Details

analyze128.0ms (1.3%)

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)

sample36.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	207×	body	128	valid
6.0ms	256×	pre	128	true
6.0ms	25×	body	1024	valid
2.0ms	13×	body	512	valid
1.0ms	8×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify166.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5371	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

Error

25.3b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b

(/.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))

1.0b

(+.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)

20.5b

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

rewrite96.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_2471`
47×	`*-un-lft-identity_binary64_2465`
25×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
17×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
14×	`associate-/r/_binary64_2411`
11×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `distribute-lft-out_binary64_2416`
10×	`associate-/l*_binary64_2410`
9×	`associate-/l/_binary64_2412`
7×	`associate-/r*_binary64_2409` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462`
5×	`add-log-exp_binary64_2504`
4×	`frac-times_binary64_2475`
3×	`flip--_binary64_2440` `pow1_binary64_2526` `flip3--_binary64_2469`
2×	`associate-l/_binary64_2408` `associate-r/_binary64_2407` `clear-num_binary64_2464` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `cbrt-unprod_binary64_2498`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556`

Counts

3 → 111

Calls

3 calls:

41.0ms

(+.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)

24.0ms

(/.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)))

series728.0ms (7.4%)

Counts

3 → 9

Calls

3 calls:

369.0ms

(+.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)

295.0ms

(/.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))

64.0ms

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

simplify103.0ms (1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4941	5261
1	4941	5261

prune221.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	7	121

Error

4.5b

Counts

121 → 7

Compiler

Compiled 5248 to 2745 computations (47.7% saved)

localize16.0ms (0.2%)

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))))
2.3b	(+.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)
2.3b	(.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)))))

rewrite165.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

321×	`times-frac_binary64_2471`
290×	`*-un-lft-identity_binary64_2465`
211×	`add-sqr-sqrt_binary64_2487`
140×	`add-cube-cbrt_binary64_2500`
90×	`associate-r_binary64_2405`
44×	`distribute-lft-out_binary64_2416`
31×	`difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417`
26×	`associate-/l*_binary64_2410`
24×	`associate-/r/_binary64_2411`
20×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
15×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
12×	`div-inv_binary64_2462`
7×	`associate-/r*_binary64_2409` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
6×	`add-log-exp_binary64_2504` `pow1_binary64_2526`
4×	`associate-l_binary64_2406`
3×	`associate-/l/_binary64_2412` `div-sub_binary64_2470` `unswap-sqr_binary64_2433` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
2×	`associate-*l/_binary64_2408` `frac-times_binary64_2475` `clear-num_binary64_2464` `frac-2neg_binary64_2476`
1×	`-commutative_binary64_2396` `+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `associate-r/_binary64_2407` `pow-prod-down_binary64_2536` `flip3--_binary64_2469`

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))))
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series895.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

361.0ms	(+.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)
311.0ms	(.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)))))
167.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
56.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify164.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5014	13438

prune734.0ms (7.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	304	3	307
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	307	7	314

Error

4.5b

Counts

314 → 7

Compiler

Compiled 14545 to 7666 computations (47.3% saved)

localize19.0ms (0.2%)

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 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
1.5b	(log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.3b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)

rewrite157.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

191×	`times-frac_binary64_2471`
181×	`*-un-lft-identity_binary64_2465`
134×	`add-sqr-sqrt_binary64_2487`
110×	`log-pow_binary64_2554`
106×	`associate-r_binary64_2405`
105×	`exp-prod_binary64_2517`
91×	`add-cube-cbrt_binary64_2500`
26×	`distribute-lft-out_binary64_2416`
19×	`difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417`
14×	`associate-/r/_binary64_2411`
11×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
10×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
7×	`div-inv_binary64_2462`
6×	`add-log-exp_binary64_2504`
5×	`associate-/l*_binary64_2410`
4×	`associate-l_binary64_2406`
3×	`associate-/r*_binary64_2409` `log-prod_binary64_2551`
2×	`associate-*l/_binary64_2408` `frac-times_binary64_2475` `associate-/l/_binary64_2412` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
1×	`log-div_binary64_2552` `-commutative_binary64_2396` `+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `associate-r/_binary64_2407` `clear-num_binary64_2464` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `flip3--_binary64_2469` `rem-log-exp_binary64_2506` `exp-diff_binary64_2513`

Counts

4 → 215

Calls

4 calls:

58.0ms	(.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
33.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
14.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series955.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

405.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
404.0ms	(.f64 (+.f64 alpha beta) (/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
90.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
56.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify106.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5254	7380

prune489.0ms (5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	227	7	234

Error

4.5b

Counts

234 → 7

Compiler

Compiled 10742 to 5849 computations (45.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.3b	(+.f64 (.f64 (.f64 (+.f64 alpha beta) (.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)))))) (/.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
5.5b	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
5.5b	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
5.5b	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite110.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64_2496`
49×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
45×	`times-frac_binary64_2471`
31×	`add-cube-cbrt_binary64_2500`
9×	`difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417`
6×	`add-log-exp_binary64_2504` `associate-/r/_binary64_2411`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
3×	`cbrt-div_binary64_2497` `pow1/3_binary64_2547` `div-inv_binary64_2462`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556`

Counts

4 → 101

Calls

4 calls:

60.0ms	(+.f64 (.f64 (.f64 (+.f64 alpha beta) (.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)))))) (/.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
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))))
9.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series1.4s (13.8%)

Counts

4 → 12

Calls

4 calls:

408.0ms	(+.f64 (.f64 (.f64 (+.f64 alpha beta) (.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)))))) (/.f64 (cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
329.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
314.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
310.0ms	(cbrt.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

simplify106.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4919	3861
1	4919	3861

prune277.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	113	7	120

Error

4.5b

Counts

120 → 7

Compiler

Compiled 7276 to 3704 computations (49.1% saved)

regimes724.0ms (7.3%)

Accuracy

Total 1.7b remaining (22.8%)

Threshold costs 0b (0%)

Compiler

Compiled 11757 to 7769 computations (33.9% saved)

bsearch4.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	105
1	48	105

end0.0ms (0%)

sample2.1s (21%)

Algorithm

1×

intervals

Results

363.0ms	6485×	body	128	valid
183.0ms	8000×	pre	128	true
155.0ms	697×	body	1024	valid
78.0ms	456×	body	512	valid
33.0ms	307×	body	256	valid
16.0ms	55×	body	2048	valid

Compiler

Compiled 1726 to 1137 computations (34.1% saved)

Details

analyze128.0ms (1.3%)

sample36.0ms (0.4%)

simplify166.0ms (1.7%)

prune3.0ms (0%)

localize12.0ms (0.1%)

rewrite96.0ms (1%)

series728.0ms (7.4%)

simplify103.0ms (1%)

prune221.0ms (2.2%)

localize16.0ms (0.2%)

rewrite165.0ms (1.7%)

series895.0ms (9.1%)

simplify164.0ms (1.7%)

prune734.0ms (7.4%)

localize19.0ms (0.2%)

rewrite157.0ms (1.6%)

series955.0ms (9.7%)

simplify106.0ms (1.1%)

prune489.0ms (5%)

localize16.0ms (0.2%)

rewrite110.0ms (1.1%)

series1.4s (13.8%)

simplify106.0ms (1.1%)

prune277.0ms (2.8%)

regimes724.0ms (7.3%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (21%)

Profiling