Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	193×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	33×	body	1024	valid
2.0ms	21×	body	512	valid
0.0ms	7×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify311.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	5139	19

prune2.0ms (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

Merged error: 15.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.4b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_2143`
26×	`add-sqr-sqrt_binary64_2165`
25×	`times-frac_binary64_2149`
19×	`distribute-lft-out_binary64_2094`
14×	`add-cube-cbrt_binary64_2178`
6×	`distribute-lft-out--_binary64_2095` `difference-of-squares_binary64_2112`
5×	`associate-/r_binary64_2087` `associate-/l_binary64_2088`
4×	`add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
2×	`pow1_binary64_2204` `associate-/r/_binary64_2089` `flip3-+_binary64_2146` `flip-+_binary64_2117` `div-sub_binary64_2148` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `+-commutative_binary64_2073` `clear-num_binary64_2142` `flip--_binary64_2118` `associate-+l-_binary64_2078` `div-inv_binary64_2140` `sum-log_binary64_2234` `flip3--_binary64_2147` `div-exp_binary64_2194` `frac-2neg_binary64_2154`

Counts

2 → 65

Calls

2 calls:

22.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
15.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series161.0ms (3.4%)

Counts

2 → 6

Calls

2 calls:

93.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
67.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5220	1488

prune347.0ms (7.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 15.3b

Counts

72 → 13

Compiler

Compiled 7276 to 4849 computations (33.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
1.4b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite88.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64_2143`
54×	`add-sqr-sqrt_binary64_2165`
37×	`times-frac_binary64_2149`
27×	`add-cube-cbrt_binary64_2178`
24×	`distribute-lft-out_binary64_2094`
16×	`cancel-sign-sub-inv_binary64_2109`
11×	`add-log-exp_binary64_2182`
10×	`associate-/r*_binary64_2087` `difference-of-squares_binary64_2112`
8×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
6×	`associate-/l*_binary64_2088`
5×	`distribute-lft-out--_binary64_2095`
4×	`pow1_binary64_2204` `diff-log_binary64_2235` `associate-/r/_binary64_2089` `associate--r+_binary64_2079` `difference-of-sqr-1_binary64_2113`
3×	`flip--_binary64_2118` `sub-neg_binary64_2136` `flip3--_binary64_2147`
2×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `div-inv_binary64_2140` `flip3-+_binary64_2146` `frac-sub_binary64_2152` `flip-+_binary64_2117` `div-exp_binary64_2194` `frac-2neg_binary64_2154`
1×	`associate--r-_binary64_2082`

Counts

4 → 128

Calls

4 calls:

37.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
9.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

series312.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
93.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
68.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
55.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4929	2917
1	4929	2917

prune517.0ms (11%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	134	6	140
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	146	7	153

Merged error: 2.2b

Counts

153 → 7

Compiler

Compiled 11242 to 7479 computations (33.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
1.4b	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
1.4b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite70.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64_2143`
50×	`add-sqr-sqrt_binary64_2165`
36×	`times-frac_binary64_2149`
28×	`add-cube-cbrt_binary64_2178`
24×	`distribute-lft-out_binary64_2094`
11×	`log-pow_binary64_2232`
10×	`associate-/r*_binary64_2087` `exp-prod_binary64_2195`
8×	`add-exp-log_binary64_2181` `difference-of-squares_binary64_2112` `add-cbrt-cube_binary64_2179`
7×	`log-prod_binary64_2229`
6×	`add-log-exp_binary64_2182` `associate-/l*_binary64_2088` `cancel-sign-sub-inv_binary64_2109`
5×	`pow1_binary64_2204`
4×	`associate-/r/_binary64_2089` `exp-sum_binary64_2189` `difference-of-sqr-1_binary64_2113`
2×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `sub-neg_binary64_2136` `distribute-lft-out--_binary64_2095` `div-inv_binary64_2140` `flip3-+_binary64_2146` `flip-+_binary64_2117` `div-exp_binary64_2194` `frac-2neg_binary64_2154`
1×	`diff-log_binary64_2235` `flip--_binary64_2118` `rem-log-exp_binary64_2184` `log-div_binary64_2230` `flip3--_binary64_2147` `exp-diff_binary64_2191`

Counts

4 → 122

Calls

4 calls:

20.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
19.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
9.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series415.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
105.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
66.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
56.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify53.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5005	2196

prune175.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Merged error: 2.2b

Counts

141 → 7

Compiler

Compiled 3964 to 2481 computations (37.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
0.4b	(exp.f64 (log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
1.4b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
13.3b	(log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite117.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_2143`
39×	`add-sqr-sqrt_binary64_2165`
20×	`times-frac_binary64_2149`
18×	`add-cube-cbrt_binary64_2178`
14×	`log-prod_binary64_2229`
12×	`distribute-lft-out_binary64_2094`
8×	`log-div_binary64_2230` `difference-of-squares_binary64_2112`
7×	`distribute-lft-out--_binary64_2095` `add-exp-log_binary64_2181` `exp-sum_binary64_2189`
6×	`pow1_binary64_2204` `add-log-exp_binary64_2182` `add-cbrt-cube_binary64_2179`
5×	`flip--_binary64_2118` `associate-/r*_binary64_2087` `flip3--_binary64_2147`
4×	`exp-prod_binary64_2195` `exp-diff_binary64_2191` `frac-sub_binary64_2152`
3×	`associate-/l*_binary64_2088` `cancel-sign-sub-inv_binary64_2109`
2×	`associate-/r/_binary64_2089` `log-pow_binary64_2232` `difference-of-sqr-1_binary64_2113`
1×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `rem-log-exp_binary64_2184` `sub-neg_binary64_2136` `div-inv_binary64_2140` `rem-exp-log_binary64_2183` `flip3-+_binary64_2146` `flip-+_binary64_2117` `div-exp_binary64_2194` `frac-2neg_binary64_2154`

Counts

4 → 101

Calls

4 calls:

38.0ms	(log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
37.0ms	(exp.f64 (log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
9.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))

series463.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(exp.f64 (log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
141.0ms	(log.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
98.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
56.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4953	3014
1	4953	3014

prune221.0ms (4.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	111	9	120

Merged error: 2.2b

Counts

120 → 9

Compiler

Compiled 4898 to 3145 computations (35.8% saved)

regimes70.0ms (1.5%)

Compiler: Compiled 674 to 478 computations (29.1% saved)

bsearch15.0ms (0.3%)

Steps

Iters	Range		Point
6	7928399419.02299	118427829976.21632	12210785709.035353

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	193	75
1	193	75

end0.0ms (0%)

sample1.0s (21.5%)

Algorithm

1×

intervals

Results

201.0ms	5993×	body	128	valid
135.0ms	8000×	pre	128	true
131.0ms	1001×	body	1024	valid
54.0ms	582×	body	512	valid
21.0ms	330×	body	256	valid
15.0ms	94×	body	2048	valid

Compiler

Compiled 405 to 289 computations (28.6% saved)

Details

analyze3.0ms (0.1%)

sample24.0ms (0.5%)

simplify311.0ms (6.6%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite44.0ms (0.9%)

series161.0ms (3.4%)

simplify65.0ms (1.4%)

prune347.0ms (7.4%)

localize12.0ms (0.2%)

rewrite88.0ms (1.9%)

series312.0ms (6.7%)

simplify70.0ms (1.5%)

prune517.0ms (11%)

localize13.0ms (0.3%)

rewrite70.0ms (1.5%)

series415.0ms (8.9%)

simplify53.0ms (1.1%)

prune175.0ms (3.7%)

localize13.0ms (0.3%)

rewrite117.0ms (2.5%)

series463.0ms (9.9%)

simplify85.0ms (1.8%)

prune221.0ms (4.7%)

regimes70.0ms (1.5%)

bsearch15.0ms (0.3%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.0s (21.5%)

Profiling