Details

analyze229.0ms (3.2%)

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)

sample75.0ms (1%)

Algorithm

1×

intervals

Results

26.0ms	35×	body	4096	valid
16.0ms	170×	body	128	valid
12.0ms	23×	body	2048	valid
9.0ms	21×	body	1024	valid
1.0ms	4×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify164.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

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

Merged error: 29.9b

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	(pow.f64 (-.f64 A C) 2)
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)
0.5b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
35.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite48.0ms (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:

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	(/.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 (3.3%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
77.0ms	(-.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)))
15.0ms	(pow.f64 (-.f64 A C) 2)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4965	2955
1	4965	2955

prune162.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	96	9	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	9	106

Merged error: 17.6b

Counts

106 → 9

Compiler

Compiled 3365 to 1723 computations (48.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B))))) B)) PI.f64))
0.1b	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))) B)) PI.f64)
1.6b	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
35.0b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

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`
3×	`associate-/l_binary64_2069` `sqrt-prod_binary64_2140` `associate-/r_binary64_2068` `associate-l_binary64_2065`
2×	`cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `sqrt-div_binary64_2141` `prod-exp_binary64_2173` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `associate-r/_binary64_2066` `frac-2neg_binary64_2135`

Counts

4 → 86

Calls

4 calls:

10.0ms	(+.f64 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)))
7.0ms	(.f64 180 (/.f64 (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 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))) B)) PI.f64)

series340.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(.f64 180 (/.f64 (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 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))) B)) PI.f64)
78.0ms	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
66.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5048	3260

prune143.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 17.6b

Counts

107 → 10

Compiler

Compiled 3336 to 1853 computations (44.5% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 A C))
0.7b	(pow.f64 (cbrt.f64 (-.f64 A C)) 4)
14.0b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (cbrt.f64 (-.f64 A C)) 2)) (.f64 B B))))
35.0b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (cbrt.f64 (-.f64 A C)) 2)) (.f64 B B)))

rewrite59.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
12×	`add-cube-cbrt_binary64_2159`
10×	`cbrt-prod_binary64_2155`
9×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163`
8×	`unpow-prod-down_binary64_2203`
7×	`sqrt-prod_binary64_2140`
6×	`sqrt-div_binary64_2141` `pow1_binary64_2185`
5×	`distribute-lft-out--_binary64_2076` `add-exp-log_binary64_2162`
4×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `associate--l+_binary64_2061` `frac-sub_binary64_2133` `add-cbrt-cube_binary64_2160`
3×	`pow-unpow_binary64_2201` `diff-log_binary64_2216` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`cbrt-div_binary64_2156` `pow-pow_binary64_2196` `pow1/3_binary64_2206` `sub-neg_binary64_2117`
1×	`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` `pow-to-exp_binary64_2193`

Counts

4 → 84

Calls

4 calls:

22.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (cbrt.f64 (-.f64 A C)) 2)) (.f64 B B))))
14.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (cbrt.f64 (-.f64 A C)) 2)) (.f64 B B)))
9.0ms	(pow.f64 (cbrt.f64 (-.f64 A C)) 4)
3.0ms	(cbrt.f64 (-.f64 A C))

series532.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

274.0ms	(pow.f64 (cbrt.f64 (-.f64 A C)) 4)
111.0ms	(cbrt.f64 (-.f64 A C))
78.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (cbrt.f64 (-.f64 A C)) 2)) (.f64 B B))))
69.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (cbrt.f64 (-.f64 A C)) 2)) (.f64 B B)))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4961	2146
1	4961	2146

prune147.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	95	11	106

Merged error: 17.5b

Counts

106 → 11

Compiler

Compiled 3442 to 1744 computations (49.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 A C))
0.7b	(pow.f64 (cbrt.f64 (-.f64 A C)) 4)
16.1b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 A C))) 2) (cbrt.f64 (cbrt.f64 (-.f64 A C)))) 2)) (*.f64 B B))))
35.0b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 A C))) 2) (cbrt.f64 (cbrt.f64 (-.f64 A C)))) 2)) (*.f64 B B)))

rewrite58.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
12×	`add-cube-cbrt_binary64_2159`
10×	`cbrt-prod_binary64_2155`
9×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163`
8×	`unpow-prod-down_binary64_2203`
7×	`sqrt-prod_binary64_2140`
6×	`sqrt-div_binary64_2141` `pow1_binary64_2185`
5×	`distribute-lft-out--_binary64_2076` `add-exp-log_binary64_2162`
4×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `associate--l+_binary64_2061` `frac-sub_binary64_2133` `add-cbrt-cube_binary64_2160`
3×	`pow-unpow_binary64_2201` `diff-log_binary64_2216` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`cbrt-div_binary64_2156` `pow-pow_binary64_2196` `pow1/3_binary64_2206` `sub-neg_binary64_2117`
1×	`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` `pow-to-exp_binary64_2193`

Counts

4 → 84

Calls

4 calls:

21.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 A C))) 2) (cbrt.f64 (cbrt.f64 (-.f64 A C)))) 2)) (*.f64 B B))))
13.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 A C))) 2) (cbrt.f64 (cbrt.f64 (-.f64 A C)))) 2)) (*.f64 B B)))
6.0ms	(pow.f64 (cbrt.f64 (-.f64 A C)) 4)
4.0ms	(cbrt.f64 (-.f64 A C))

series536.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(pow.f64 (cbrt.f64 (-.f64 A C)) 4)
119.0ms	(cbrt.f64 (-.f64 A C))
83.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 A C))) 2) (cbrt.f64 (cbrt.f64 (-.f64 A C)))) 2)) (*.f64 B B))))
68.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (cbrt.f64 (-.f64 A C)) 4) (pow.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 A C))) 2) (cbrt.f64 (cbrt.f64 (-.f64 A C)))) 2)) (*.f64 B B)))

simplify98.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4878	2130
1	4878	2130

prune141.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	96	11	107

Merged error: 17.5b

Counts

107 → 11

Compiler

Compiled 3608 to 1700 computations (52.9% saved)

regimes791.0ms (10.9%)

Compiler: Compiled 7448 to 5385 computations (27.7% saved)

bsearch3.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	87
1	67	87

end0.0ms (0%)

sample3.2s (43.6%)

Algorithm

1×

intervals

Results

699.0ms	920×	body	4096	valid
555.0ms	5445×	body	128	valid
480.0ms	827×	body	2048	valid
205.0ms	466×	body	1024	valid
74.0ms	228×	body	512	valid
23.0ms	114×	body	256	valid

Compiler

Compiled 1120 to 810 computations (27.7% saved)

Details

analyze229.0ms (3.2%)

sample75.0ms (1%)

simplify164.0ms (2.3%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite48.0ms (0.7%)

series238.0ms (3.3%)

simplify71.0ms (1%)

prune162.0ms (2.2%)

localize16.0ms (0.2%)

rewrite37.0ms (0.5%)

series340.0ms (4.7%)

simplify60.0ms (0.8%)

prune143.0ms (2%)

localize19.0ms (0.3%)

rewrite59.0ms (0.8%)

series532.0ms (7.3%)

simplify74.0ms (1%)

prune147.0ms (2%)

localize24.0ms (0.3%)

rewrite58.0ms (0.8%)

series536.0ms (7.4%)

simplify98.0ms (1.3%)

prune141.0ms (1.9%)

regimes791.0ms (10.9%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (43.6%)

Profiling