Details

analyze74.0ms (3.6%)

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
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample14.0ms (0.7%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	6×	body	128	nan

Compiler

Compiled 13 to 13 computations (0% saved)

simplify166.0ms (8.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

prune2.0ms (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

Merged error: 22.6b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) y)
21.1b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_11556` `add-log-exp_binary64_11571`
3×	`add-cube-cbrt_binary64_11567` `*-un-lft-identity_binary64_11535` `pow1_binary64_11593` `sqrt-prod_binary64_11550`
2×	`add-cbrt-cube_binary64_11568` `flip-+_binary64_11509` `sqrt-div_binary64_11551` `add-exp-log_binary64_11570` `flip3-+_binary64_11538`
1×	`+-commutative_binary64_11467` `sum-log_binary64_11623` `pow1/2_binary64_11612` `rem-sqrt-square_binary64_11548` `sqrt-pow1_binary64_11552`

Counts

2 → 26

Calls

2 calls:

5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
5.0ms	(+.f64 (*.f64 x x) y)

series87.0ms (4.2%)

Counts

2 → 6

Calls

2 calls:

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

simplify71.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5412	392

prune26.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Merged error: 0b

Counts

33 → 5

Compiler

Compiled 396 to 143 computations (63.9% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (cbrt.f64 (+.f64 (*.f64 x x) y)))
0.2b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 x x) y))) (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 x x) y))))
21.8b	(cbrt.f64 (+.f64 (*.f64 x x) y))
21.8b	(cbrt.f64 (+.f64 (*.f64 x x) y))

rewrite33.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_11556`
14×	`cbrt-prod_binary64_11563` `sqrt-prod_binary64_11550`
12×	`add-cube-cbrt_binary64_11567` `*-un-lft-identity_binary64_11535`
9×	`associate-r_binary64_11477`
8×	`cbrt-div_binary64_11564`
7×	`pow1_binary64_11593`
6×	`add-cbrt-cube_binary64_11568` `add-exp-log_binary64_11570`
4×	`flip-+_binary64_11509` `sqrt-div_binary64_11551` `add-log-exp_binary64_11571` `flip3-+_binary64_11538`
3×	`associate-l_binary64_11478` `unswap-sqr_binary64_11503` `pow1/3_binary64_11614`
2×	`associate-*r/_binary64_11479` `rem-sqrt-square_binary64_11548` `sqrt-pow1_binary64_11552`
1×	`cbrt-unprod_binary64_11565` `*-commutative_binary64_11468` `pow1/2_binary64_11612` `prod-exp_binary64_11581` `pow-prod-down_binary64_11603`

Counts

4 → 74

Calls

4 calls:

10.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 x x) y))) (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 x x) y))))
5.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (*.f64 x x) y)))
4.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))
4.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))

series526.0ms (25.7%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 x x) y))) (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 x x) y))))
116.0ms	(sqrt.f64 (cbrt.f64 (+.f64 (*.f64 x x) y)))
111.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))
106.0ms	(cbrt.f64 (+.f64 (*.f64 x x) y))

simplify93.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4815	1672
1	4815	1672

prune75.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	86	5	91

Merged error: 0b

Counts

91 → 5

Compiler

Compiled 1892 to 396 computations (79.1% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.2b	(*.f64 y (/.f64 -1/2 x))

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_11556`
13×	`associate-r_binary64_11477`
10×	`times-frac_binary64_11541`
9×	`add-cube-cbrt_binary64_11567` `*-un-lft-identity_binary64_11535`
6×	`add-cbrt-cube_binary64_11568` `add-exp-log_binary64_11570`
3×	`associate-l_binary64_11478` `pow1_binary64_11593`
2×	`unswap-sqr_binary64_11503` `cbrt-unprod_binary64_11565` `prod-exp_binary64_11581`
1×	`associate-r/_binary64_11479` `div-inv_binary64_11532` `cbrt-undiv_binary64_11566` `div-exp_binary64_11583` `-commutative_binary64_11468` `add-log-exp_binary64_11571` `pow-prod-down_binary64_11603`

Counts

1 → 32

Calls

1 calls:

7.0ms

(*.f64 y (/.f64 -1/2 x))

series30.0ms (1.4%)

Counts

1 → 3

Calls

1 calls:

30.0ms

(*.f64 y (/.f64 -1/2 x))

simplify75.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5184	348

prune30.0ms (1.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	35	5	40

Merged error: 0b

Counts

40 → 5

Compiler

Compiled 438 to 278 computations (36.5% saved)

localize5.0ms (0.2%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms (0%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	3	3
Total	5	5

Merged error: 0b

Counts

5 → 5

Compiler

Compiled 0 to 0 computations (0% saved)

regimes131.0ms (6.4%)

Compiler: Compiled 470 to 352 computations (25.1% saved)

bsearch30.0ms (1.5%)

Steps

Iters	Range		Point
8	1.0924148319804382e+120	1.739192605735799e+124	1.710370274005485e+124
9	-8.779533170392781e+154	-9.970843626604297e+148	-1.3448548219911838e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	41
1	35	41

end0.0ms (0%)

sample536.0ms (26.2%)

Algorithm

1×

intervals

Results

212.0ms	8000×	body	128	valid
4.0ms	159×	body	128	nan

Compiler

Compiled 140 to 102 computations (27.1% saved)

Details

analyze74.0ms (3.6%)

sample14.0ms (0.7%)

simplify166.0ms (8.1%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite11.0ms (0.5%)

series87.0ms (4.2%)

simplify71.0ms (3.4%)

prune26.0ms (1.3%)

localize7.0ms (0.4%)

rewrite33.0ms (1.6%)

series526.0ms (25.7%)

simplify93.0ms (4.5%)

prune75.0ms (3.7%)

localize5.0ms (0.2%)

rewrite10.0ms (0.5%)

series30.0ms (1.4%)

simplify75.0ms (3.7%)

prune30.0ms (1.4%)

localize5.0ms (0.2%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.3%)

prune0.0ms (0%)

regimes131.0ms (6.4%)

bsearch30.0ms (1.5%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample536.0ms (26.2%)

Profiling