Details

analyze240.0ms (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)

sample77.0ms (1%)

Algorithm

1×

intervals

Results

25.0ms	27×	body	4096	valid
18.0ms	182×	body	128	valid
14.0ms	23×	body	2048	valid
6.0ms	13×	body	1024	valid
3.0ms	8×	body	512	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify164.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

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: 30.7b

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 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) PI.f64))
0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
1.2b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite54.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_2146`
29×	`*-un-lft-identity_binary64_2124`
24×	`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`
9×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163`
7×	`sqrt-prod_binary64_2140` `pow1_binary64_2185`
6×	`sqrt-div_binary64_2141`
4×	`associate--l+_binary64_2061` `frac-sub_binary64_2133`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `diff-log_binary64_2216` `associate-l_binary64_2065` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`difference-of-squares_binary64_2093` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `prod-exp_binary64_2173` `sub-neg_binary64_2117` `div-inv_binary64_2121` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `associate--l-_binary64_2062` `-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `associate-r/_binary64_2066` `frac-2neg_binary64_2135`

Counts

4 → 105

Calls

4 calls:

20.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
9.0ms	(.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	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)

series344.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(.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))
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)
78.0ms	(-.f64 (-.f64 C 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)))

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5083	4058

prune183.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 18.5b

Counts

118 → 11

Compiler

Compiled 4033 to 2081 computations (48.4% saved)

localize15.0ms (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)) 180)
0.0b	(/.f64 (.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) 180) PI.f64)
1.2b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_2146`
17×	`*-un-lft-identity_binary64_2124`
12×	`add-cube-cbrt_binary64_2159`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`cancel-sign-sub-inv_binary64_2090` `add-log-exp_binary64_2163`
7×	`sqrt-prod_binary64_2140` `pow1_binary64_2185`
6×	`sqrt-div_binary64_2141`
4×	`associate--l+_binary64_2061` `frac-sub_binary64_2133`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `associate-/r_binary64_2068` `diff-log_binary64_2216` `associate-l_binary64_2065` `flip3-+_binary64_2127` `associate-r*_binary64_2064` `flip-+_binary64_2098` `times-frac_binary64_2130`
2×	`difference-of-squares_binary64_2093` `cbrt-undiv_binary64_2158` `prod-exp_binary64_2173` `sub-neg_binary64_2117` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `unswap-sqr_binary64_2092` `sqrt-pow1_binary64_2142` `associate--l-_binary64_2062` `associate-/l_binary64_2069` `-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 85

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

series332.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(/.f64 (.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) 180) PI.f64)
76.0ms	(-.f64 (-.f64 C 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)))
67.0ms	(.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) B)) 180)

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4947	2970
1	4947	2970

prune131.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	98	10	108

Merged error: 18.5b

Counts

108 → 10

Compiler

Compiled 3077 to 1624 computations (47.2% saved)

localize15.0ms (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)
0.4b	(-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
1.5b	(+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
35.9b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite43.0ms (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)))))
9.0ms	(+.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)))
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)

series292.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

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)
74.0ms	(-.f64 C (+.f64 A (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
73.0ms	(+.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)))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4998	2493
1	4998	2493

prune127.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 18.4b

Counts

96 → 11

Compiler

Compiled 2817 to 1577 computations (44% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
10.0b	(-.f64 (-.f64 C A) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))
37.1b	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
37.1b	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2146`
11×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`cbrt-div_binary64_2156` `cbrt-prod_binary64_2155`
9×	`add-log-exp_binary64_2163` `associate-r_binary64_2064`
8×	`sqrt-prod_binary64_2140`
6×	`sqrt-div_binary64_2141` `pow1_binary64_2185` `associate-*r/_binary64_2066` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
4×	`cancel-sign-sub-inv_binary64_2090` `associate--l+_binary64_2061` `frac-sub_binary64_2133`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `unswap-sqr_binary64_2092` `diff-log_binary64_2216` `associate-l_binary64_2065`
2×	`pow1/3_binary64_2206` `sub-neg_binary64_2117`
1×	`pow-prod-down_binary64_2195` `associate--l-_binary64_2062` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`

Counts

4 → 76

Calls

4 calls:

14.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
9.0ms	(-.f64 (-.f64 C A) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

series761.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

306.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))))
154.0ms	(-.f64 (-.f64 C A) (.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))))
152.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
149.0ms	(cbrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

simplify106.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5468	3524

prune169.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	88	11	99

Merged error: 18.4b

Counts

99 → 11

Compiler

Compiled 4010 to 2119 computations (47.2% saved)

regimes673.0ms (8.9%)

Compiler: Compiled 8064 to 5693 computations (29.4% saved)

bsearch97.0ms (1.3%)

Steps

Iters	Range		Point
5	1.0422969658807638e-273	3.3832004906079596e-273	1.1652315596202954e-273
6	-3.0810856141609166e-277	-2.95952533030439e-278	-3.032600957837696e-278

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	72	77
1	72	77

end0.0ms (0%)

sample3.4s (44.4%)

Algorithm

1×

intervals

Results

723.0ms	886×	body	4096	valid
610.0ms	5462×	body	128	valid
507.0ms	825×	body	2048	valid
224.0ms	479×	body	1024	valid
78.0ms	236×	body	512	valid
24.0ms	112×	body	256	valid

Compiler

Compiled 1201 to 850 computations (29.2% saved)

Details

analyze240.0ms (3.2%)

sample77.0ms (1%)

simplify164.0ms (2.2%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

rewrite54.0ms (0.7%)

series344.0ms (4.5%)

simplify81.0ms (1.1%)

prune183.0ms (2.4%)

localize15.0ms (0.2%)

rewrite45.0ms (0.6%)

series332.0ms (4.4%)

simplify90.0ms (1.2%)

prune131.0ms (1.7%)

localize15.0ms (0.2%)

rewrite43.0ms (0.6%)

series292.0ms (3.9%)

simplify79.0ms (1%)

prune127.0ms (1.7%)

localize19.0ms (0.3%)

rewrite51.0ms (0.7%)

series761.0ms (10.1%)

simplify106.0ms (1.4%)

prune169.0ms (2.2%)

regimes673.0ms (8.9%)

bsearch97.0ms (1.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (44.4%)

Profiling