Details

analyze476.0ms (7.1%)

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)

sample43.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	44×	body	2048	valid
9.0ms	162×	body	128	valid
4.0ms	21×	body	1024	valid
3.0ms	10×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	23×	body	128	nan
1.0ms	17×	body	128	invalid
1.0ms	7×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify417.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (256.0ms)

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: 36.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.1%)

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))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite42.0ms (0.6%)

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:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
10.0ms	(-.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))

series521.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6789	1967

prune129.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 5.5b

Counts

83 → 9

Compiler

Compiled 2070 to 1250 computations (39.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.6b	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
9.3b	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
22×	`times-frac_binary64_1768`
19×	`*-un-lft-identity_binary64_1762`
17×	`cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
13×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792`
12×	`add-sqr-sqrt_binary64_1783`
11×	`associate-/l*_binary64_1709` `add-cube-cbrt_binary64_1794`
6×	`associate-/r/_binary64_1710` `add-log-exp_binary64_1798`
5×	`associate-/r*_binary64_1708` `pow1_binary64_1820`
4×	`div-inv_binary64_1759` `distribute-lft-out_binary64_1715`
3×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `sqrt-prod_binary64_1777`
2×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `clear-num_binary64_1761` `flip--_binary64_1737` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `diff-log_binary64_1851` `associate-/l/_binary64_1711` `sqrt-pow1_binary64_1779` `sub-neg_binary64_1755` `pow1/2_binary64_1839`

Counts

4 → 101

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
13.0ms	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series865.0ms (12.9%)

Counts

4 → 12

Calls

4 calls:

388.0ms	(/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
286.0ms	(/.f64 (/.f64 (.f64 a (.f64 -3 c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4960	3153
1	4960	3153

prune150.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	113	9	122

Merged error: 5.5b

Counts

122 → 9

Compiler

Compiled 3303 to 2041 computations (38.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.6b	(.f64 a (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
5.6b	(/.f64 (.f64 a (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
16×	`prod-exp_binary64_1808` `cbrt-unprod_binary64_1792`
14×	`cbrt-undiv_binary64_1793` `div-exp_binary64_1810`
11×	`add-sqr-sqrt_binary64_1783`
10×	`-un-lft-identity_binary64_1762` `associate-r*_binary64_1704`
8×	`add-cube-cbrt_binary64_1794`
7×	`pow1_binary64_1820`
6×	`add-log-exp_binary64_1798`
5×	`times-frac_binary64_1768`
3×	`sqrt-prod_binary64_1777` `associate-l_binary64_1705`
2×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `div-inv_binary64_1759` `associate-*r/_binary64_1706` `flip--_binary64_1737` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `diff-log_binary64_1851` `pow-prod-down_binary64_1830` `associate-/l/_binary64_1711` `flip3-+_binary64_1765` `clear-num_binary64_1761` `associate-/r_binary64_1708` `flip-+_binary64_1736` `unswap-sqr_binary64_1730` `sqrt-pow1_binary64_1779` `sub-neg_binary64_1755` `-commutative_binary64_1695` `distribute-lft-out_binary64_1715` `associate-/l*_binary64_1709` `pow1/2_binary64_1839`

Counts

4 → 86

Calls

4 calls:

19.0ms	(.f64 a (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
16.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series846.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

391.0ms	(.f64 a (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
282.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
109.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4989	2384
1	4989	2384

prune122.0ms (1.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	98	9	107

Merged error: 5.5b

Counts

107 → 9

Compiler

Compiled 2706 to 1686 computations (37.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) 3) a)
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 147

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) 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)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series529.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) 3) a)
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
68.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4975	5785
1	4975	5785

prune211.0ms (3.1%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	2	3	5
Picked	0	1	1
Done	0	3	3
Total	159	9	168

Merged error: 5.5b

Counts

168 → 9

Compiler

Compiled 4663 to 2738 computations (41.3% saved)

regimes283.0ms (4.2%)

Compiler: Compiled 804 to 649 computations (19.3% saved)

bsearch117.0ms (1.7%)

Steps

Iters	Range	Point
11	1.1788099211829084e-33	4.825546432485297e-13	8.627093492358085e-16
9	1.2540755325014634e-301	2.359896871153042e-296	3.768751181218888e-301
9	-3.0558196015139103e+154	-1.140147330439728e+149	-1.8784026798326835e+149

Iters

Range

Point

1.1788099211829084e-33

4.825546432485297e-13

8.627093492358085e-16

1.2540755325014634e-301

2.359896871153042e-296

3.768751181218888e-301

-3.0558196015139103e+154

-1.140147330439728e+149

-1.8784026798326835e+149

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	121	98
1	121	98

end0.0ms (0%)

sample1.4s (21.4%)

Algorithm

1×

intervals

Results

294.0ms	1128×	body	2048	valid
287.0ms	5188×	body	128	valid
147.0ms	719×	body	1024	valid
127.0ms	405×	body	4096	valid
55.0ms	369×	body	512	valid
36.0ms	697×	body	128	nan
23.0ms	388×	body	128	invalid
19.0ms	191×	body	256	valid

Compiler

Compiled 262 to 201 computations (23.3% saved)

Details

analyze476.0ms (7.1%)

sample43.0ms (0.6%)

simplify417.0ms (6.2%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite42.0ms (0.6%)

series521.0ms (7.8%)

simplify77.0ms (1.1%)

prune129.0ms (1.9%)

localize14.0ms (0.2%)

rewrite51.0ms (0.8%)

series865.0ms (12.9%)

simplify75.0ms (1.1%)

prune150.0ms (2.2%)

localize14.0ms (0.2%)

rewrite56.0ms (0.8%)

series846.0ms (12.6%)

simplify65.0ms (1%)

prune122.0ms (1.8%)

localize11.0ms (0.2%)

rewrite56.0ms (0.8%)

series529.0ms (7.9%)

simplify93.0ms (1.4%)

prune211.0ms (3.1%)

regimes283.0ms (4.2%)

bsearch117.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (21.4%)

Profiling