Details

analyze67.0ms (2.4%)

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
12.5%	87.4%	0.1%	4
31.2%	68.7%	0.1%	5
43.7%	56.2%	0.1%	6
54.6%	42.1%	3.2%	7
63.2%	30.4%	6.3%	8
69.9%	21.5%	8.7%	9
75.3%	15.2%	9.5%	10
79%	10.1%	10.8%	11
82%	7%	11%	12
83.9%	4.4%	11.8%	13
84.7%	3.5%	11.8%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample16.0ms (0.6%)

Algorithm

1×

intervals

Results

5.0ms	180×	body	128	valid
2.0ms	29×	body	1024	valid
2.0ms	24×	body	512	valid
1.0ms	23×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 19 to 19 computations (0% saved)

simplify296.0ms (10.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5043	10

prune5.0ms (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

Merged error: 0.0b

Counts

2 → 2

Compiler

Compiled 39 to 34 computations (12.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (-.f64 1 y) (*.f64 x y))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64_18006`
4×	`associate-+l+_binary64_17900`
3×	`cancel-sign-sub-inv_binary64_17933`
2×	`add-cube-cbrt_binary64_18002` `sum-log_binary64_18058` `add-sqr-sqrt_binary64_17989` `*-un-lft-identity_binary64_17967`
1×	`associate-+l-_binary64_17902` `sub-neg_binary64_17960` `pow1_binary64_18028` `add-exp-log_binary64_18005` `flip-+_binary64_17941` `+-commutative_binary64_17897` `diff-log_binary64_18059` `add-cbrt-cube_binary64_18003` `flip3-+_binary64_17970`

Counts

1 → 17

Calls

1 calls:

9.0ms

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

series29.0ms (1.1%)

Counts

1 → 3

Calls

1 calls:

29.0ms

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

simplify68.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5024	264

prune19.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	19	3	22

Merged error: 0.0b

Counts

22 → 3

Compiler

Compiled 283 to 163 computations (42.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 y x) (-.f64 1 y))
0.0b	(sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y)))
0.0b	(sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y)))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 y x) (-.f64 1 y))) (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))))

rewrite52.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_17989`
24×	`sqrt-prod_binary64_17983`
21×	`pow1_binary64_18028`
16×	`sqrt-div_binary64_17984`
15×	`add-cube-cbrt_binary64_18002` `*-un-lft-identity_binary64_17967`
10×	`sqrt-pow1_binary64_17985` `pow1/2_binary64_18047`
9×	`flip-+_binary64_17941` `add-log-exp_binary64_18006` `flip3-+_binary64_17970`
8×	`swap-sqr_binary64_17934`
6×	`add-exp-log_binary64_18005` `associate-l_binary64_17908` `associate-r_binary64_17907` `add-cbrt-cube_binary64_18003`
5×	`pow-prod-up_binary64_18037`
4×	`unswap-sqr_binary64_17935` `frac-times_binary64_17977` `rem-sqrt-square_binary64_17980` `associate-+r+_binary64_17899`
3×	`pow-prod-down_binary64_18038` `pow-sqr_binary64_17940` `cancel-sign-sub-inv_binary64_17933`
2×	`associate-l/_binary64_17910` `sum-log_binary64_18058` `associate-r/_binary64_17909`
1×	`cbrt-unprod_binary64_18000` `sub-neg_binary64_17960` `*-commutative_binary64_17898` `prod-exp_binary64_18016` `sqrt-unprod_binary64_17987` `rem-square-sqrt_binary64_17979` `associate-+r-_binary64_17901` `+-commutative_binary64_17897` `diff-log_binary64_18059` `pow-plus_binary64_18030` `sqr-abs_binary64_17982` `pow2_binary64_18048`

Counts

4 → 105

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y x) (-.f64 1 y))) (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))))
8.0ms	(+.f64 (*.f64 y x) (-.f64 1 y))
7.0ms	(sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y)))
7.0ms	(sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y)))

series170.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y)))
53.0ms	(sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y)))
35.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y x) (-.f64 1 y))) (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))))
27.0ms	(+.f64 (*.f64 y x) (-.f64 1 y))

simplify77.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5016	1956

prune137.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	117	3	120

Merged error: 0b

Counts

120 → 3

Compiler

Compiled 2699 to 1563 computations (42.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 (-.f64 1 x) (-.f64 1 y))
2.9b	(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_17989`
14×	`*-un-lft-identity_binary64_17967`
12×	`cancel-sign-sub-inv_binary64_17933`
8×	`add-cube-cbrt_binary64_18002` `distribute-lft-in_binary64_17916` `distribute-rgt-in_binary64_17917` `associate-+r+_binary64_17899`
6×	`flip3--_binary64_17971` `flip--_binary64_17942` `associate-l_binary64_17908` `associate-r_binary64_17907`
4×	`sub-neg_binary64_17960` `pow1_binary64_18028` `add-exp-log_binary64_18005` `frac-times_binary64_17977` `add-log-exp_binary64_18006` `difference-of-squares_binary64_17936` `add-cbrt-cube_binary64_18003`
2×	`associate-l/_binary64_17910` `associate-r/_binary64_17909` `distribute-lft-out--_binary64_17919`
1×	`cbrt-unprod_binary64_18000` `*-commutative_binary64_17898` `prod-exp_binary64_18016` `unswap-sqr_binary64_17935` `pow-prod-down_binary64_18038` `flip-+_binary64_17941` `sum-log_binary64_18058` `+-commutative_binary64_17897` `flip3-+_binary64_17970`

Counts

2 → 59

Calls

2 calls:

12.0ms	(*.f64 (-.f64 1 x) (-.f64 1 y))
5.0ms	(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))

series59.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

32.0ms	(+.f64 x (*.f64 (-.f64 1 x) (-.f64 1 y)))
27.0ms	(*.f64 (-.f64 1 x) (-.f64 1 y))

simplify74.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4929	826
1	4929	826

prune54.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	3	68

Merged error: 0b

Counts

68 → 3

Compiler

Compiled 976 to 616 computations (36.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y)))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 y x) (-.f64 1 y))) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))) 3)))
0.1b	(pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))) 3)
5.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))) 3))

rewrite70.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_17989`
48×	`cbrt-prod_binary64_17998`
35×	`sqrt-prod_binary64_17983`
23×	`add-cube-cbrt_binary64_18002` `*-un-lft-identity_binary64_17967`
22×	`cube-prod_binary64_17995` `unpow-prod-down_binary64_18046`
21×	`associate-r_binary64_17907`
18×	`sqrt-div_binary64_17984`
14×	`unswap-sqr_binary64_17935`
10×	`cube-div_binary64_17996`
9×	`pow1_binary64_18028` `flip-+_binary64_17941` `flip3-+_binary64_17970`
8×	`cbrt-div_binary64_17999`
7×	`add-exp-log_binary64_18005`
6×	`associate-l_binary64_17908` `add-cbrt-cube_binary64_18003`
5×	`sqr-pow_binary64_17939`
4×	`frac-times_binary64_17977` `add-log-exp_binary64_18006`
3×	`pow-pow_binary64_18039` `unpow3_binary64_18033` `pow-unpow_binary64_18044` `cube-mult_binary64_17997`
2×	`sqrt-pow1_binary64_17985` `pow1/2_binary64_18047` `associate-l/_binary64_17910` `associate-r/_binary64_17909`
1×	`rem-cube-cbrt_binary64_17990` `pow1/3_binary64_18049` `cbrt-unprod_binary64_18000` `rem-cbrt-cube_binary64_17991` `*-commutative_binary64_17898` `prod-exp_binary64_18016` `pow-to-exp_binary64_18036` `pow-prod-down_binary64_18038` `sqrt-pow2_binary64_17986` `rem-sqrt-square_binary64_17980` `pow-exp_binary64_18035`

Counts

4 → 138

Calls

4 calls:

27.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y x) (-.f64 1 y))) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))) 3)))
10.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))) 3))
9.0ms	(pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))) 3)
7.0ms	(sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y)))

series679.0ms (24.4%)

Counts

4 → 12

Calls

4 calls:

539.0ms	(pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))) 3)
54.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))) 3))
52.0ms	(sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y)))
34.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y x) (-.f64 1 y))) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (-.f64 1 y))) 3)))

simplify86.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4981	3233
1	4981	3233

prune190.0ms (6.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	150	3	153

Merged error: 0b

Counts

153 → 3

Compiler

Compiled 3809 to 2284 computations (40% saved)

regimes39.0ms (1.4%)

Compiler: Compiled 172 to 148 computations (14% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms (0%)

sample530.0ms (19.1%)

Algorithm

1×

intervals

Results

149.0ms	5884×	body	128	valid
64.0ms	747×	body	1024	valid
61.0ms	849×	body	512	valid
23.0ms	513×	body	256	valid
2.0ms	75×	body	128	invalid
1.0ms	7×	body	2048	valid

Compiler

Compiled 60 to 52 computations (13.3% saved)

Details

analyze67.0ms (2.4%)

sample16.0ms (0.6%)

simplify296.0ms (10.6%)

prune5.0ms (0.2%)

localize5.0ms (0.2%)

rewrite10.0ms (0.4%)

series29.0ms (1.1%)

simplify68.0ms (2.4%)

prune19.0ms (0.7%)

localize8.0ms (0.3%)

rewrite52.0ms (1.9%)

series170.0ms (6.1%)

simplify77.0ms (2.8%)

prune137.0ms (4.9%)

localize6.0ms (0.2%)

rewrite23.0ms (0.8%)

series59.0ms (2.1%)

simplify74.0ms (2.6%)

prune54.0ms (1.9%)

localize12.0ms (0.4%)

rewrite70.0ms (2.5%)

series679.0ms (24.4%)

simplify86.0ms (3.1%)

prune190.0ms (6.8%)

regimes39.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample530.0ms (19.1%)

Profiling