Details

analyze277.0ms (5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample44.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	118×	body	256	valid
11.0ms	276×	pre	128	true
7.0ms	45×	body	512	valid
5.0ms	93×	body	128	valid
1.0ms	20×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify397.0ms (7.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (308.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	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

Error

51.9b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1805`
14×	`*-un-lft-identity_binary64_1783`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`add-cube-cbrt_binary64_1818` `add-log-exp_binary64_1822`
6×	`difference-of-squares_binary64_1752` `associate-/l*_binary64_1728` `sqrt-prod_binary64_1799` `times-frac_binary64_1789`
5×	`pow1_binary64_1844`
4×	`flip3--_binary64_1787` `cancel-sign-sub-inv_binary64_1749` `flip--_binary64_1758`
3×	`distribute-lft-out--_binary64_1735`
2×	`associate-/l/_binary64_1730` `diff-log_binary64_1875` `sqrt-div_binary64_1800` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `sub-neg_binary64_1776`
1×	`div-sub_binary64_1788` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `pow1/2_binary64_1863` `associate-/r*_binary64_1727` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series269.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
64.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune96.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	3	87

Error

0.1b

Counts

87 → 3

Compiler

Compiled 2001 to 1178 computations (41.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
22×	`times-frac_binary64_1789`
20×	`*-un-lft-identity_binary64_1783`
17×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
13×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
11×	`associate-/l*_binary64_1728`
10×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
8×	`add-log-exp_binary64_1822`
6×	`associate-/r/_binary64_1729`
5×	`distribute-lft-out_binary64_1734` `associate-/r*_binary64_1727`
4×	`flip-+_binary64_1757` `div-inv_binary64_1780` `flip3-+_binary64_1786` `pow1_binary64_1844`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `+-commutative_binary64_1713` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `sum-log_binary64_1874` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series460.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
157.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune150.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	107	7	114

Error

Counts

114 → 7

Compiler

Compiled 3206 to 1974 computations (38.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1783`
15×	`add-sqr-sqrt_binary64_1805`
14×	`add-cube-cbrt_binary64_1818`
12×	`times-frac_binary64_1789`
8×	`add-log-exp_binary64_1822`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
5×	`distribute-lft-out_binary64_1734` `pow1_binary64_1844`
4×	`associate-/r*_binary64_1727`
3×	`associate-/l*_binary64_1728` `sqrt-prod_binary64_1799`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `sqrt-div_binary64_1800` `flip3-+_binary64_1786` `flip--_binary64_1758`
1×	`+-commutative_binary64_1713` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `pow1/2_binary64_1863` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series326.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune106.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	86	5	91

Error

Counts

91 → 5

Compiler

Compiled 2282 to 1416 computations (37.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
0.1b	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))))
0.2b	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)
0.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_1783`
23×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
18×	`cbrt-prod_binary64_1814`
12×	`unpow-prod-down_binary64_1862` `sqrt-prod_binary64_1799` `times-frac_binary64_1789` `cube-prod_binary64_1811`
7×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
6×	`add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`distribute-lft-out_binary64_1734`
4×	`associate-/r*_binary64_1727` `sqrt-div_binary64_1800` `cube-div_binary64_1812`
3×	`associate-/l*_binary64_1728` `pow-unpow_binary64_1860` `pow-pow_binary64_1855`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `sqr-pow_binary64_1755` `cube-mult_binary64_1813` `flip-+_binary64_1757` `unpow3_binary64_1849` `cbrt-div_binary64_1815` `flip3-+_binary64_1786` `flip--_binary64_1758`
1×	`+-commutative_binary64_1713` `rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `div-inv_binary64_1780` `pow1/2_binary64_1863` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `sqrt-pow1_binary64_1801` `pow1/3_binary64_1865` `clear-num_binary64_1782` `pow-to-exp_binary64_1852` `sqrt-pow2_binary64_1802` `pow-exp_binary64_1851`

Counts

4 → 108

Calls

4 calls:

12.0ms	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))))
10.0ms	(+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
6.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))
6.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)

series338.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 c (+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))))
67.0ms	(+.f64 b (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)))
60.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3))
42.0ms	(pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))) 3)

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5050	2889

prune141.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Error

Counts

125 → 5

Compiler

Compiled 3217 to 2038 computations (36.6% saved)

regimes308.0ms (5.6%)

Accuracy

Total 0.1b remaining (98.6%)

Threshold costs 0.1b (98.6%)

Compiler

Compiled 4144 to 3162 computations (23.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.1s (37.6%)

Algorithm

1×

intervals

Results

362.0ms	3747×	body	256	valid
273.0ms	8824×	pre	128	true
214.0ms	1470×	body	512	valid
143.0ms	2783×	body	128	valid
38.0ms	824×	body	128	nan

Compiler

Compiled 1072 to 819 computations (23.6% saved)

Details

analyze277.0ms (5%)

sample44.0ms (0.8%)

simplify397.0ms (7.2%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

rewrite35.0ms (0.6%)

series269.0ms (4.9%)

simplify89.0ms (1.6%)

prune96.0ms (1.7%)

localize17.0ms (0.3%)

rewrite47.0ms (0.9%)

series460.0ms (8.3%)

simplify67.0ms (1.2%)

prune150.0ms (2.7%)

localize12.0ms (0.2%)

rewrite31.0ms (0.6%)

series326.0ms (5.9%)

simplify77.0ms (1.4%)

prune106.0ms (1.9%)

localize14.0ms (0.3%)

rewrite45.0ms (0.8%)

series338.0ms (6.1%)

simplify70.0ms (1.3%)

prune141.0ms (2.6%)

regimes308.0ms (5.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (37.6%)

Profiling