Details

analyze230.0ms (3.6%)

Algorithm

1×

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)

sample71.0ms (1.1%)

Algorithm

1×

intervals

Results

21.0ms	185×	body	128	valid
16.0ms	29×	body	2048	valid
14.0ms	18×	body	4096	valid
7.0ms	15×	body	1024	valid
2.0ms	7×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify160.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4970	33
1	4970	33

prune5.0ms (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

27.2b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 A C) 2)
0.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) PI.f64))
0.1b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
33.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2146`
25×	`*-un-lft-identity_binary64_2124`
18×	`add-cube-cbrt_binary64_2159`
13×	`associate-r_binary64_2064`
10×	`add-exp-log_binary64_2162` `times-frac_binary64_2130`
9×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
8×	`pow1_binary64_2185`
7×	`sqrt-prod_binary64_2140`
6×	`sqrt-div_binary64_2141`
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` `diff-log_binary64_2216` `associate-l_binary64_2065` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`unswap-sqr_binary64_2092` `prod-exp_binary64_2173` `sub-neg_binary64_2117` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `pow-pow_binary64_2196` `sqrt-pow1_binary64_2142` `associate--l-_binary64_2062` `pow-exp_binary64_2192` `-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `sqr-pow_binary64_2096` `pow1/2_binary64_2204` `unpow2_binary64_2189` `pow-to-exp_binary64_2193` `associate-r/_binary64_2066` `div-inv_binary64_2121` `div-exp_binary64_2175`

Counts

4 → 98

Calls

4 calls:

16.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
10.0ms	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) PI.f64))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
6.0ms	(pow.f64 (-.f64 A C) 2)

series264.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) PI.f64))
73.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
67.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
14.0ms	(pow.f64 (-.f64 A C) 2)

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4968	2986
1	4968	2986

prune161.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	8	111

Error

18.4b

Counts

111 → 8

Compiler

Compiled 3467 to 1775 computations (48.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 A C) 2)
0.0b	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B))) PI.f64)
0.1b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
33.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
12×	`add-cube-cbrt_binary64_2159`
10×	`add-exp-log_binary64_2162`
9×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
7×	`sqrt-prod_binary64_2140`
6×	`sqrt-div_binary64_2141` `pow1_binary64_2185`
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-/r*_binary64_2068` `diff-log_binary64_2216` `flip3-+_binary64_2127` `flip-+_binary64_2098` `times-frac_binary64_2130`
2×	`cbrt-undiv_binary64_2158` `sub-neg_binary64_2117` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `pow-pow_binary64_2196` `sqrt-pow1_binary64_2142` `associate--l-_binary64_2062` `pow-exp_binary64_2192` `associate-/l*_binary64_2069` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `sqr-pow_binary64_2096` `pow1/2_binary64_2204` `unpow2_binary64_2189` `pow-to-exp_binary64_2193` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 87

Calls

4 calls:

20.0ms	(-.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)))
6.0ms	(/.f64 (.f64 180 (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)

series261.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B))) PI.f64)
74.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
62.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
13.0ms	(pow.f64 (-.f64 A C) 2)

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5066	2523

prune124.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Error

18.4b

Counts

107 → 9

Compiler

Compiled 2938 to 1521 computations (48.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 A C) 2)
0.0b	(/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)))
0.1b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
33.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite42.0ms (0.6%)

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:

17.0ms	(-.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	(pow.f64 (-.f64 A C) 2)
3.0ms	(/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)))

series265.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)))
70.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
64.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
14.0ms	(pow.f64 (-.f64 A C) 2)

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4968	2979
1	4968	2979

prune137.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Error

18.4b

Counts

114 → 8

Compiler

Compiled 3297 to 1683 computations (49% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B)))
0.1b	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B))) PI.f64)
1.0b	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
33.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2146`
11×	`add-exp-log_binary64_2162` `*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`
9×	`add-cube-cbrt_binary64_2159`
7×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163`
3×	`sqrt-prod_binary64_2140` `associate-/r_binary64_2068` `associate-l_binary64_2065` `associate-r*_binary64_2064` `times-frac_binary64_2130`
2×	`cbrt-undiv_binary64_2158` `sqrt-div_binary64_2141` `prod-exp_binary64_2173` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `unswap-sqr_binary64_2092` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `associate-/l_binary64_2069` `-commutative_binary64_2055` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 66

Calls

4 calls:

10.0ms	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
5.0ms	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B))) PI.f64)
4.0ms	(.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B)))

series326.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(/.f64 (.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B))) PI.f64)
79.0ms	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
63.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
63.0ms	(.f64 180 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B)))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5097	2197

prune94.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	74	12	86

Error

18.4b

Counts

86 → 12

Compiler

Compiled 2136 to 1176 computations (44.9% saved)

regimes608.0ms (9.5%)

Accuracy

Total 5.4b remaining (22.1%)

Threshold costs 0b (0%)

Compiler

Compiled 7553 to 5504 computations (27.1% saved)

bsearch47.0ms (0.7%)

Steps

Iters	Range		Point
10	1.704313321832674e+140	1.9288246449212064e+154	1.314127621982934e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	58
1	63	58

end0.0ms (0%)

sample3.2s (49.3%)

Algorithm

1×

intervals

Results

644.0ms	835×	body	4096	valid
550.0ms	5410×	body	128	valid
511.0ms	869×	body	2048	valid
225.0ms	508×	body	1024	valid
84.0ms	253×	body	512	valid
29.0ms	125×	body	256	valid

Compiler

Compiled 1116 to 814 computations (27.1% saved)

Details

analyze230.0ms (3.6%)

sample71.0ms (1.1%)

simplify160.0ms (2.5%)

prune5.0ms (0.1%)

localize19.0ms (0.3%)

rewrite50.0ms (0.8%)

series264.0ms (4.1%)

simplify78.0ms (1.2%)

prune161.0ms (2.5%)

localize15.0ms (0.2%)

rewrite47.0ms (0.7%)

series261.0ms (4.1%)

simplify51.0ms (0.8%)

prune124.0ms (1.9%)

localize15.0ms (0.2%)

rewrite42.0ms (0.6%)

series265.0ms (4.1%)

simplify70.0ms (1.1%)

prune137.0ms (2.1%)

localize15.0ms (0.2%)

rewrite33.0ms (0.5%)

series326.0ms (5.1%)

simplify58.0ms (0.9%)

prune94.0ms (1.5%)

regimes608.0ms (9.5%)

bsearch47.0ms (0.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (49.3%)

Profiling