Details

analyze400.0ms (6.3%)

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)

sample76.0ms (1.2%)

Algorithm

1×

intervals

Results

22.0ms	180×	body	128	valid
20.0ms	25×	body	4096	valid
17.0ms	30×	body	2048	valid
4.0ms	9×	body	1024	valid
3.0ms	8×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4970	33
1	4970	33

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.6b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
0.0b	(pow.f64 (-.f64 A C) 2)
0.7b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
36.5b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
18×	`add-cube-cbrt_binary64_2159`
9×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163` `times-frac_binary64_2130`
7×	`sqrt-prod_binary64_2140` `add-exp-log_binary64_2162`
6×	`sqrt-div_binary64_2141` `pow1_binary64_2185` `add-cbrt-cube_binary64_2160`
5×	`unpow-prod-down_binary64_2203`
4×	`distribute-lft-out--_binary64_2076` `associate--l+_binary64_2061` `frac-sub_binary64_2133`
3×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `pow-unpow_binary64_2201` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `diff-log_binary64_2216` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`sub-neg_binary64_2117`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `pow-pow_binary64_2196` `sqrt-pow1_binary64_2142` `associate--l-_binary64_2062` `pow-exp_binary64_2192` `rem-sqrt-square_binary64_2137` `sqr-pow_binary64_2096` `pow1/2_binary64_2204` `unpow2_binary64_2189` `pow-to-exp_binary64_2193` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 93

Calls

4 calls:

16.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
5.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
5.0ms	(pow.f64 (-.f64 A C) 2)

series238.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
72.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
70.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
15.0ms	(pow.f64 (-.f64 A C) 2)

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4965	2955
1	4965	2955

prune165.0ms (2.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	12	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	12	106

Error

20.0b

Counts

106 → 12

Compiler

Compiled 3480 to 1803 computations (48.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64_2124`
44×	`add-sqr-sqrt_binary64_2146`
37×	`times-frac_binary64_2130`
31×	`add-cube-cbrt_binary64_2159`
13×	`associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`distribute-lft-out--_binary64_2076`
9×	`associate-/l*_binary64_2069`
6×	`pow1_binary64_2185` `associate-/r*_binary64_2068`
4×	`difference-of-squares_binary64_2093` `add-log-exp_binary64_2163`
3×	`cbrt-undiv_binary64_2158` `associate-l_binary64_2065` `div-inv_binary64_2121` `div-exp_binary64_2175`
2×	`clear-num_binary64_2123` `unswap-sqr_binary64_2092` `prod-exp_binary64_2173` `associate-/l/_binary64_2071` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `-commutative_binary64_2055` `associate-r/_binary64_2066` `div-sub_binary64_2129`

Counts

4 → 108

Calls

4 calls:

12.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64))
10.0ms	(/.f64 (-.f64 (-.f64 C A) B) B)
7.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))
5.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64)

series135.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64))
37.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64)
28.0ms	(/.f64 (-.f64 (-.f64 C A) B) B)
18.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5170	2442

prune109.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Error

20.0b

Counts

132 → 12

Compiler

Compiled 2685 to 877 computations (67.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))
0.0b	(/.f64 (-.f64 (-.f64 C A) B) B)
0.0b	(.f64 (.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) 180) (/.f64 1 PI.f64))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_2124`
29×	`add-sqr-sqrt_binary64_2146`
27×	`add-exp-log_binary64_2162` `times-frac_binary64_2130`
21×	`add-cube-cbrt_binary64_2159`
17×	`add-cbrt-cube_binary64_2160`
13×	`associate-r_binary64_2064`
12×	`distribute-lft-out--_binary64_2076` `prod-exp_binary64_2173`
8×	`pow1_binary64_2185`
6×	`associate-/l*_binary64_2069` `cbrt-unprod_binary64_2157`
5×	`div-exp_binary64_2175`
4×	`difference-of-squares_binary64_2093`
3×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163`
2×	`1-exp_binary64_2168` `div-inv_binary64_2121` `associate-/l/_binary64_2071` `rec-exp_binary64_2174`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `un-div-inv_binary64_2122` `-commutative_binary64_2055` `associate-l_binary64_2065` `associate-r/_binary64_2066` `div-sub_binary64_2129` `frac-2neg_binary64_2135`

Counts

3 → 87

Calls

3 calls:

11.0ms	(.f64 (.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) 180) (/.f64 1 PI.f64))
10.0ms	(/.f64 (-.f64 (-.f64 C A) B) B)
8.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))

series95.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

51.0ms	(.f64 (.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) 180) (/.f64 1 PI.f64))
27.0ms	(/.f64 (-.f64 (-.f64 C A) B) B)
17.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5122	1766

prune94.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	96	12	108

Error

20.0b

Counts

108 → 12

Compiler

Compiled 2161 to 971 computations (55.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B))))
0.0b	(pow.f64 (-.f64 A C) 2)
0.7b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
36.5b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64_2130`
59×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
52×	`add-cube-cbrt_binary64_2159`
16×	`add-exp-log_binary64_2162`
13×	`associate-/r*_binary64_2068`
9×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
7×	`sqrt-prod_binary64_2140` `pow1_binary64_2185` `div-exp_binary64_2175`
6×	`sqrt-div_binary64_2141`
5×	`unpow-prod-down_binary64_2203` `div-inv_binary64_2121`
4×	`distribute-lft-out--_binary64_2076` `associate--l+_binary64_2061` `frac-sub_binary64_2133`
3×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `pow-unpow_binary64_2201` `associate-/l*_binary64_2069` `diff-log_binary64_2216` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`sub-neg_binary64_2117` `1-exp_binary64_2168` `rec-exp_binary64_2174`
1×	`clear-num_binary64_2123` `associate-/r/_binary64_2070` `pow-pow_binary64_2196` `sqrt-pow1_binary64_2142` `associate--l-_binary64_2062` `pow-exp_binary64_2192` `rem-sqrt-square_binary64_2137` `sqr-pow_binary64_2096` `pow1/2_binary64_2204` `unpow2_binary64_2189` `pow-flip_binary64_2198` `pow-to-exp_binary64_2193` `inv-pow_binary64_2209` `frac-2neg_binary64_2135`

Counts

4 → 142

Calls

4 calls:

16.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
6.0ms	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B))))
5.0ms	(pow.f64 (-.f64 A C) 2)

series243.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B))))
73.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
71.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
14.0ms	(pow.f64 (-.f64 A C) 2)

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4989	5604
1	4989	5604

prune229.0ms (3.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	154	12	166

Error

20.0b

Counts

166 → 12

Compiler

Compiled 5315 to 2758 computations (48.1% saved)

regimes561.0ms (8.8%)

Accuracy

Total 9.2b remaining (32.3%)

Threshold costs 0b (0%)

Compiler

Compiled 6286 to 4496 computations (28.5% saved)

bsearch255.0ms (4%)

Steps

Iters	Range		Point
7	2.6919320679959254e+150	6.095502281268703e+152	4.617632627264863e+151
9	3.745338881164429e-198	8.056420300479344e-193	2.405665199649213e-196
8	4.6398571787184005e-302	1.6485377435190205e-298	5.241670643923542e-301
10	-1.7642014608293367e-166	-5.512545412013262e-177	-9.829888247783205e-172
8	-4.550467215923454e+34	-1.6749320969193452e+31	-3.2780186347505555e+32

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	172
1	91	172

end0.0ms (0%)

sample3.2s (49.6%)

Algorithm

1×

intervals

Results

690.0ms	857×	body	4096	valid
587.0ms	5374×	body	128	valid
557.0ms	925×	body	2048	valid
201.0ms	449×	body	1024	valid
87.0ms	261×	body	512	valid
34.0ms	134×	body	256	valid

Compiler

Compiled 1008 to 708 computations (29.8% saved)

Details

analyze400.0ms (6.3%)

sample76.0ms (1.2%)

simplify74.0ms (1.2%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite43.0ms (0.7%)

series238.0ms (3.7%)

simplify71.0ms (1.1%)

prune165.0ms (2.6%)

localize9.0ms (0.1%)

rewrite43.0ms (0.7%)

series135.0ms (2.1%)

simplify75.0ms (1.2%)

prune109.0ms (1.7%)

localize10.0ms (0.2%)

rewrite36.0ms (0.6%)

series95.0ms (1.5%)

simplify70.0ms (1.1%)

prune94.0ms (1.5%)

localize19.0ms (0.3%)

rewrite51.0ms (0.8%)

series243.0ms (3.8%)

simplify97.0ms (1.5%)

prune229.0ms (3.6%)

regimes561.0ms (8.8%)

bsearch255.0ms (4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.2s (49.6%)

Profiling