Details

analyze127.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample38.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	208×	body	128	valid
6.0ms	256×	pre	128	true
4.0ms	5×	body	2048	valid
3.0ms	19×	body	512	valid
3.0ms	14×	body	1024	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify216.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5063	43

prune3.0ms (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: 22.8b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

1.6b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

17.2b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite92.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_2442`
47×	`*-un-lft-identity_binary64_2436`
25×	`add-sqr-sqrt_binary64_2457` `add-cube-cbrt_binary64_2468`
17×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
14×	`associate-/r/_binary64_2384`
11×	`flip3-+_binary64_2439` `distribute-lft-out_binary64_2389` `flip-+_binary64_2410`
10×	`associate-/l*_binary64_2383`
9×	`associate-/l/_binary64_2385`
7×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `div-exp_binary64_2484` `associate-/r*_binary64_2382`
5×	`add-log-exp_binary64_2472`
4×	`frac-times_binary64_2446`
3×	`flip3--_binary64_2440` `pow1_binary64_2494` `flip--_binary64_2411`
2×	`prod-exp_binary64_2482` `associate-r/_binary64_2380` `cbrt-unprod_binary64_2466` `clear-num_binary64_2435` `frac-2neg_binary64_2447` `associate-l/_binary64_2381`
1×	`sum-log_binary64_2524` `+-commutative_binary64_2368`

Counts

3 → 111

Calls

3 calls:

36.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

23.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

16.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.4s (10.7%)

Counts

3 → 9

Calls

3 calls:

693.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

601.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

126.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify99.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4937	5261
1	4937	5261

prune246.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	8	121

Merged error: 5.5b

Counts

121 → 8

Compiler

Compiled 5259 to 2755 computations (47.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
1.5b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
4.0b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite167.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

321×	`times-frac_binary64_2442`
290×	`*-un-lft-identity_binary64_2436`
211×	`add-sqr-sqrt_binary64_2457`
140×	`add-cube-cbrt_binary64_2468`
90×	`associate-r_binary64_2378`
44×	`distribute-lft-out_binary64_2389`
31×	`distribute-lft-out--_binary64_2390` `difference-of-squares_binary64_2405`
26×	`associate-/l*_binary64_2383`
24×	`associate-/r/_binary64_2384`
20×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
15×	`flip3-+_binary64_2439` `flip-+_binary64_2410`
12×	`div-inv_binary64_2433`
7×	`cbrt-undiv_binary64_2467` `div-exp_binary64_2484` `associate-/r*_binary64_2382`
6×	`add-log-exp_binary64_2472` `pow1_binary64_2494`
4×	`associate-l_binary64_2379`
3×	`prod-exp_binary64_2482` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `div-sub_binary64_2441` `associate-/l/_binary64_2385`
2×	`clear-num_binary64_2435` `frac-2neg_binary64_2447` `associate-*l/_binary64_2381` `frac-times_binary64_2446`
1×	`-commutative_binary64_2369` `pow-prod-down_binary64_2504` `flip3--_binary64_2440` `associate-r/_binary64_2380` `sum-log_binary64_2524` `+-commutative_binary64_2368` `flip--_binary64_2411`

Counts

4 → 295

Calls

4 calls:

45.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
30.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
26.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.8s (13.3%)

Counts

4 → 12

Calls

4 calls:

713.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
595.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
328.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
119.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify156.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4971	13438
1	4971	13438

prune697.0ms (5.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	303	4	307
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	307	8	315

Merged error: 5.5b

Counts

315 → 8

Compiler

Compiled 14579 to 7687 computations (47.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.1b	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
1.5b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
4.0b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite191.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

306×	`times-frac_binary64_2442`
275×	`*-un-lft-identity_binary64_2436`
196×	`add-sqr-sqrt_binary64_2457`
133×	`add-cube-cbrt_binary64_2468`
90×	`associate-r_binary64_2378`
44×	`distribute-lft-out_binary64_2389`
27×	`distribute-lft-out--_binary64_2390` `difference-of-squares_binary64_2405`
22×	`associate-/r/_binary64_2384`
21×	`associate-/l*_binary64_2383`
18×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
15×	`flip3-+_binary64_2439` `flip-+_binary64_2410`
12×	`cbrt-prod_binary64_2464`
11×	`div-inv_binary64_2433`
6×	`cbrt-undiv_binary64_2467` `add-log-exp_binary64_2472` `div-exp_binary64_2484` `pow1_binary64_2494`
4×	`associate-/r_binary64_2382` `associate-l*_binary64_2379`
3×	`prod-exp_binary64_2482` `unpow-prod-down_binary64_2512` `cbrt-unprod_binary64_2466` `cube-prod_binary64_2461` `unswap-sqr_binary64_2404`
2×	`div-sub_binary64_2441` `associate-*l/_binary64_2381` `frac-times_binary64_2446` `cube-div_binary64_2462` `cbrt-div_binary64_2465`
1×	`pow1/3_binary64_2515` `-commutative_binary64_2369` `pow-prod-down_binary64_2504` `rem-cbrt-cube_binary64_2459` `associate-r/_binary64_2380` `sum-log_binary64_2524` `cube-mult_binary64_2463` `clear-num_binary64_2435` `unpow3_binary64_2499` `sqr-pow_binary64_2408` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `associate-/l/_binary64_2385`

Counts

4 → 278

Calls

4 calls:

45.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
36.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
33.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
22.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))

series2.3s (17.4%)

Counts

4 → 12

Calls

4 calls:

703.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
682.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1) 3))
600.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
314.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))

simplify143.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5037	13897

prune822.0ms (6.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	284	6	290
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	287	11	298

Merged error: 5.4b

Counts

298 → 11

Compiler

Compiled 15055 to 8377 computations (44.4% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
4.0b	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
4.0b	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
8.1b	(+.f64 (.f64 (+.f64 alpha beta) (.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))))) 1)

rewrite134.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64_2464`
49×	`add-sqr-sqrt_binary64_2457` `*-un-lft-identity_binary64_2436`
45×	`times-frac_binary64_2442`
31×	`add-cube-cbrt_binary64_2468`
9×	`distribute-lft-out--_binary64_2390` `difference-of-squares_binary64_2405`
6×	`add-log-exp_binary64_2472` `associate-/r/_binary64_2384`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `pow1_binary64_2494`
3×	`pow1/3_binary64_2515` `div-inv_binary64_2433` `cbrt-div_binary64_2465`
1×	`sum-log_binary64_2524` `+-commutative_binary64_2368`

Counts

4 → 101

Calls

4 calls:

75.0ms	(+.f64 (.f64 (+.f64 alpha beta) (.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))))) 1)
14.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
10.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
10.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series2.4s (18.5%)

Counts

4 → 12

Calls

4 calls:

712.0ms	(+.f64 (.f64 (+.f64 alpha beta) (.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))))) 1)
597.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
580.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
557.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5730	3874

prune391.0ms (3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	113	11	124

Merged error: 5.4b

Counts

124 → 11

Compiler

Compiled 8848 to 4861 computations (45.1% saved)

regimes148.0ms (1.1%)

Compiler: Compiled 1872 to 1268 computations (32.3% saved)

bsearch35.0ms (0.3%)

Steps

Iters	Range		Point
8	1.619500821867951e+95	1.712277581802335e+99	1.6543164008522536e+95

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	65	79
1	65	79

end0.0ms (0%)

sample1.4s (10.8%)

Algorithm

1×

intervals

Results

376.0ms	6510×	body	128	valid
193.0ms	8000×	pre	128	true
156.0ms	672×	body	1024	valid
76.0ms	459×	body	512	valid
34.0ms	307×	body	256	valid
15.0ms	52×	body	2048	valid

Compiler

Compiled 557 to 379 computations (32% saved)

Details

analyze127.0ms (1%)

sample38.0ms (0.3%)

simplify216.0ms (1.6%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite92.0ms (0.7%)

series1.4s (10.7%)

simplify99.0ms (0.7%)

prune246.0ms (1.9%)

localize16.0ms (0.1%)

rewrite167.0ms (1.3%)

series1.8s (13.3%)

simplify156.0ms (1.2%)

prune697.0ms (5.3%)

localize17.0ms (0.1%)

rewrite191.0ms (1.4%)

series2.3s (17.4%)

simplify143.0ms (1.1%)

prune822.0ms (6.2%)

localize28.0ms (0.2%)

rewrite134.0ms (1%)

series2.4s (18.5%)

simplify94.0ms (0.7%)

prune391.0ms (3%)

regimes148.0ms (1.1%)

bsearch35.0ms (0.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (10.8%)

Profiling