Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	73×	body	1024	valid
6.0ms	31×	body	512	valid
4.0ms	127×	body	128	valid
1.0ms	22×	body	256	valid
0.0ms	3×	body	2048	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify92.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

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

32.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_2140`
14×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
6×	`cancel-sign-sub-inv_binary64_2090`
5×	`add-cube-cbrt_binary64_2159`
4×	`difference-of-squares_binary64_2093` `add-log-exp_binary64_2163`
3×	`distribute-lft-out--_binary64_2076` `pow1_binary64_2185`
2×	`distribute-lft-out_binary64_2075` `sqrt-div_binary64_2141` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `flip-+_binary64_2098`

Counts

2 → 40

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series54.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

37.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
17.0ms	(sqrt.f64 (+.f64 x 1))

simplify78.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune46.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	3	47

Error

0.1b

Counts

47 → 3

Compiler

Compiled 699 to 459 computations (34.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite27.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_2124`
24×	`sqrt-prod_binary64_2140`
21×	`distribute-lft-out_binary64_2075`
18×	`times-frac_binary64_2130`
16×	`add-sqr-sqrt_binary64_2146`
15×	`add-cube-cbrt_binary64_2159`
7×	`add-exp-log_binary64_2162`
6×	`associate-/r*_binary64_2068`
5×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
3×	`associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`associate-/r/_binary64_2070` `sqrt-div_binary64_2141` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `pow-flip_binary64_2198` `1-exp_binary64_2168` `div-inv_binary64_2121` `inv-pow_binary64_2209` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series66.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
22.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune93.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	77	10	87

Error

Counts

87 → 10

Compiler

Compiled 1520 to 1083 computations (28.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite118.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_2124`
290×	`sqrt-prod_binary64_2140`
172×	`times-frac_binary64_2130`
144×	`add-sqr-sqrt_binary64_2146`
116×	`distribute-lft-out_binary64_2075`
88×	`add-cube-cbrt_binary64_2159`
43×	`swap-sqr_binary64_2091`
31×	`pow1_binary64_2185`
27×	`sqrt-pow1_binary64_2142` `associate-l_binary64_2065` `associate-r_binary64_2064`
16×	`unswap-sqr_binary64_2092`
14×	`associate-/r/_binary64_2070` `add-exp-log_binary64_2162`
12×	`associate-/r*_binary64_2068`
11×	`pow-flip_binary64_2198` `inv-pow_binary64_2209`
10×	`add-cbrt-cube_binary64_2160`
9×	`pow-prod-up_binary64_2194` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `div-inv_binary64_2121`
7×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
6×	`associate-/l*_binary64_2069`
5×	`pow-prod-down_binary64_2195` `sqrt-div_binary64_2141` `pow-sqr_binary64_2097`
4×	`add-log-exp_binary64_2163` `div-exp_binary64_2175`
3×	`sqr-abs_binary64_2139`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `1-exp_binary64_2168` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`sqrt-unprod_binary64_2144` `-commutative_binary64_2055` `associate-l/_binary64_2067` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `rem-square-sqrt_binary64_2136` `associate-*r/_binary64_2066` `pow2_binary64_2205` `frac-times_binary64_2134` `cbrt-unprod_binary64_2157`

Counts

4 → 281

Calls

4 calls:

43.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
17.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series142.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
32.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
32.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
28.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify117.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5033	6769

prune509.0ms (15.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	292	1	293
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	294	9	303

Error

Counts

303 → 9

Compiler

Compiled 7470 to 5466 computations (26.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.5b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)

rewrite36.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64_2124`
28×	`sqrt-prod_binary64_2140`
13×	`distribute-lft-out_binary64_2075`
11×	`add-sqr-sqrt_binary64_2146`
9×	`unpow-prod-down_binary64_2203` `add-cube-cbrt_binary64_2159`
8×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163`
5×	`add-exp-log_binary64_2162`
4×	`sqrt-div_binary64_2141` `add-cbrt-cube_binary64_2160`
3×	`pow-unpow_binary64_2201` `pow-pow_binary64_2196` `sqrt-pow1_binary64_2142` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`rem-sqrt-square_binary64_2137`
1×	`sqrt-pow2_binary64_2143` `sum-log_binary64_2215` `pow-exp_binary64_2192` `sqr-pow_binary64_2096` `+-commutative_binary64_2054` `pow-to-exp_binary64_2193`

Counts

4 → 74

Calls

4 calls:

11.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

series141.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
42.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
21.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
12.0ms	(sqrt.f64 (+.f64 1 x))

simplify62.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4952	1657
1	4952	1657

prune103.0ms (3.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	86	9	95

Error

Counts

95 → 9

Compiler

Compiled 1804 to 1388 computations (23.1% saved)

regimes124.0ms (3.9%)

Accuracy

Total 0.2b remaining (95.7%)

Threshold costs 0.2b (95.7%)

Compiler

Compiled 1364 to 1121 computations (17.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.3s (39.4%)

Algorithm

1×

intervals

Results

206.0ms	1926×	body	1024	valid
125.0ms	4351×	body	128	valid
83.0ms	1025×	body	512	valid
33.0ms	206×	body	2048	valid
26.0ms	492×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 672 to 555 computations (17.4% saved)

Details

analyze3.0ms (0.1%)

sample24.0ms (0.7%)

simplify92.0ms (2.9%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite15.0ms (0.5%)

series54.0ms (1.7%)

simplify78.0ms (2.4%)

prune46.0ms (1.4%)

localize6.0ms (0.2%)

rewrite27.0ms (0.8%)

series66.0ms (2.1%)

simplify61.0ms (1.9%)

prune93.0ms (2.9%)

localize12.0ms (0.4%)

rewrite118.0ms (3.7%)

series142.0ms (4.4%)

simplify117.0ms (3.6%)

prune509.0ms (15.8%)

localize12.0ms (0.4%)

rewrite36.0ms (1.1%)

series141.0ms (4.4%)

simplify62.0ms (1.9%)

prune103.0ms (3.2%)

regimes124.0ms (3.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (39.4%)

Profiling