Details

analyze167.0ms (0.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5646	316
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 63 to 34 computations (46% saved)

sample46.0ms (0.2%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5395	79

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

52.7b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
35.0b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
45.1b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite842.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

38.2b

Rules

86×	`times-frac_binary64_1789`
66×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-/r/_binary64_1729`
61×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
46×	`add-sqr-sqrt_binary64_1805`
44×	`*-un-lft-identity_binary64_1783` `frac-times_binary64_1793`
34×	`associate-*r/_binary64_1725`
30×	`add-cube-cbrt_binary64_1818`
28×	`difference-of-squares_binary64_1752`
22×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-*l/_binary64_1726`
19×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
16×	`pow1_binary64_1844`
14×	`associate-/l*_binary64_1728` `difference-of-sqr-1_binary64_1753`
9×	`div-inv_binary64_1780` `associate-/l/_binary64_1730`
7×	`associate-/r*_binary64_1727`
6×	`associate-r_binary64_1723`
4×	`add-log-exp_binary64_1822` `pow-prod-down_binary64_1854` `associate-l_binary64_1724`
3×	`swap-sqr_binary64_1750`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `*-commutative_binary64_1714`
1×	`flip3--_binary64_1787` `flip--_binary64_1758` `pow2_binary64_1864` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `pow-sqr_binary64_1756` `unswap-sqr_binary64_1751`

Counts

4 → 228

Calls

4 calls:

42.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
27.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
14.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
14.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))

Compiler

Compiled 19221 to 7168 computations (62.7% saved)

series5.6s (24.4%)

Error

9.7b

Counts

4 → 87

Calls

4 calls:

3.9s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
639.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
484.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
235.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 19279 to 12732 computations (34% saved)

simplify197.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5083	22946

prune975.0ms (4.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	309	6	315
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	310	6	316

Error

8.1b

Counts

316 → 6

Compiler

Compiled 22825 to 9824 computations (57% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

8.1b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 8.1b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune11.0ms (0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	0	0
Total	6	6

Error

8.1b

Counts

6 → 6

Compiler

Compiled 228 to 147 computations (35.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
0.3b	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
35.1b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
35.8b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite1.5s (6.5%)

Algorithm

1×	rewrite-expression-head

Error

8.1b

Rules

376×	`*-un-lft-identity_binary64_1783`
342×	`times-frac_binary64_1789`
205×	`add-sqr-sqrt_binary64_1805`
129×	`add-cube-cbrt_binary64_1818`
91×	`distribute-lft-out_binary64_1734`
38×	`associate-/r/_binary64_1729` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
32×	`associate-/l*_binary64_1728`
25×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
21×	`associate-/r*_binary64_1727`
20×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
19×	`div-inv_binary64_1780` `difference-of-sqr-1_binary64_1753`
11×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
6×	`associate-/l/_binary64_1730`
4×	`pow1_binary64_1844` `add-log-exp_binary64_1822` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
2×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-*r/_binary64_1725`
1×	`flip3--_binary64_1787` `flip--_binary64_1758`

Counts

4 → 333

Calls

4 calls:

25.0ms	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
21.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
12.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
10.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

Compiler

Compiled 26191 to 12414 computations (52.6% saved)

series2.7s (11.7%)

Error

7.8b

Counts

4 → 72

Calls

4 calls:

1.6s	(/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1))
464.0ms	(/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (*.f64 2 i)))))
281.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
156.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 15292 to 10089 computations (34% saved)

simplify199.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

405 → 405

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5172	24604

prune1.5s (6.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	403	2	405
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	404	7	411

Error

7.8b

Counts

411 → 7

Compiler

Compiled 30259 to 14305 computations (52.7% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (sqrt.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))))
35.1b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
35.8b	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
35.8b	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

rewrite887.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

126×	`*-un-lft-identity_binary64_1783`
98×	`add-sqr-sqrt_binary64_1805` `sqrt-prod_binary64_1799`
96×	`times-frac_binary64_1789`
64×	`add-cube-cbrt_binary64_1818`
29×	`swap-sqr_binary64_1750`
28×	`distribute-lft-out_binary64_1734`
21×	`associate-l_binary64_1724` `associate-r_binary64_1723`
19×	`pow1_binary64_1844`
15×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
14×	`associate-/r/_binary64_1729`
12×	`associate-/r*_binary64_1727`
10×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
9×	`unswap-sqr_binary64_1751`
8×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
7×	`div-inv_binary64_1780` `associate-/l*_binary64_1728`
6×	`associate-/l/_binary64_1730`
5×	`pow-prod-up_binary64_1853`
4×	`div-exp_binary64_1834` `add-log-exp_binary64_1822` `cbrt-undiv_binary64_1817` `rem-sqrt-square_binary64_1796` `sqrt-div_binary64_1800`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-*r/_binary64_1725` `pow-prod-down_binary64_1854` `pow-sqr_binary64_1756`
2×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `sqr-abs_binary64_1798`
1×	`pow2_binary64_1864` `pow-plus_binary64_1846` `sqrt-unprod_binary64_1803` `rem-square-sqrt_binary64_1795` `frac-times_binary64_1793` `associate-l/_binary64_1726` `-commutative_binary64_1714`

Counts

4 → 207

Calls

4 calls:

40.0ms	(.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (sqrt.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))))
12.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
11.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
11.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))

Compiler

Compiled 20239 to 8543 computations (57.8% saved)

series1.2s (5.2%)

Error

7.8b

Counts

4 → 69

Calls

4 calls:

293.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
285.0ms	(/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))
280.0ms	(.f64 (sqrt.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (.f64 i 2)) alpha))) (sqrt.f64 (/.f64 (+.f64 (.f64 beta alpha) (.f64 i (+.f64 alpha (+.f64 i beta)))) (+.f64 (+.f64 beta (*.f64 i 2)) alpha))))
155.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))

Compiler

Compiled 14452 to 8654 computations (40.1% saved)

simplify135.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4978	9127
1	4978	9127

prune1.2s (5.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	275	1	276
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	275	8	283

Error

7.8b

Counts

283 → 8

Compiler

Compiled 21460 to 9828 computations (54.2% saved)

regimes1.3s (5.8%)

Accuracy

Total 3.5b remaining (31.7%)

Threshold costs 0b (0%)

Compiler

Compiled 23908 to 13673 computations (42.8% saved)

bsearch38.0ms (0.2%)

Steps

Iters	Range		Point
6	3.6589032390569236e+116	1.9818225258949245e+117	1.958072606935226e+117

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	89
1	47	89

Compiler

Compiled 120 to 76 computations (36.7% saved)

end0.0ms (0%)

sample4.3s (18.7%)

Algorithm

1×

intervals

Results

669.0ms	8000×	body	128	valid
171.0ms	8000×	pre	128	true

Compiler

Compiled 6032 to 3454 computations (42.7% saved)

Details

analyze167.0ms (0.7%)

sample46.0ms (0.2%)

simplify42.0ms (0.2%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite842.0ms (3.7%)

series5.6s (24.4%)

simplify197.0ms (0.9%)

prune975.0ms (4.3%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune11.0ms (0%)

localize20.0ms (0.1%)

rewrite1.5s (6.5%)

series2.7s (11.7%)

simplify199.0ms (0.9%)

prune1.5s (6.4%)

localize31.0ms (0.1%)

rewrite887.0ms (3.9%)

series1.2s (5.2%)

simplify135.0ms (0.6%)

prune1.2s (5.3%)

regimes1.3s (5.8%)

bsearch38.0ms (0.2%)

simplify12.0ms (0.1%)

end0.0ms (0%)

sample4.3s (18.7%)

Profiling