Details

analyze451.0ms (8.9%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
6.0ms	27×	body	2048	valid
5.0ms	24×	body	1024	valid
5.0ms	15×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	18×	body	128	invalid
1.0ms	17×	body	128	nan
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify423.0ms (8.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (260.0ms)

Iter	Nodes	Cost
0	1707	24
1	1707	24

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: 32.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
21.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite41.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1783`
13×	`*-un-lft-identity_binary64_1762`
9×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
8×	`add-log-exp_binary64_1798`
7×	`add-cube-cbrt_binary64_1794`
6×	`times-frac_binary64_1768` `difference-of-squares_binary64_1731` `sqrt-prod_binary64_1777` `associate-/l*_binary64_1709`
5×	`pow1_binary64_1820`
4×	`flip3--_binary64_1766` `flip--_binary64_1737`
3×	`distribute-lft-out--_binary64_1716`
2×	`diff-log_binary64_1851` `associate-/l/_binary64_1711` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `sub-neg_binary64_1755` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `div-sub_binary64_1767` `prod-exp_binary64_1808` `clear-num_binary64_1761` `associate-/r*_binary64_1708` `div-inv_binary64_1759` `cbrt-unprod_binary64_1792` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`

Counts

4 → 70

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series545.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
137.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	6789	1967

prune126.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 4.1b

Counts

83 → 10

Compiler

Compiled 2099 to 1272 computations (39.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
21.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1783`
10×	`pow1_binary64_1820`
9×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
8×	`add-log-exp_binary64_1798` `*-un-lft-identity_binary64_1762`
6×	`add-cube-cbrt_binary64_1794`
4×	`sqrt-prod_binary64_1777`
3×	`flip3--_binary64_1766` `pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `cbrt-unprod_binary64_1792` `flip--_binary64_1737` `associate-r_binary64_1704`
2×	`diff-log_binary64_1851` `difference-of-squares_binary64_1731` `sub-neg_binary64_1755` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `distribute-lft-out--_binary64_1716` `sqrt-pow1_binary64_1779` `-commutative_binary64_1695` `associate-l*_binary64_1705` `pow1/2_binary64_1839`

Counts

4 → 58

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(.f64 (.f64 3 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series345.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
30.0ms	(.f64 (.f64 3 a) c)

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4939	1210
1	4939	1210

prune77.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	69	11	80

Merged error: 4.1b

Counts

80 → 11

Compiler

Compiled 1689 to 1035 computations (38.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
21.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1783`
10×	`pow1_binary64_1820`
9×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
8×	`add-log-exp_binary64_1798` `*-un-lft-identity_binary64_1762`
6×	`add-cube-cbrt_binary64_1794`
4×	`sqrt-prod_binary64_1777`
3×	`flip3--_binary64_1766` `pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `cbrt-unprod_binary64_1792` `flip--_binary64_1737` `associate-r_binary64_1704`
2×	`diff-log_binary64_1851` `difference-of-squares_binary64_1731` `sub-neg_binary64_1755` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `distribute-lft-out--_binary64_1716` `sqrt-pow1_binary64_1779` `-commutative_binary64_1695` `associate-l*_binary64_1705` `pow1/2_binary64_1839`

Counts

4 → 58

Calls

4 calls:

12.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(.f64 (.f64 3 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series323.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
27.0ms	(.f64 (.f64 3 a) c)

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4939	1210
1	4939	1210

prune81.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	70	11	81

Merged error: 4.1b

Counts

81 → 11

Compiler

Compiled 1811 to 1160 computations (35.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
0.3b	(/.f64 1/3 a)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
21.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1783`
15×	`*-un-lft-identity_binary64_1762`
13×	`add-cube-cbrt_binary64_1794`
9×	`times-frac_binary64_1768`
8×	`add-log-exp_binary64_1798`
6×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
5×	`pow1_binary64_1820`
4×	`sqrt-prod_binary64_1777`
3×	`flip3--_binary64_1766` `associate-/r_binary64_1708` `flip--_binary64_1737` `associate-/l_binary64_1709`
2×	`diff-log_binary64_1851` `difference-of-squares_binary64_1731` `sub-neg_binary64_1755` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `clear-num_binary64_1761` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `distribute-lft-out--_binary64_1716` `div-exp_binary64_1810` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`

Counts

4 → 67

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
3.0ms	(/.f64 1/3 a)

series340.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
20.0ms	(/.f64 1/3 a)

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4899	1294
1	4899	1294

prune80.0ms (1.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	79	11	90

Merged error: 4.1b

Counts

90 → 11

Compiler

Compiled 1721 to 1023 computations (40.6% saved)

regimes302.0ms (6%)

Compiler: Compiled 848 to 693 computations (18.3% saved)

bsearch88.0ms (1.7%)

Steps

Iters	Range		Point
8	3.764613681933625e+19	1.1673516847644042e+22	7.906987275663061e+21
6	4.491341529797546e-86	3.134263723070825e-85	4.5622646438935884e-86
9	-1.3188993218331007e+98	-4.0076058830102145e+92	-2.264426810687682e+97

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	121	98
1	121	98

end0.0ms (0%)

sample1.4s (27.6%)

Algorithm

1×

intervals

Results

270.0ms	5205×	body	128	valid
268.0ms	1089×	body	2048	valid
155.0ms	772×	body	1024	valid
122.0ms	406×	body	4096	valid
54.0ms	365×	body	512	valid
38.0ms	694×	body	128	nan
20.0ms	395×	body	128	invalid
16.0ms	163×	body	256	valid

Compiler

Compiled 283 to 219 computations (22.6% saved)

Details

analyze451.0ms (8.9%)

sample38.0ms (0.7%)

simplify423.0ms (8.3%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite41.0ms (0.8%)

series545.0ms (10.8%)

simplify77.0ms (1.5%)

prune126.0ms (2.5%)

localize11.0ms (0.2%)

rewrite30.0ms (0.6%)

series345.0ms (6.8%)

simplify56.0ms (1.1%)

prune77.0ms (1.5%)

localize12.0ms (0.2%)

rewrite33.0ms (0.7%)

series323.0ms (6.4%)

simplify55.0ms (1.1%)

prune81.0ms (1.6%)

localize11.0ms (0.2%)

rewrite27.0ms (0.5%)

series340.0ms (6.7%)

simplify79.0ms (1.6%)

prune80.0ms (1.6%)

regimes302.0ms (6%)

bsearch88.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (27.6%)

Profiling