Details

analyze234.0ms (1.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample17.0ms (0.1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
0.0ms	14×	body	128	invalid

Compiler

Compiled 23 to 24 computations (-4.3% saved)

simplify101.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	111	16
1	111	16

prune2.0ms (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: 7.4b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

3.6b	(.f64 y (+.f64 1 (.f64 z z)))
4.1b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64_7245`
26×	`add-exp-log_binary64_7277`
20×	`add-sqr-sqrt_binary64_7261`
18×	`*-un-lft-identity_binary64_7239` `add-cube-cbrt_binary64_7274`
16×	`add-cbrt-cube_binary64_7275`
13×	`associate-/l*_binary64_7184`
12×	`div-exp_binary64_7290`
6×	`cbrt-undiv_binary64_7273`
5×	`prod-exp_binary64_7288`
4×	`associate-*r/_binary64_7181` `pow1_binary64_7300`
3×	`cbrt-unprod_binary64_7272` `div-inv_binary64_7236` `associate-r_binary64_7179` `associate-l_binary64_7180`
2×	`flip-+_binary64_7213` `flip3-+_binary64_7242` `add-log-exp_binary64_7278` `1-exp_binary64_7283` `associate-/r/_binary64_7185` `rec-exp_binary64_7289`
1×	`associate-/r_binary64_7183` `distribute-lft-in_binary64_7188` `pow-prod-down_binary64_7310` `distribute-rgt-in_binary64_7189` `frac-2neg_binary64_7250` `unswap-sqr_binary64_7207` `associate-/l/_binary64_7186` `-commutative_binary64_7170` `clear-num_binary64_7238`

Counts

2 → 74

Calls

2 calls:

9.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
5.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series243.0ms (1.3%)

Counts

2 → 18

Calls

2 calls:

164.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
79.0ms	(.f64 y (+.f64 1 (.f64 z z)))

Compiler

Compiled 345 to 326 computations (5.5% saved)

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	6101	1437

prune92.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 5.5b

Counts

93 → 7

Compiler

Compiled 1495 to 886 computations (40.7% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

3.1b	(.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (+.f64 1 (.f64 z z))))
4.3b	(/.f64 (/.f64 1 x) (+.f64 1 (*.f64 z z)))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

173×	`times-frac_binary64_7245`
126×	`add-sqr-sqrt_binary64_7261`
93×	`*-un-lft-identity_binary64_7239`
86×	`add-cube-cbrt_binary64_7274`
76×	`add-exp-log_binary64_7277`
45×	`associate-r_binary64_7179`
40×	`div-exp_binary64_7290`
28×	`add-cbrt-cube_binary64_7275`
20×	`prod-exp_binary64_7288`
13×	`associate-/l_binary64_7184` `associate-l*_binary64_7180`
12×	`unswap-sqr_binary64_7207` `cbrt-undiv_binary64_7273`
10×	`1-exp_binary64_7283` `div-inv_binary64_7236` `rec-exp_binary64_7289`
6×	`cbrt-unprod_binary64_7272`
4×	`associate-/r/_binary64_7185` `pow1_binary64_7300`
3×	`associate-/r*_binary64_7183`
2×	`flip-+_binary64_7213` `flip3-+_binary64_7242` `add-log-exp_binary64_7278`
1×	`associate-r/_binary64_7181` `associate-l/_binary64_7182` `pow-prod-down_binary64_7310` `frac-times_binary64_7249` `frac-2neg_binary64_7250` `associate-/l/_binary64_7186` `*-commutative_binary64_7170` `clear-num_binary64_7238`

Counts

2 → 182

Calls

2 calls:

26.0ms	(.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (+.f64 1 (.f64 z z))))
8.0ms	(/.f64 (/.f64 1 x) (+.f64 1 (*.f64 z z)))

series224.0ms (1.2%)

Counts

2 → 15

Calls

2 calls:

156.0ms	(.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (+.f64 1 (.f64 z z))))
68.0ms	(/.f64 (/.f64 1 x) (+.f64 1 (*.f64 z z)))

Compiler

Compiled 328 to 310 computations (5.5% saved)

simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4941	4343
1	4941	4343

prune224.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	193	4	197
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	195	9	204

Merged error: 5.5b

Counts

204 → 9

Compiler

Compiled 4232 to 2605 computations (38.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (*.f64 z z))))
3.1b	(.f64 (/.f64 1 y) (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (*.f64 z z)))))
16.1b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
16.1b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite381.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

1578×	`times-frac_binary64_7245`
870×	`add-sqr-sqrt_binary64_7261`
700×	`*-un-lft-identity_binary64_7239`
673×	`add-cube-cbrt_binary64_7274`
573×	`sqrt-prod_binary64_7255`
510×	`associate-r_binary64_7179`
107×	`add-exp-log_binary64_7277`
62×	`div-exp_binary64_7290`
52×	`div-inv_binary64_7236`
45×	`unswap-sqr_binary64_7207`
41×	`add-cbrt-cube_binary64_7275`
24×	`prod-exp_binary64_7288`
20×	`sqrt-div_binary64_7256`
19×	`cbrt-undiv_binary64_7273`
16×	`associate-/r/_binary64_7185`
13×	`associate-/l_binary64_7184` `associate-l*_binary64_7180`
11×	`1-exp_binary64_7283` `rec-exp_binary64_7289`
10×	`flip-+_binary64_7213` `flip3-+_binary64_7242`
8×	`cbrt-unprod_binary64_7272` `pow1_binary64_7300`
6×	`associate-/r*_binary64_7183`
4×	`add-log-exp_binary64_7278`
2×	`pow1/2_binary64_7319` `rem-sqrt-square_binary64_7252` `sqrt-pow1_binary64_7257`
1×	`associate-r/_binary64_7181` `associate-l/_binary64_7182` `pow-prod-down_binary64_7310` `frac-times_binary64_7249` `frac-2neg_binary64_7250` `associate-/l/_binary64_7186` `*-commutative_binary64_7170` `clear-num_binary64_7238`

Counts

4 → 758

Calls

4 calls:

200.0ms	(.f64 (/.f64 1 y) (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (*.f64 z z)))))
9.0ms	(/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (*.f64 z z))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series390.0ms (2%)

Counts

4 → 37

Calls

4 calls:

168.0ms	(.f64 (/.f64 1 y) (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (*.f64 z z)))))
126.0ms	(/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (*.f64 z z))))
49.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
48.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

Compiler

Compiled 1096 to 966 computations (11.9% saved)

simplify277.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

795 → 795

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4962	22398
1	4962	22398

prune2.2s (11.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	794	1	795
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	797	7	804

Merged error: 5.5b

Counts

804 → 7

Compiler

Compiled 27434 to 16942 computations (38.2% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.8b	(/.f64 (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))) y) (sqrt.f64 (+.f64 1 (.f64 z z))))
2.4b	(/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (*.f64 z z)))) y)
16.1b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
16.1b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite652.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

6852×	`times-frac_binary64_7245`
2927×	`add-sqr-sqrt_binary64_7261`
2925×	`*-un-lft-identity_binary64_7239` `add-cube-cbrt_binary64_7274`
1752×	`sqrt-prod_binary64_7255`
340×	`associate-/l*_binary64_7184`
184×	`div-inv_binary64_7236`
56×	`sqrt-div_binary64_7256`
52×	`associate-/r/_binary64_7185`
41×	`add-exp-log_binary64_7277`
28×	`flip-+_binary64_7213` `flip3-+_binary64_7242` `div-exp_binary64_7290`
27×	`add-cbrt-cube_binary64_7275`
16×	`cbrt-undiv_binary64_7273`
9×	`associate-/r*_binary64_7183`
6×	`pow1_binary64_7300`
4×	`add-log-exp_binary64_7278`
2×	`pow1/2_binary64_7319` `rem-sqrt-square_binary64_7252` `1-exp_binary64_7283` `frac-2neg_binary64_7250` `associate-/l/_binary64_7186` `rec-exp_binary64_7289` `sqrt-pow1_binary64_7257` `clear-num_binary64_7238`

Counts

4 → 2209

Calls

4 calls:

94.0ms	(/.f64 (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))) y) (sqrt.f64 (+.f64 1 (.f64 z z))))
24.0ms	(/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (*.f64 z z)))) y)
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series481.0ms (2.5%)

Counts

4 → 40

Calls

4 calls:

221.0ms	(/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (*.f64 z z)))) y)
160.0ms	(/.f64 (/.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))) y) (sqrt.f64 (+.f64 1 (.f64 z z))))
53.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
46.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

Compiler

Compiled 1156 to 1000 computations (13.5% saved)

simplify1.1s (5.8%)

Algorithm

1×	egg-herbie

Counts

2249 → 2249

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4965	127404
1	4965	127404

prune10.4s (54.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	2249	0	2249
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	2249	7	2256

Merged error: 5.5b

Counts

2256 → 7

Compiler

Compiled 91325 to 53297 computations (41.6% saved)

regimes553.0ms (2.9%)

Compiler: Compiled 5903 to 5047 computations (14.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	12	16

end0.0ms (0%)

sample1.2s (6.4%)

Algorithm

1×

intervals

Results

298.0ms	8000×	body	128	valid
16.0ms	437×	body	128	invalid

Compiler

Compiled 777 to 655 computations (15.7% saved)

Details

analyze234.0ms (1.2%)

sample17.0ms (0.1%)

simplify101.0ms (0.5%)

prune2.0ms (0%)

localize7.0ms (0%)

rewrite21.0ms (0.1%)

series243.0ms (1.3%)

simplify83.0ms (0.4%)

prune92.0ms (0.5%)

localize8.0ms (0%)

rewrite58.0ms (0.3%)

series224.0ms (1.2%)

simplify104.0ms (0.5%)

prune224.0ms (1.2%)

localize13.0ms (0.1%)

rewrite381.0ms (2%)

series390.0ms (2%)

simplify277.0ms (1.5%)

prune2.2s (11.5%)

localize9.0ms (0%)

rewrite652.0ms (3.4%)

series481.0ms (2.5%)

simplify1.1s (5.8%)

prune10.4s (54.4%)

regimes553.0ms (2.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (6.4%)

Profiling