Details

analyze8.6s (11.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	25%	75%	2
0%	25%	75%	3
0%	25%	75%	4
0%	25%	75%	5
0%	25%	75%	6
0%	25%	75%	7
0%	25%	75%	8
1.6%	23.4%	75%	9
1.6%	23.4%	75%	10
1.6%	23.4%	75%	11
1.6%	23.4%	75%	12
1.6%	23.4%	75%	13
1.6%	23.4%	75%	14

Compiler

Compiled 50 to 40 computations (20% saved)

sample11.3s (15.2%)

Algorithm

1×

intervals

Results

8.6s	465×	body	8192	exit
1.0s	324×	body	1024	overflowed
773.0ms	2010×	body	128	overflowed
305.0ms	170×	body	512	overflowed
142.0ms	3338×	pre	128	true
100.0ms	113×	body	256	overflowed
58.0ms	251×	body	128	valid
23.0ms	1×	body	8192	valid
7.0ms	3×	body	1024	valid
2.0ms	1×	body	512	valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify218.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5010	68

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 3.8b

Counts

2 → 1

Compiler

Compiled 86 to 70 computations (18.6% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
0.3b	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
1.2b	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p)
2.0b	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))

rewrite211.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

1192×	`add-exp-log_binary64_2808`
692×	`pow-exp_binary64_2838`
684×	`prod-exp_binary64_2819`
593×	`div-exp_binary64_2821`
344×	`pow-to-exp_binary64_2839`
116×	`1-exp_binary64_2814` `rec-exp_binary64_2820`
42×	`*-un-lft-identity_binary64_2773`
36×	`unpow-prod-down_binary64_2849`
33×	`add-sqr-sqrt_binary64_2794`
29×	`times-frac_binary64_2779`
22×	`add-cube-cbrt_binary64_2805`
16×	`add-cbrt-cube_binary64_2806`
8×	`pow1_binary64_2831`
6×	`difference-of-squares_binary64_2742` `pow-unpow_binary64_2847` `distribute-lft-out_binary64_2726` `add-log-exp_binary64_2809` `pow-pow_binary64_2842`
4×	`cbrt-unprod_binary64_2803` `cbrt-undiv_binary64_2804` `associate-/r/_binary64_2721` `div-inv_binary64_2770`
2×	`sqr-pow_binary64_2745` `pow-flip_binary64_2844` `flip3-+_binary64_2776` `distribute-lft-out--_binary64_2727` `inv-pow_binary64_2855` `flip-+_binary64_2747`
1×	`frac-2neg_binary64_2784` `diff-log_binary64_2862` `sub-neg_binary64_2766` `flip3--_binary64_2777` `associate-/r_binary64_2719` `flip--_binary64_2748` `clear-num_binary64_2772` `associate-/l_binary64_2720`

Counts

4 → 471

Calls

4 calls:

61.0ms	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))
13.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
9.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
9.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p)

series1.9s (2.6%)

Counts

4 → 12

Calls

4 calls:

1.6s	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))
118.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p)
107.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
62.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))

simplify229.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

483 → 483

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5390	27317

prune1.6s (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	480	3	483
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	481	3	484

Merged error: 0.1b

Counts

484 → 3

Compiler

Compiled 20902 to 13294 computations (36.4% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(.f64 (.f64 s 1/2) (-.f64 c_p c_n))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-exp-log_binary64_2808` `pow1_binary64_2831` `add-cbrt-cube_binary64_2806`
5×	`associate-r_binary64_2715`
4×	`add-sqr-sqrt_binary64_2794` `*-un-lft-identity_binary64_2773`
3×	`cbrt-unprod_binary64_2803` `pow-prod-down_binary64_2841` `prod-exp_binary64_2819`
2×	`sub-neg_binary64_2766` `add-cube-cbrt_binary64_2805` `associate-*r/_binary64_2717`
1×	`distribute-rgt-in_binary64_2725` `difference-of-squares_binary64_2742` `flip3--_binary64_2777` `associate-l_binary64_2716` `flip--_binary64_2748` `*-commutative_binary64_2706` `add-log-exp_binary64_2809` `distribute-lft-in_binary64_2724` `distribute-lft-out--_binary64_2727`

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.f64 (*.f64 s 1/2) (-.f64 c_p c_n))

series73.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

73.0ms

(*.f64 (*.f64 s 1/2) (-.f64 c_p c_n))

simplify65.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4910	319
1	4910	319

prune23.0ms (0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	27	3	30

Merged error: 0.1b

Counts

30 → 3

Compiler

Compiled 440 to 284 computations (35.5% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 c_p (+.f64 (.f64 t 1/2) (log.f64 1/2)))
0.2b	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
0.3b	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
1.0b	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (+.f64 1 (.f64 c_p (+.f64 (.f64 t 1/2) (log.f64 1/2)))) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))

rewrite105.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`add-exp-log_binary64_2808`
130×	`prod-exp_binary64_2819`
102×	`div-exp_binary64_2821`
95×	`pow-exp_binary64_2838`
56×	`pow-to-exp_binary64_2839`
29×	`*-un-lft-identity_binary64_2773`
28×	`add-sqr-sqrt_binary64_2794`
18×	`unpow-prod-down_binary64_2849` `add-cbrt-cube_binary64_2806`
17×	`times-frac_binary64_2779`
15×	`add-cube-cbrt_binary64_2805`
13×	`1-exp_binary64_2814` `rec-exp_binary64_2820`
8×	`pow1_binary64_2831`
6×	`difference-of-squares_binary64_2742` `add-log-exp_binary64_2809`
5×	`cbrt-unprod_binary64_2803`
4×	`cbrt-undiv_binary64_2804` `associate-/r/_binary64_2721`
3×	`div-inv_binary64_2770` `pow-unpow_binary64_2847` `flip3-+_binary64_2776` `associate-l_binary64_2716` `distribute-lft-out_binary64_2726` `associate-r_binary64_2715` `flip-+_binary64_2747` `pow-pow_binary64_2842`
2×	`distribute-lft-out--_binary64_2727` `associate-r/_binary64_2717` `associate-l/_binary64_2718`
1×	`sqr-pow_binary64_2745` `frac-2neg_binary64_2784` `distribute-rgt-in_binary64_2725` `pow-prod-down_binary64_2841` `unswap-sqr_binary64_2741` `diff-log_binary64_2862` `sub-neg_binary64_2766` `pow-flip_binary64_2844` `flip3--_binary64_2777` `associate-/r_binary64_2719` `flip--_binary64_2748` `-commutative_binary64_2706` `distribute-lft-in_binary64_2724` `clear-num_binary64_2772` `associate-/l*_binary64_2720` `inv-pow_binary64_2855`

Counts

4 → 173

Calls

4 calls:

47.0ms	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (+.f64 1 (.f64 c_p (+.f64 (.f64 t 1/2) (log.f64 1/2)))) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))
12.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
9.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
7.0ms	(.f64 c_p (+.f64 (.f64 t 1/2) (log.f64 1/2)))

series2.0s (2.8%)

Counts

4 → 12

Calls

4 calls:

1.8s	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (+.f64 1 (.f64 c_p (+.f64 (.f64 t 1/2) (log.f64 1/2)))) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))
106.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
88.0ms	(.f64 c_p (+.f64 (.f64 t 1/2) (log.f64 1/2)))
59.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5544	8702

prune569.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	185	3	188

Merged error: 0.1b

Counts

188 → 3

Compiler

Compiled 9127 to 6339 computations (30.5% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
0.3b	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
1.2b	(pow.f64 (+.f64 1 (exp.f64 (neg.f64 t))) c_p)
1.9b	(/.f64 (/.f64 (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n) (pow.f64 (+.f64 1 (exp.f64 (neg.f64 t))) c_p)) (*.f64 (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n) (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)))

rewrite228.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

567×	`add-exp-log_binary64_2808`
444×	`times-frac_binary64_2779`
423×	`div-exp_binary64_2821`
318×	`unpow-prod-down_binary64_2849`
313×	`*-un-lft-identity_binary64_2773`
299×	`pow-exp_binary64_2838`
296×	`add-sqr-sqrt_binary64_2794`
206×	`pow-to-exp_binary64_2839`
180×	`prod-exp_binary64_2819`
124×	`associate-/l*_binary64_2720`
109×	`add-cube-cbrt_binary64_2805`
102×	`difference-of-squares_binary64_2742`
48×	`sqr-pow_binary64_2745`
34×	`distribute-lft-out_binary64_2726` `distribute-lft-out--_binary64_2727`
31×	`1-exp_binary64_2814` `rec-exp_binary64_2820`
21×	`div-inv_binary64_2770`
16×	`add-cbrt-cube_binary64_2806`
7×	`pow1_binary64_2831`
6×	`cbrt-undiv_binary64_2804` `pow-unpow_binary64_2847` `add-log-exp_binary64_2809`
4×	`pow-pow_binary64_2842`
2×	`cbrt-unprod_binary64_2803` `associate-/r/_binary64_2721`
1×	`frac-2neg_binary64_2784` `associate-/l/_binary64_2722` `diff-log_binary64_2862` `sub-neg_binary64_2766` `pow-flip_binary64_2844` `flip3-+_binary64_2776` `flip3--_binary64_2777` `associate-/r*_binary64_2719` `flip--_binary64_2748` `clear-num_binary64_2772` `inv-pow_binary64_2855` `flip-+_binary64_2747`

Counts

4 → 528

Calls

4 calls:

71.0ms	(/.f64 (/.f64 (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n) (pow.f64 (+.f64 1 (exp.f64 (neg.f64 t))) c_p)) (*.f64 (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n) (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)))
12.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))
9.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
5.0ms	(pow.f64 (+.f64 1 (exp.f64 (neg.f64 t))) c_p)

series1.7s (2.3%)

Counts

4 → 12

Calls

4 calls:

1.4s	(/.f64 (/.f64 (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n) (pow.f64 (+.f64 1 (exp.f64 (neg.f64 t))) c_p)) (*.f64 (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n) (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)))
112.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
80.0ms	(pow.f64 (+.f64 1 (exp.f64 (neg.f64 t))) c_p)
72.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))

simplify296.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

540 → 540

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4972	35935
1	4972	35935

prune2.5s (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	538	2	540
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	540	3	543

Merged error: 0.1b

Counts

543 → 3

Compiler

Compiled 29489 to 18948 computations (35.7% saved)

regimes197.0ms (0.3%)

Compiler: Compiled 2220 to 1856 computations (16.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	13
1	23	13

end0.0ms (0%)

sample41.8s (56.7%)

Algorithm

1×

intervals

Results

32.6s	2651×	body	8192	exit
3.6s	1857×	body	1024	overflowed
2.6s	11778×	body	128	overflowed
1.1s	1052×	body	512	overflowed
503.0ms	19225×	pre	128	true
293.0ms	556×	body	256	overflowed
183.0ms	1306×	body	128	valid
26.0ms	2×	body	8192	valid
20.0ms	10×	body	1024	valid
7.0ms	1×	body	4096	invalid
5.0ms	1×	body	4096	valid
5.0ms	6×	body	512	valid
3.0ms	1×	body	2048	overflowed
1.0ms	3×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 50 to 44 computations (12% saved)

Details

analyze8.6s (11.7%)

sample11.3s (15.2%)

simplify218.0ms (0.3%)

prune5.0ms (0%)

localize22.0ms (0%)

rewrite211.0ms (0.3%)

series1.9s (2.6%)

simplify229.0ms (0.3%)

prune1.6s (2.1%)

localize6.0ms (0%)

rewrite10.0ms (0%)

series73.0ms (0.1%)

simplify65.0ms (0.1%)

prune23.0ms (0%)

localize26.0ms (0%)

rewrite105.0ms (0.1%)

series2.0s (2.8%)

simplify96.0ms (0.1%)

prune569.0ms (0.8%)

localize22.0ms (0%)

rewrite228.0ms (0.3%)

series1.7s (2.3%)

simplify296.0ms (0.4%)

prune2.5s (3.4%)

regimes197.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample41.8s (56.7%)

end0.0ms (0%)

Profiling