	9.2%	0.1%	11
93.8%	6.1%	0.1%	12
95.3%	4.6%	0.1%	13
96.8%	3.1%	0.1%	14

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample11.0ms (0.4%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

128

valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify171.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 10 to 8 computations (20% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (+.f64 x y) x)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_15579` `add-log-exp_binary64_15615`
3×	`distribute-lft-out_binary64_15532` `sum-log_binary64_15667`
1×	`associate-+l+_binary64_15514` `add-exp-log_binary64_15614` `pow1_binary64_15637` `+-commutative_binary64_15511` `add-sqr-sqrt_binary64_15600` `flip3-+_binary64_15582` `add-cube-cbrt_binary64_15611` `add-cbrt-cube_binary64_15612` `flip-+_binary64_15553`

Counts

1 → 15

Calls

1 calls:

7.0ms

(+.f64 (+.f64 x y) x)

series35.0ms (1.4%)

Counts

1 → 3

Calls

1 calls:

34.0ms

(+.f64 (+.f64 x y) x)

simplify70.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4898	169
1	4898	169

prune11.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	2	19

Merged error: 0.0b

Counts

19 → 2

Compiler

Compiled 163 to 42 computations (74.2% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x (+.f64 x y)))
0.0b	(+.f64 x (+.f64 x y))
0.0b	(+.f64 x (+.f64 x y))
0.3b	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (sqrt.f64 (+.f64 x (+.f64 x y))))

rewrite46.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_15579`
43×	`sqrt-prod_binary64_15594`
33×	`distribute-lft-out_binary64_15532`
26×	`add-sqr-sqrt_binary64_15600`
20×	`pow1_binary64_15637`
16×	`swap-sqr_binary64_15546`
14×	`add-log-exp_binary64_15615` `sqrt-div_binary64_15595`
13×	`add-cube-cbrt_binary64_15611`
9×	`pow1/2_binary64_15656` `sqrt-pow1_binary64_15596` `flip3-+_binary64_15582` `flip-+_binary64_15553`
8×	`associate-r_binary64_15521` `associate-l_binary64_15522`
6×	`add-exp-log_binary64_15614` `add-cbrt-cube_binary64_15612` `sum-log_binary64_15667`
5×	`pow-prod-up_binary64_15646`
4×	`frac-times_binary64_15589` `unswap-sqr_binary64_15547`
3×	`pow-prod-down_binary64_15647` `pow-sqr_binary64_15552`
2×	`+-commutative_binary64_15511` `associate-l/_binary64_15524` `associate-+r+_binary64_15513` `associate-r/_binary64_15523`
1×	`sqrt-unprod_binary64_15598` `rem-sqrt-square_binary64_15592` `rem-square-sqrt_binary64_15591` `pow-plus_binary64_15639` `prod-exp_binary64_15625` `cbrt-unprod_binary64_15609` `pow2_binary64_15657` `*-commutative_binary64_15512`

Counts

4 → 116

Calls

4 calls:

17.0ms	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (sqrt.f64 (+.f64 x (+.f64 x y))))
6.0ms	(+.f64 x (+.f64 x y))
6.0ms	(+.f64 x (+.f64 x y))
6.0ms	(sqrt.f64 (+.f64 x (+.f64 x y)))

series169.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (sqrt.f64 (+.f64 x (+.f64 x y))))
51.0ms	(sqrt.f64 (+.f64 x (+.f64 x y)))
34.0ms	(+.f64 x (+.f64 x y))
32.0ms	(+.f64 x (+.f64 x y))

simplify67.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5002	1517

prune79.0ms (3.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	128	2	130

Merged error: 0b

Counts

130 → 2

Compiler

Compiled 1901 to 377 computations (80.2% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 x y))))) (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 x y)))))
0.2b	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 x y)))))
0.6b	(cbrt.f64 (+.f64 x (+.f64 x y)))
0.6b	(cbrt.f64 (+.f64 x (+.f64 x y)))

rewrite54.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64_15579`
16×	`add-sqr-sqrt_binary64_15600`
15×	`cbrt-prod_binary64_15607`
14×	`sqrt-prod_binary64_15594` `associate-r_binary64_15521` `sqrt-div_binary64_15595`
12×	`distribute-lft-out_binary64_15532` `add-cube-cbrt_binary64_15611`
11×	`add-exp-log_binary64_15614` `pow1_binary64_15637` `add-cbrt-cube_binary64_15612`
10×	`cbrt-div_binary64_15608` `associate-*l/_binary64_15524`
9×	`flip3-+_binary64_15582` `associate-l_binary64_15522` `flip-+_binary64_15553`
4×	`pow-prod-down_binary64_15647` `frac-times_binary64_15589` `add-log-exp_binary64_15615` `prod-exp_binary64_15625` `cbrt-unprod_binary64_15609`
2×	`associate-r/_binary64_15523` `-commutative_binary64_15512` `unswap-sqr_binary64_15547` `pow1/3_binary64_15658`

Counts

4 → 90

Calls

4 calls:

22.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 x y))))) (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 x y)))))
9.0ms	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 x y)))))
6.0ms	(cbrt.f64 (+.f64 x (+.f64 x y)))
6.0ms	(cbrt.f64 (+.f64 x (+.f64 x y)))

series1.1s (43.6%)

Counts

4 → 12

Calls

4 calls:

444.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 x y))))) (sqrt.f64 (cbrt.f64 (+.f64 x (+.f64 x y)))))
267.0ms	(cbrt.f64 (+.f64 x (+.f64 x y)))
259.0ms	(cbrt.f64 (+.f64 x (+.f64 x y)))
132.0ms	(*.f64 (sqrt.f64 (+.f64 x (+.f64 x y))) (fabs.f64 (cbrt.f64 (+.f64 x (+.f64 x y)))))

simplify76.0ms (3%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5637	3024

prune103.0ms (4.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	102	2	104

Merged error: 0b

Counts

104 → 2

Compiler

Compiled 3191 to 593 computations (81.4% saved)

regimes39.0ms (1.6%)

Compiler: Compiled 218 to 118 computations (45.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

end0.0ms (0%)

sample404.0ms (16%)

Algorithm

1×

intervals

Results

142.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 84 to 50 computations (40.5% saved)

Details

analyze55.0ms (2.2%)

sample11.0ms (0.4%)

simplify171.0ms (6.8%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

rewrite8.0ms (0.3%)

series35.0ms (1.4%)

simplify70.0ms (2.8%)

prune11.0ms (0.4%)

localize9.0ms (0.4%)

rewrite46.0ms (1.8%)

series169.0ms (6.7%)

simplify67.0ms (2.6%)

prune79.0ms (3.1%)

localize10.0ms (0.4%)

rewrite54.0ms (2.1%)

series1.1s (43.6%)

simplify76.0ms (3%)

prune103.0ms (4.1%)

regimes39.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample404.0ms (16%)

Profiling