Details

analyze331.0ms (8.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample78.0ms (2%)

Algorithm

1×

intervals

Results

30.0ms	123×	body	2048	nan
14.0ms	256×	body	128	valid
11.0ms	66×	body	1024	nan
4.0ms	29×	body	512	nan
1.0ms	19×	body	256	nan
1.0ms	22×	body	128	nan
0.0ms	1×	body	4096	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify257.0ms (6.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

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

Error

31.6b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

29.5b	(sqrt.f64 (-.f64 (*.f64 x x) 1))
0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
29.5b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`sqrt-prod_binary64_2140` `*-un-lft-identity_binary64_2124`
5×	`add-sqr-sqrt_binary64_2146`
4×	`add-log-exp_binary64_2163`
3×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
2×	`difference-of-squares_binary64_2093` `sqrt-div_binary64_2141` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `difference-of-sqr-1_binary64_2094` `flip-+_binary64_2098`

Counts

2 → 30

Calls

4 calls:

13.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
0.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series81.0ms (2.1%)

Counts

2 → 13

Calls

2 calls:

48.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
33.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 195 to 172 computations (11.8% saved)

simplify81.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5073	547

prune55.0ms (1.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	1	44

Error

Counts

44 → 1

Compiler

Compiled 554 to 361 computations (34.8% saved)

localize11.0ms (0.3%)

Local error

Found 6 expressions with local error:

0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.0b	(sqrt.f64 (-.f64 x 1))
0.0b	(sqrt.f64 (-.f64 x 1))
0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_2146`
22×	`sqrt-prod_binary64_2140`
16×	`*-un-lft-identity_binary64_2124`
14×	`sqrt-div_binary64_2141`
10×	`associate-r_binary64_2064`
8×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
7×	`associate-l_binary64_2065`
5×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
4×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `unswap-sqr_binary64_2092` `flip3-+_binary64_2127` `frac-times_binary64_2134` `flip-+_binary64_2098`
3×	`pow-prod-down_binary64_2195` `sqrt-pow1_binary64_2142` `pow1/2_binary64_2204`
2×	`distribute-lft-out--_binary64_2076` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `difference-of-sqr-1_binary64_2094`
1×	`sqrt-unprod_binary64_2144` `sum-log_binary64_2215` `*-commutative_binary64_2055` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `+-commutative_binary64_2054` `cbrt-unprod_binary64_2157`

Counts

3 → 73

Calls

6 calls:

23.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
4.0ms	(sqrt.f64 (-.f64 x 1))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.0ms	(sqrt.f64 (-.f64 x 1))
0.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series109.0ms (2.8%)

Counts

3 → 15

Calls

3 calls:

53.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
39.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
17.0ms	(sqrt.f64 (-.f64 x 1))

Compiler

Compiled 254 to 221 computations (13% saved)

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4916	1372
1	4916	1372

prune129.0ms (3.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	1	89

Error

Counts

89 → 1

Compiler

Compiled 1496 to 1125 computations (24.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	51
1	43	51

regimes76.0ms (2%)

Accuracy

Total 0.0b remaining (16.9%)

Threshold costs 0.0b (16.9%)

Compiler

Compiled 202 to 176 computations (12.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample2.5s (64.4%)

Algorithm

1×

intervals

Results

796.0ms	3938×	body	2048	nan
424.0ms	8000×	body	128	valid
315.0ms	1953×	body	1024	nan
117.0ms	1017×	body	512	nan
46.0ms	546×	body	256	nan
25.0ms	542×	body	128	nan
1.0ms	2×	body	4096	nan

Compiler

Compiled 118 to 105 computations (11% saved)

Pareto

0.3326121687457301

Details

analyze331.0ms (8.6%)

sample78.0ms (2%)

simplify257.0ms (6.7%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite26.0ms (0.7%)

series81.0ms (2.1%)

simplify81.0ms (2.1%)

prune55.0ms (1.4%)

localize11.0ms (0.3%)

rewrite36.0ms (0.9%)

series109.0ms (2.8%)

simplify80.0ms (2.1%)

prune129.0ms (3.4%)

simplify4.0ms (0.1%)

regimes76.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.5s (64.4%)

Profiling