Details

analyze512.0ms (10.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample20.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify190.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	514	22
1	514	22

prune2.0ms (0%)

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: 23.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(-.f64 (.f64 b c) (.f64 a d))
23.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
9×	`times-frac_binary64_2105`
7×	`add-log-exp_binary64_2135`
5×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
3×	`pow1_binary64_2157` `associate-/r_binary64_2045` `associate-/l_binary64_2046`
2×	`flip3-+_binary64_2102` `associate-/l/_binary64_2048` `associate-/r/_binary64_2047` `flip3--_binary64_2103` `flip--_binary64_2074` `flip-+_binary64_2073`
1×	`sub-neg_binary64_2092` `cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `sum-log_binary64_2187` `frac-2neg_binary64_2110` `div-sub_binary64_2104` `+-commutative_binary64_2031` `clear-num_binary64_2098` `div-inv_binary64_2096` `diff-log_binary64_2188`

Counts

3 → 54

Calls

3 calls:

9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

series322.0ms (6.5%)

Counts

3 → 9

Calls

3 calls:

202.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
76.0ms	(-.f64 (.f64 b c) (.f64 a d))
44.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6056	1456

prune78.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 23.1b

Counts

64 → 10

Compiler

Compiled 1730 to 337 computations (80.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
14.8b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite86.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_2105`
164×	`add-sqr-sqrt_binary64_2120`
162×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
156×	`sqrt-prod_binary64_2114`
27×	`associate-/l*_binary64_2046`
22×	`sqrt-div_binary64_2115`
18×	`associate-/r/_binary64_2047`
12×	`associate-/r*_binary64_2045`
11×	`flip3-+_binary64_2102` `add-cbrt-cube_binary64_2132` `flip-+_binary64_2073` `add-exp-log_binary64_2134`
9×	`div-inv_binary64_2096`
6×	`pow1_binary64_2157`
4×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `add-log-exp_binary64_2135`
3×	`associate-/l/_binary64_2048` `div-sub_binary64_2104`
2×	`frac-2neg_binary64_2110` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `clear-num_binary64_2098` `sqrt-pow1_binary64_2116`
1×	`flip3--_binary64_2103` `flip--_binary64_2074`

Counts

4 → 266

Calls

4 calls:

20.0ms	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series542.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
197.0ms	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
49.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
45.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify175.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4979	13644
1	4979	13644

prune289.0ms (5.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	270	8	278
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	276	12	288

Merged error: 20.8b

Counts

288 → 12

Compiler

Compiled 11272 to 1175 computations (89.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
14.9b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite61.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_2105`
100×	`add-sqr-sqrt_binary64_2120`
98×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
54×	`sqrt-prod_binary64_2114`
27×	`associate-/r*_binary64_2045`
17×	`add-exp-log_binary64_2134`
11×	`add-cbrt-cube_binary64_2132` `associate-/r/_binary64_2047`
9×	`associate-/l*_binary64_2046`
8×	`div-exp_binary64_2147`
7×	`pow1_binary64_2157`
6×	`sqrt-div_binary64_2115` `div-inv_binary64_2096`
5×	`flip3--_binary64_2103` `flip--_binary64_2074`
4×	`cbrt-undiv_binary64_2130` `add-log-exp_binary64_2135`
3×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
2×	`1-exp_binary64_2140` `rec-exp_binary64_2146` `associate-/l/_binary64_2048` `frac-2neg_binary64_2110` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `clear-num_binary64_2098` `sqrt-pow1_binary64_2116`
1×	`pow-flip_binary64_2170` `inv-pow_binary64_2181`

Counts

4 → 193

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
10.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series449.0ms (9%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
154.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
40.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify119.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4946	7468
1	4946	7468

prune212.0ms (4.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	204	13	217

Merged error: 20.8b

Counts

217 → 13

Compiler

Compiled 8349 to 1195 computations (85.7% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
14.9b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite60.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_2120`
28×	`times-frac_binary64_2105` `add-exp-log_binary64_2134`
26×	`*-un-lft-identity_binary64_2099`
24×	`add-cube-cbrt_binary64_2131` `associate-r_binary64_2041`
23×	`sqrt-prod_binary64_2114`
18×	`add-cbrt-cube_binary64_2132`
9×	`div-exp_binary64_2147`
8×	`pow1_binary64_2157` `prod-exp_binary64_2145` `sqrt-div_binary64_2115`
6×	`associate-/l/_binary64_2048` `associate-/r*_binary64_2045`
5×	`cbrt-undiv_binary64_2130` `unswap-sqr_binary64_2067`
4×	`flip3-+_binary64_2102` `associate-*l/_binary64_2044` `associate-/r/_binary64_2047` `add-log-exp_binary64_2135` `flip3--_binary64_2103` `flip--_binary64_2074` `frac-times_binary64_2109` `flip-+_binary64_2073` `cbrt-unprod_binary64_2129`
3×	`associate-l_binary64_2042`
2×	`associate-*r/_binary64_2043` `1-exp_binary64_2140` `un-div-inv_binary64_2097` `rec-exp_binary64_2146` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `div-inv_binary64_2096` `sqrt-pow1_binary64_2116`
1×	`-commutative_binary64_2032` `frac-2neg_binary64_2110` `pow-prod-down_binary64_2167` `clear-num_binary64_2098` `associate-/l_binary64_2046`

Counts

4 → 122

Calls

4 calls:

19.0ms	(/.f64 (.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
17.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series529.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

248.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
188.0ms	(/.f64 (.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
47.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5206	3285

prune113.0ms (2.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	134	13	147

Merged error: 20.8b

Counts

147 → 13

Compiler

Compiled 4227 to 663 computations (84.3% saved)

regimes139.0ms (2.8%)

Compiler: Compiled 1472 to 930 computations (36.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	41
1	45	41

end0.0ms (0%)

sample835.0ms (16.8%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	128	valid
20.0ms	491×	body	128	invalid

Compiler

Compiled 357 to 219 computations (38.7% saved)

Details

analyze512.0ms (10.3%)

sample20.0ms (0.4%)

simplify190.0ms (3.8%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite22.0ms (0.4%)

series322.0ms (6.5%)

simplify65.0ms (1.3%)

prune78.0ms (1.6%)

localize12.0ms (0.2%)

rewrite86.0ms (1.7%)

series542.0ms (10.9%)

simplify175.0ms (3.5%)

prune289.0ms (5.8%)

localize17.0ms (0.3%)

rewrite61.0ms (1.2%)

series449.0ms (9%)

simplify119.0ms (2.4%)

prune212.0ms (4.3%)

localize18.0ms (0.4%)

rewrite60.0ms (1.2%)

series529.0ms (10.7%)

simplify79.0ms (1.6%)

prune113.0ms (2.3%)

regimes139.0ms (2.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample835.0ms (16.8%)

Profiling