Details

analyze407.0ms (3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4999	132
1	4999	132
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 24 to 21 computations (12.5% saved)

sample73.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	24×	body	4096	valid
18.0ms	182×	body	128	valid
15.0ms	26×	body	2048	valid
4.0ms	11×	body	1024	valid
3.0ms	10×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify74.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4970	33
1	4970	33

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

28.7b

Counts

2 → 1

Compiler

Compiled 44 to 37 computations (15.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (atan.f64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) PI.f64)
0.1b	(*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))
0.7b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))
35.7b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))

rewrite478.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

28.4b

Rules

69×	`*-un-lft-identity_binary64_2124`
46×	`add-sqr-sqrt_binary64_2146`
36×	`cancel-sign-sub-inv_binary64_2090`
30×	`add-cube-cbrt_binary64_2159`
26×	`sqrt-prod_binary64_2140`
20×	`times-frac_binary64_2130`
16×	`unpow-prod-down_binary64_2203`
15×	`add-exp-log_binary64_2162`
14×	`sqrt-div_binary64_2141` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
13×	`associate-l_binary64_2065`
12×	`distribute-lft-out_binary64_2075` `frac-sub_binary64_2133` `associate--l+_binary64_2061`
11×	`add-cbrt-cube_binary64_2160`
10×	`distribute-lft-out--_binary64_2076`
9×	`add-log-exp_binary64_2163` `flip3--_binary64_2128` `flip--_binary64_2099`
7×	`pow1_binary64_2185` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-r_binary64_2064`
6×	`sub-neg_binary64_2117` `frac-times_binary64_2134` `associate-*r/_binary64_2066`
4×	`difference-of-squares_binary64_2093` `prod-exp_binary64_2173`
3×	`diff-log_binary64_2216` `div-exp_binary64_2175` `unswap-sqr_binary64_2092` `associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`cbrt-unprod_binary64_2157` `cbrt-undiv_binary64_2158` `div-inv_binary64_2121`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `associate--l-_binary64_2062` `pow-prod-down_binary64_2195` `1-exp_binary64_2168` `rec-exp_binary64_2174` `associate-l/_binary64_2067` `-commutative_binary64_2055` `frac-2neg_binary64_2135` `clear-num_binary64_2123`

Counts

4 → 158

Calls

4 calls:

33.0ms	(*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))
21.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))
11.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
5.0ms	(/.f64 (atan.f64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) PI.f64)

Compiler

Compiled 6455 to 3950 computations (38.8% saved)

series1.7s (12.5%)

Error

0.2b

Counts

4 → 103

Calls

4 calls:

493.0ms	(*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))
413.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))
334.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))
212.0ms	(/.f64 (atan.f64 (*.f64 (/.f64 1 B) (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2)))))) PI.f64)

Compiler

Compiled 8772 to 6750 computations (23.1% saved)

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5056	9343

prune463.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	252	9	261
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	253	9	262

Error

0.1b

Counts

262 → 9

Compiler

Compiled 8968 to 4475 computations (50.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (neg.f64 (+.f64 A (sqrt.f64 (+.f64 (.f64 B B) (*.f64 A A))))) B)) PI.f64))
0.0b	(/.f64 (atan.f64 (/.f64 (neg.f64 (+.f64 A (sqrt.f64 (+.f64 (.f64 B B) (.f64 A A))))) B)) PI.f64)
0.5b	(+.f64 A (sqrt.f64 (+.f64 (.f64 B B) (.f64 A A))))
28.8b	(sqrt.f64 (+.f64 (.f64 B B) (.f64 A A)))

rewrite120.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

27×	`add-sqr-sqrt_binary64_2146`
23×	`*-un-lft-identity_binary64_2124`
21×	`add-cube-cbrt_binary64_2159`
19×	`times-frac_binary64_2130`
13×	`associate-r_binary64_2064`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163`
4×	`distribute-frac-neg_binary64_2087`
3×	`sqrt-prod_binary64_2140` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `associate-l_binary64_2065`
2×	`flip3-+_binary64_2127` `sqrt-div_binary64_2141` `flip-+_binary64_2098` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `div-inv_binary64_2121` `atan-neg_binary64_2308` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `sum-log_binary64_2215` `distribute-lft-out_binary64_2075` `+-commutative_binary64_2054` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `pow-prod-down_binary64_2195` `distribute-rgt-neg-out_binary64_2084` `associate-r/_binary64_2066` `-commutative_binary64_2055`

Counts

4 → 88

Calls

4 calls:

7.0ms	(.f64 180 (/.f64 (atan.f64 (/.f64 (neg.f64 (+.f64 A (sqrt.f64 (+.f64 (.f64 B B) (*.f64 A A))))) B)) PI.f64))
6.0ms	(+.f64 A (sqrt.f64 (+.f64 (.f64 B B) (.f64 A A))))
4.0ms	(sqrt.f64 (+.f64 (.f64 B B) (.f64 A A)))
3.0ms	(/.f64 (atan.f64 (/.f64 (neg.f64 (+.f64 A (sqrt.f64 (+.f64 (.f64 B B) (.f64 A A))))) B)) PI.f64)

Compiler

Compiled 2776 to 575 computations (79.3% saved)

series509.0ms (3.8%)

Error

0.1b

Counts

4 → 50

Calls

4 calls:

130.0ms	(sqrt.f64 (+.f64 (.f64 B B) (.f64 A A)))
122.0ms	(.f64 180 (/.f64 (atan.f64 (/.f64 (neg.f64 (+.f64 A (sqrt.f64 (+.f64 (.f64 B B) (*.f64 A A))))) B)) PI.f64))
113.0ms	(+.f64 A (sqrt.f64 (+.f64 (.f64 B B) (.f64 A A))))
87.0ms	(/.f64 (atan.f64 (/.f64 (neg.f64 (+.f64 A (sqrt.f64 (+.f64 (.f64 B B) (.f64 A A))))) B)) PI.f64)

Compiler

Compiled 2479 to 2055 computations (17.1% saved)

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5034	3539

prune138.0ms (1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	137	10	147

Error

0.1b

Counts

147 → 10

Compiler

Compiled 3582 to 1118 computations (68.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 B B) (.f64 C C))
0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 C (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C)))) B)) PI.f64)
0.5b	(-.f64 C (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))))
29.5b	(sqrt.f64 (+.f64 (.f64 B B) (.f64 C C)))

rewrite98.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

20×	`add-sqr-sqrt_binary64_2146`
17×	`*-un-lft-identity_binary64_2124`
15×	`add-cube-cbrt_binary64_2159`
9×	`times-frac_binary64_2130`
8×	`add-log-exp_binary64_2163`
7×	`sqrt-prod_binary64_2140`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `cancel-sign-sub-inv_binary64_2090`
5×	`pow1_binary64_2185`
3×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`flip3-+_binary64_2127` `sqrt-div_binary64_2141` `flip-+_binary64_2098` `difference-of-squares_binary64_2093`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `distribute-lft-out--_binary64_2076` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 73

Calls

4 calls:

7.0ms	(-.f64 C (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))))
4.0ms	(+.f64 (.f64 B B) (.f64 C C))
4.0ms	(sqrt.f64 (+.f64 (.f64 B B) (.f64 C C)))
3.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 C (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C)))) B)) PI.f64)

Compiler

Compiled 2108 to 537 computations (74.5% saved)

series543.0ms (4%)

Error

0.1b

Counts

4 → 59

Calls

4 calls:

150.0ms	(-.f64 C (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))))
135.0ms	(sqrt.f64 (+.f64 (.f64 B B) (.f64 C C)))
98.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 C (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C)))) B)) PI.f64)
93.0ms	(+.f64 (.f64 B B) (.f64 C C))

Compiler

Compiled 2680 to 2199 computations (17.9% saved)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5007	2730

prune132.0ms (1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	132	10	142

Error

0.1b

Counts

142 → 10

Compiler

Compiled 3078 to 1123 computations (63.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(atan.f64 (/.f64 (neg.f64 (-.f64 A B)) B))
0.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (neg.f64 (-.f64 A B)) B)) PI.f64))
0.0b	(/.f64 (neg.f64 (-.f64 A B)) B)
0.0b	(/.f64 (atan.f64 (/.f64 (neg.f64 (-.f64 A B)) B)) PI.f64)

rewrite156.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

68×	`add-sqr-sqrt_binary64_2146`
63×	`*-un-lft-identity_binary64_2124`
61×	`times-frac_binary64_2130`
47×	`add-cube-cbrt_binary64_2159`
20×	`distribute-rgt-neg-in_binary64_2082` `distribute-lft-neg-in_binary64_2081`
17×	`associate-/l*_binary64_2069`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `associate-r_binary64_2064`
8×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
6×	`pow1_binary64_2185` `distribute-frac-neg_binary64_2087` `associate-/r*_binary64_2068`
4×	`add-log-exp_binary64_2163` `neg-mul-1_binary64_2120`
3×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `div-inv_binary64_2121` `atan-neg_binary64_2308` `associate-l_binary64_2065`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `distribute-neg-frac_binary64_2088` `associate-/l/_binary64_2071` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092`
1×	`neg-sub0_binary64_2119` `div-sub_binary64_2129` `flip3--_binary64_2128` `flip--_binary64_2099` `pow-prod-down_binary64_2195` `distribute-rgt-neg-out_binary64_2084` `associate-r/_binary64_2066` `-commutative_binary64_2055`

Counts

4 → 144

Calls

4 calls:

8.0ms	(/.f64 (neg.f64 (-.f64 A B)) B)
7.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (neg.f64 (-.f64 A B)) B)) PI.f64))
4.0ms	(atan.f64 (/.f64 (neg.f64 (-.f64 A B)) B))
3.0ms	(/.f64 (atan.f64 (/.f64 (neg.f64 (-.f64 A B)) B)) PI.f64)

Compiler

Compiled 2878 to 908 computations (68.5% saved)

series288.0ms (2.1%)

Error

0.1b

Counts

4 → 30

Calls

4 calls:

94.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (neg.f64 (-.f64 A B)) B)) PI.f64))
83.0ms	(/.f64 (neg.f64 (-.f64 A B)) B)
66.0ms	(/.f64 (atan.f64 (/.f64 (neg.f64 (-.f64 A B)) B)) PI.f64)
28.0ms	(atan.f64 (/.f64 (neg.f64 (-.f64 A B)) B))

Compiler

Compiled 834 to 692 computations (17% saved)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4963	2816
1	4963	2816

prune135.0ms (1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	174	10	184

Error

0.1b

Counts

184 → 10

Compiler

Compiled 2825 to 924 computations (67.3% saved)

regimes2.3s (16.7%)

Accuracy

Total 16.8b remaining (96.7%)

Threshold costs 0b (0%)

Compiler

Compiled 19450 to 15830 computations (18.6% saved)

bsearch5.0ms (0%)

Compiler: Compiled 18 to 15 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	139
1	93	139

end0.0ms (0%)

sample5.5s (40.8%)

Algorithm

1×

intervals

Results

692.0ms	888×	body	4096	valid
557.0ms	5384×	body	128	valid
505.0ms	847×	body	2048	valid
212.0ms	488×	body	1024	valid
79.0ms	251×	body	512	valid
29.0ms	142×	body	256	valid

Compiler

Compiled 2726 to 2211 computations (18.9% saved)

Details

analyze407.0ms (3%)

sample73.0ms (0.5%)

simplify74.0ms (0.5%)

prune8.0ms (0.1%)

localize16.0ms (0.1%)

rewrite478.0ms (3.5%)

series1.7s (12.5%)

simplify106.0ms (0.8%)

prune463.0ms (3.4%)

localize12.0ms (0.1%)

rewrite120.0ms (0.9%)

series509.0ms (3.8%)

simplify87.0ms (0.6%)

prune138.0ms (1%)

localize14.0ms (0.1%)

rewrite98.0ms (0.7%)

series543.0ms (4%)

simplify88.0ms (0.7%)

prune132.0ms (1%)

localize8.0ms (0.1%)

rewrite156.0ms (1.2%)

series288.0ms (2.1%)

simplify88.0ms (0.7%)

prune135.0ms (1%)

regimes2.3s (16.7%)

bsearch5.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.5s (40.8%)

Profiling