Details

analyze40.0ms (0.2%)

Algorithm

1×

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)

sample44.0ms (0.2%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify135.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5395	79

prune5.0ms (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

54.5b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize19.0ms (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))))
36.8b	(/.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))
46.5b	(/.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))))

rewrite846.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

37.9b

Rules

86×	`times-frac_binary64_2130`
66×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/r/_binary64_2070`
61×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
46×	`add-sqr-sqrt_binary64_2146`
44×	`*-un-lft-identity_binary64_2124` `frac-times_binary64_2134`
34×	`associate-*r/_binary64_2066`
30×	`add-cube-cbrt_binary64_2159`
28×	`difference-of-squares_binary64_2093`
22×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `associate-*l/_binary64_2067`
19×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
16×	`pow1_binary64_2185`
14×	`associate-/l*_binary64_2069` `difference-of-sqr-1_binary64_2094`
9×	`div-inv_binary64_2121` `associate-/l/_binary64_2071`
7×	`associate-/r*_binary64_2068`
6×	`associate-r_binary64_2064`
4×	`add-log-exp_binary64_2163` `pow-prod-down_binary64_2195` `associate-l_binary64_2065`
3×	`swap-sqr_binary64_2091`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `*-commutative_binary64_2055`
1×	`flip3--_binary64_2128` `flip--_binary64_2099` `pow2_binary64_2205` `pow-prod-up_binary64_2194` `pow-plus_binary64_2187` `pow-sqr_binary64_2097` `unswap-sqr_binary64_2092`

Counts

4 → 228

Calls

4 calls:

40.0ms	(/.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))))
13.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
13.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 19221 to 7168 computations (62.7% saved)

series10.4s (54.4%)

Error

9.5b

Counts

4 → 95

Calls

4 calls:

8.6s	(/.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))
736.0ms	(/.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))))
480.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
247.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 25883 to 17359 computations (32.9% saved)

simplify214.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5873	25621

prune1.5s (7.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	316	7	323
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	317	7	324

Error

7.6b

Counts

324 → 7

Compiler

Compiled 24689 to 10858 computations (56% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 7.6b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune10.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

7.6b

Counts

7 → 7

Compiler

Compiled 196 to 127 computations (35.2% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.7b	(/.f64 1/64 (*.f64 i i))
9.4b	(/.f64 (.f64 alpha alpha) (.f64 i i))
11.6b	(/.f64 (.f64 beta beta) (.f64 i i))

rewrite97.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

7.3b

Rules

32×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
9×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
5×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `times-frac_binary64_2130` `-un-lft-identity_binary64_2124` `associate-/l_binary64_2069`
3×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `associate-/r*_binary64_2068`

Counts

3 → 63

Calls

3 calls:

8.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
6.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
4.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1972 to 684 computations (65.3% saved)

series212.0ms (1.1%)

Error

7.6b

Counts

3 → 15

Calls

3 calls:

88.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
85.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
24.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1125 to 756 computations (32.8% saved)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5084	712

prune90.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	77	8	85

Error

7.3b

Counts

85 → 8

Compiler

Compiled 2291 to 927 computations (59.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (/.f64 beta i) 6)
0.7b	(/.f64 1/64 (*.f64 i i))
9.4b	(/.f64 (.f64 alpha alpha) (.f64 i i))
14.9b	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))

rewrite150.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

7.3b

Rules

26×	`unpow-prod-down_binary64_2203`
24×	`add-exp-log_binary64_2162`
22×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `times-frac_binary64_2130` `*-un-lft-identity_binary64_2124`
21×	`add-cbrt-cube_binary64_2160`
17×	`cbrt-prod_binary64_2155`
7×	`div-exp_binary64_2175`
6×	`cbrt-undiv_binary64_2158`
5×	`pow1_binary64_2185` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
4×	`add-log-exp_binary64_2163` `div-inv_binary64_2121` `associate-/l*_binary64_2069`
3×	`pow-unpow_binary64_2201`
2×	`sqr-pow_binary64_2096` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-/r*_binary64_2068` `pow-exp_binary64_2192`
1×	`pow1/3_binary64_2206` `pow-pow_binary64_2196` `pow-to-exp_binary64_2193`

Counts

4 → 95

Calls

4 calls:

6.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
5.0ms	(pow.f64 (/.f64 beta i) 6)
4.0ms	(/.f64 1/64 (*.f64 i i))
4.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))

Compiler

Compiled 2961 to 1449 computations (51.1% saved)

series336.0ms (1.8%)

Error

7.3b

Counts

4 → 21

Calls

4 calls:

106.0ms	(pow.f64 (/.f64 beta i) 6)
92.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
89.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))
27.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1566 to 1144 computations (26.9% saved)

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5069	1309

prune136.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	116	8	124

Error

7.3b

Counts

124 → 8

Compiler

Compiled 3182 to 1603 computations (49.6% saved)

regimes1.1s (5.8%)

Accuracy

Total 3.2b remaining (27.2%)

Threshold costs 0b (0%)

Compiler

Compiled 19380 to 11205 computations (42.2% saved)

bsearch27.0ms (0.1%)

Steps

Iters	Range		Point
5	8.113889814503846e+121	2.0659321366427148e+122	2.0327187607865832e+122

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	46	89
1	46	89

end0.0ms (0%)

sample3.7s (19.1%)

Algorithm

1×

intervals

Results

633.0ms	8000×	body	128	valid
176.0ms	8000×	pre	128	true

Compiler

Compiled 4900 to 2836 computations (42.1% saved)

Details

analyze40.0ms (0.2%)

sample44.0ms (0.2%)

simplify135.0ms (0.7%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite846.0ms (4.4%)

series10.4s (54.4%)

simplify214.0ms (1.1%)

prune1.5s (7.6%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0%)

prune10.0ms (0.1%)

localize13.0ms (0.1%)

rewrite97.0ms (0.5%)

series212.0ms (1.1%)

simplify56.0ms (0.3%)

prune90.0ms (0.5%)

localize15.0ms (0.1%)

rewrite150.0ms (0.8%)

series336.0ms (1.8%)

simplify66.0ms (0.3%)

prune136.0ms (0.7%)

regimes1.1s (5.8%)

bsearch27.0ms (0.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.7s (19.1%)

Profiling