Details

analyze5.0ms (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)

sample35.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	66×	body	1024	valid
8.0ms	153×	body	128	valid
4.0ms	24×	body	512	valid
1.0ms	4×	body	2048	valid
1.0ms	9×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify297.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune4.0ms (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: 26.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2120` `*-un-lft-identity_binary64_2099` `sqrt-prod_binary64_2114`
4×	`difference-of-squares_binary64_2068` `add-log-exp_binary64_2135`
3×	`add-cube-cbrt_binary64_2131` `pow1_binary64_2157` `distribute-lft-out--_binary64_2053`
2×	`distribute-lft-out_binary64_2052` `add-cbrt-cube_binary64_2132` `sqrt-div_binary64_2115` `add-exp-log_binary64_2134`
1×	`sub-neg_binary64_2092` `flip3-+_binary64_2102` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `flip3--_binary64_2103` `flip--_binary64_2074` `sqrt-pow1_binary64_2116` `flip-+_binary64_2073` `diff-log_binary64_2188`

Counts

2 → 34

Calls

2 calls:

19.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 x 1))

series186.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

137.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
49.0ms	(sqrt.f64 (+.f64 x 1))

simplify168.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	4907	747
1	4907	747

prune83.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 0.2b

Counts

41 → 3

Compiler

Compiled 647 to 430 computations (33.5% saved)

localize13.0ms (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)))

rewrite58.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_2099`
24×	`sqrt-prod_binary64_2114`
21×	`distribute-lft-out_binary64_2052`
18×	`times-frac_binary64_2105`
16×	`add-sqr-sqrt_binary64_2120`
15×	`add-cube-cbrt_binary64_2131`
7×	`add-exp-log_binary64_2134`
6×	`associate-/r*_binary64_2045`
5×	`add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-log-exp_binary64_2135`
3×	`flip3-+_binary64_2102` `associate-/l*_binary64_2046` `flip-+_binary64_2073`
2×	`div-exp_binary64_2147` `associate-/r/_binary64_2047` `sqrt-div_binary64_2115`
1×	`pow-flip_binary64_2170` `cbrt-undiv_binary64_2130` `1-exp_binary64_2140` `inv-pow_binary64_2181` `rec-exp_binary64_2146` `sum-log_binary64_2187` `frac-2neg_binary64_2110` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `+-commutative_binary64_2031` `clear-num_binary64_2098` `div-inv_binary64_2096` `sqrt-pow1_binary64_2116`

Counts

3 → 75

Calls

3 calls:

23.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
17.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 x 1))

series225.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
75.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
48.0ms	(sqrt.f64 (+.f64 x 1))

simplify127.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5545	1516

prune192.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	77	10	87

Merged error: 0.0b

Counts

87 → 10

Compiler

Compiled 1514 to 1081 computations (28.6% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.2b	(cbrt.f64 (+.f64 1 x))
0.2b	(cbrt.f64 (+.f64 1 x))
0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))

rewrite76.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_2120` `*-un-lft-identity_binary64_2099`
18×	`add-cube-cbrt_binary64_2131`
13×	`cbrt-prod_binary64_2127`
10×	`associate-r_binary64_2041` `add-exp-log_binary64_2134`
9×	`times-frac_binary64_2105` `sqrt-prod_binary64_2114`
8×	`add-cbrt-cube_binary64_2132`
7×	`pow1_binary64_2157`
6×	`cbrt-div_binary64_2128`
4×	`flip3-+_binary64_2102` `add-log-exp_binary64_2135` `flip-+_binary64_2073`
3×	`associate-l_binary64_2042` `distribute-lft-out_binary64_2052` `associate-/r_binary64_2045` `unswap-sqr_binary64_2067` `associate-/l_binary64_2046`
2×	`associate-*r/_binary64_2043` `pow1/3_binary64_2178` `div-exp_binary64_2147` `associate-/r/_binary64_2047` `sqrt-div_binary64_2115`
1×	`pow-flip_binary64_2170` `cbrt-undiv_binary64_2130` `1-exp_binary64_2140` `inv-pow_binary64_2181` `*-commutative_binary64_2032` `rec-exp_binary64_2146` `frac-2neg_binary64_2110` `prod-exp_binary64_2145` `pow-prod-down_binary64_2167` `clear-num_binary64_2098` `div-inv_binary64_2096` `cbrt-unprod_binary64_2129`

Counts

4 → 90

Calls

4 calls:

25.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
20.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
7.0ms	(cbrt.f64 (+.f64 1 x))
7.0ms	(cbrt.f64 (+.f64 1 x))

series1.4s (19.2%)

Counts

4 → 12

Calls

4 calls:

1.1s	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
157.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
76.0ms	(cbrt.f64 (+.f64 1 x))
64.0ms	(cbrt.f64 (+.f64 1 x))

simplify105.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5344	3235

prune325.0ms (4.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	102	10	112

Merged error: 0.0b

Counts

112 → 10

Compiler

Compiled 3152 to 2432 computations (22.8% saved)

localize22.0ms (0.3%)

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)))))

rewrite256.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

308×	`*-un-lft-identity_binary64_2099`
290×	`sqrt-prod_binary64_2114`
168×	`times-frac_binary64_2105`
136×	`add-sqr-sqrt_binary64_2120`
116×	`distribute-lft-out_binary64_2052`
88×	`add-cube-cbrt_binary64_2131`
43×	`swap-sqr_binary64_2066`
31×	`pow1_binary64_2157`
27×	`associate-l_binary64_2042` `associate-r_binary64_2041` `sqrt-pow1_binary64_2116`
16×	`unswap-sqr_binary64_2067`
14×	`associate-/r/_binary64_2047` `add-exp-log_binary64_2134`
12×	`associate-/r*_binary64_2045`
11×	`pow-flip_binary64_2170` `inv-pow_binary64_2181`
10×	`add-cbrt-cube_binary64_2132`
9×	`pow1/2_binary64_2176` `pow-prod-up_binary64_2166` `div-inv_binary64_2096`
7×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
6×	`associate-/l*_binary64_2046`
5×	`sqrt-div_binary64_2115` `pow-prod-down_binary64_2167` `pow-sqr_binary64_2072`
4×	`div-exp_binary64_2147` `add-log-exp_binary64_2135`
3×	`rem-sqrt-square_binary64_2112`
2×	`cbrt-undiv_binary64_2130` `1-exp_binary64_2140` `rec-exp_binary64_2146` `frac-2neg_binary64_2110` `clear-num_binary64_2098`
1×	`sqrt-unprod_binary64_2118` `rem-square-sqrt_binary64_2111` `associate-r/_binary64_2043` `-commutative_binary64_2032` `associate-*l/_binary64_2044` `prod-exp_binary64_2145` `pow2_binary64_2177` `pow-plus_binary64_2159` `frac-times_binary64_2109` `cbrt-unprod_binary64_2129`

Counts

4 → 278

Calls

4 calls:

90.0ms	(*.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)))))
25.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
24.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
23.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series515.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
113.0ms	(*.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)))))
105.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
100.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify505.0ms (7.1%)

Algorithm

1×	egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5287	6672

prune803.0ms (11.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	286	4	290
Fresh	3	4	7
Picked	1	0	1
Done	0	2	2
Total	290	10	300

Merged error: 0.0b

Counts

300 → 10

Compiler

Compiled 7204 to 5265 computations (26.9% saved)

regimes49.0ms (0.7%)

Compiler: Compiled 217 to 177 computations (18.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.6s (22.7%)

Algorithm

1×

intervals

Results

409.0ms	2025×	body	1024	valid
240.0ms	4376×	body	128	valid
154.0ms	956×	body	512	valid
56.0ms	204×	body	2048	valid
44.0ms	439×	body	256	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 241 to 199 computations (17.4% saved)

Details

analyze5.0ms (0.1%)

sample35.0ms (0.5%)

simplify297.0ms (4.2%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite31.0ms (0.4%)

series186.0ms (2.6%)

simplify168.0ms (2.4%)

prune83.0ms (1.2%)

localize13.0ms (0.2%)

rewrite58.0ms (0.8%)

series225.0ms (3.2%)

simplify127.0ms (1.8%)

prune192.0ms (2.7%)

localize20.0ms (0.3%)

rewrite76.0ms (1.1%)

series1.4s (19.2%)

simplify105.0ms (1.5%)

prune325.0ms (4.6%)

localize22.0ms (0.3%)

rewrite256.0ms (3.6%)

series515.0ms (7.3%)

simplify505.0ms (7.1%)

prune803.0ms (11.3%)

regimes49.0ms (0.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (22.7%)

Profiling