Details

analyze238.0ms (3.3%)

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)

sample86.0ms (1.2%)

Algorithm

1×

intervals

Results

33.0ms	38×	body	4096	valid
16.0ms	161×	body	128	valid
14.0ms	25×	body	2048	valid
8.0ms	19×	body	1024	valid
3.0ms	9×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify154.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

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: 31.9b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.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))))
34.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite69.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_2124`
45×	`add-sqr-sqrt_binary64_2146`
22×	`add-cube-cbrt_binary64_2159`
21×	`times-frac_binary64_2130`
16×	`distribute-lft-out--_binary64_2076`
11×	`difference-of-squares_binary64_2093` `sqrt-prod_binary64_2140`
10×	`sqrt-div_binary64_2141`
9×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163`
8×	`frac-sub_binary64_2133`
7×	`associate-/l*_binary64_2069` `add-exp-log_binary64_2162`
6×	`flip--_binary64_2099` `flip3--_binary64_2128` `pow1_binary64_2185` `associate-/l/_binary64_2071` `add-cbrt-cube_binary64_2160`
5×	`unpow-prod-down_binary64_2203` `flip3-+_binary64_2127` `flip-+_binary64_2098`
4×	`associate--l+_binary64_2061`
3×	`pow-unpow_binary64_2201` `associate-/r*_binary64_2068` `diff-log_binary64_2216`
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-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 116

Calls

4 calls:

22.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
20.0ms	(/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
5.0ms	(pow.f64 (-.f64 A C) 2)

series247.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)
76.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
60.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
14.0ms	(pow.f64 (-.f64 A C) 2)

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4954	3561
1	4954	3561

prune201.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Merged error: 12.8b

Counts

129 → 9

Compiler

Compiled 4222 to 2093 computations (50.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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)
0.5b	(-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
0.7b	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
34.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_2124`
17×	`add-sqr-sqrt_binary64_2146`
14×	`add-cube-cbrt_binary64_2159`
11×	`add-log-exp_binary64_2163`
9×	`times-frac_binary64_2130`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185`
4×	`cancel-sign-sub-inv_binary64_2090`
3×	`associate-/l_binary64_2069` `sqrt-prod_binary64_2140` `distribute-lft-out_binary64_2075` `associate-/r_binary64_2068`
2×	`sum-log_binary64_2215` `distribute-lft-out--_binary64_2076` `sqrt-div_binary64_2141` `diff-log_binary64_2216` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `clear-num_binary64_2123` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `associate--r+_binary64_2060` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 74

Calls

4 calls:

13.0ms	(-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
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)))
3.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))) B)) PI.f64)

series293.0ms (4%)

Counts

4 → 12

Calls

4 calls:

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

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4998	2493
1	4998	2493

prune127.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 12.8b

Counts

95 → 12

Compiler

Compiled 2827 to 1594 computations (43.6% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
34.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2146`
9×	`sqrt-prod_binary64_2140` `*-un-lft-identity_binary64_2124`
7×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
6×	`sqrt-div_binary64_2141` `add-log-exp_binary64_2163`
4×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`
1×	`sum-log_binary64_2215` `distribute-lft-out_binary64_2075` `+-commutative_binary64_2054`

Counts

4 → 57

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)))
8.0ms	(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)))

series282.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
69.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
68.0ms	(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)))

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5122	1234

prune179.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	68	13	81

Merged error: 12.8b

Counts

81 → 13

Compiler

Compiled 4483 to 2440 computations (45.6% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

34.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
34.2b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_2140` `add-sqr-sqrt_binary64_2146`
8×	`sqrt-div_binary64_2141` `pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
4×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `add-log-exp_binary64_2163` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`

Counts

4 → 60

Calls

4 calls:

8.0ms	(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)))
8.0ms	(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)))

series279.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(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)))
70.0ms	(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)))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5058	1232

prune207.0ms (2.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	72	13	85

Merged error: 12.8b

Counts

85 → 13

Compiler

Compiled 5180 to 2747 computations (47% saved)

regimes810.0ms (11.2%)

Compiler: Compiled 8918 to 6365 computations (28.6% saved)

bsearch74.0ms (1%)

Steps

Iters	Range		Point
10	2.6839019382855743e+40	1.9515269284962997e+55	4.396494985570493e+51

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	67	69
1	67	69

end0.0ms (0%)

sample3.5s (48.3%)

Algorithm

1×

intervals

Results

689.0ms	881×	body	4096	valid
551.0ms	5411×	body	128	valid
479.0ms	836×	body	2048	valid
215.0ms	495×	body	1024	valid
83.0ms	244×	body	512	valid
27.0ms	133×	body	256	valid

Compiler

Compiled 1318 to 945 computations (28.3% saved)

Details

analyze238.0ms (3.3%)

sample86.0ms (1.2%)

simplify154.0ms (2.1%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

rewrite69.0ms (1%)

series247.0ms (3.4%)

simplify75.0ms (1%)

prune201.0ms (2.8%)

localize18.0ms (0.2%)

rewrite41.0ms (0.6%)

series293.0ms (4%)

simplify75.0ms (1%)

prune127.0ms (1.7%)

localize27.0ms (0.4%)

rewrite43.0ms (0.6%)

series282.0ms (3.9%)

simplify57.0ms (0.8%)

prune179.0ms (2.5%)

localize30.0ms (0.4%)

rewrite43.0ms (0.6%)

series279.0ms (3.8%)

simplify76.0ms (1%)

prune207.0ms (2.8%)

regimes810.0ms (11.2%)

bsearch74.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (48.3%)

Profiling