Details

analyze1.8s (5.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4999	209
1	4999	209
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
9.4%	90.4%	0.2%	11
9.4%	90.4%	0.2%	12
10.1%	89.6%	0.2%	13
20.8%	78.9%	0.2%	14

Symmetry

(sort x y)

(sort z t)

Compiler

Compiled 14 to 14 computations (0% saved)

sample43.0ms (0.1%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	83×	body	128	invalid

Compiler

Compiled 27 to 32 computations (-18.5% saved)

simplify445.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (433.0ms)

Iter	Nodes	Cost
0	4162	19
1	4162	19

prune3.0ms (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

Error

7.2b

Counts

2 → 1

Compiler

Compiled 26 to 26 computations (0% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 z 9) t)
0.3b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
6.8b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

rewrite128.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

6.8b

Rules

13×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
8×	`pow1_binary64_20258`
6×	`add-cube-cbrt_binary64_20232` `add-sqr-sqrt_binary64_20219` `*-un-lft-identity_binary64_20197`
5×	`add-log-exp_binary64_20236`
4×	`prod-exp_binary64_20246` `cbrt-unprod_binary64_20230`
3×	`times-frac_binary64_20203` `associate-/l_binary64_20142` `pow-prod-down_binary64_20268` `associate-r*_binary64_20137`
2×	`div-exp_binary64_20248` `cbrt-undiv_binary64_20231` `flip3--_binary64_20201` `associate-/l/_binary64_20144` `flip--_binary64_20172`
1×	`frac-2neg_binary64_20208` `div-sub_binary64_20202` `clear-num_binary64_20196` `div-inv_binary64_20194` `associate-/r_binary64_20141` `diff-log_binary64_20289` `sub-neg_binary64_20190` `cancel-sign-sub-inv_binary64_20163` `associate-l_binary64_20138` `-commutative_binary64_20128`

Counts

3 → 54

Calls

3 calls:

8.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
5.0ms	(.f64 (.f64 z 9) t)
4.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

Compiler

Compiled 1161 to 671 computations (42.2% saved)

series1.1s (3.1%)

Error

6.7b

Counts

3 → 57

Calls

3 calls:

673.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
292.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
83.0ms	(.f64 (.f64 z 9) t)

Compiler

Compiled 1189 to 1166 computations (1.9% saved)

simplify53.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5092	1631

prune104.0ms (0.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	99	12	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	12	112

Error

6.6b

Counts

112 → 12

Compiler

Compiled 1166 to 680 computations (41.7% saved)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 t z) 9)
0.3b	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))
6.7b	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) 2))

rewrite200.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

35×	`add-sqr-sqrt_binary64_20219`
30×	`add-exp-log_binary64_20235`
25×	`times-frac_binary64_20203`
20×	`add-cbrt-cube_binary64_20233` `*-un-lft-identity_binary64_20197`
18×	`add-cube-cbrt_binary64_20232`
16×	`associate-r_binary64_20137`
14×	`associate-l_binary64_20138`
11×	`prod-exp_binary64_20246`
10×	`pow1_binary64_20258`
8×	`div-exp_binary64_20248`
7×	`cbrt-unprod_binary64_20230`
6×	`unswap-sqr_binary64_20165`
5×	`add-log-exp_binary64_20236`
4×	`pow-prod-down_binary64_20268` `cbrt-undiv_binary64_20231`
2×	`1-exp_binary64_20241` `rec-exp_binary64_20247` `div-inv_binary64_20194` `*-commutative_binary64_20128`
1×	`frac-times_binary64_20207` `associate-l/_binary64_20140` `associate-r/_binary64_20139` `diff-log_binary64_20289` `flip3--_binary64_20201` `sub-neg_binary64_20190` `flip--_binary64_20172` `cancel-sign-sub-inv_binary64_20163`

Counts

3 → 86

Calls

3 calls:

16.0ms	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) 2))
5.0ms	(.f64 (.f64 t z) 9)
4.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))

Compiler

Compiled 2102 to 1211 computations (42.4% saved)

series1.1s (3.2%)

Error

6.6b

Counts

3 → 57

Calls

3 calls:

673.0ms	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) 2))
302.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))
81.0ms	(.f64 (.f64 t z) 9)

Compiler

Compiled 1291 to 1268 computations (1.8% saved)

simplify64.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4958	2444
1	4958	2444

prune158.0ms (0.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	134	9	143
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	141	14	155

Error

6.6b

Counts

155 → 14

Compiler

Compiled 1785 to 1078 computations (39.6% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))
0.4b	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) (sqrt.f64 2))
0.5b	(/.f64 (/.f64 1 a) (sqrt.f64 2))
6.7b	(.f64 (/.f64 (/.f64 1 a) (sqrt.f64 2)) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) (sqrt.f64 2)))

rewrite903.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

353×	`times-frac_binary64_20203`
258×	`add-sqr-sqrt_binary64_20219`
184×	`*-un-lft-identity_binary64_20197`
178×	`add-cube-cbrt_binary64_20232`
118×	`sqrt-prod_binary64_20213`
82×	`associate-l_binary64_20138`
50×	`add-exp-log_binary64_20235`
32×	`add-cbrt-cube_binary64_20233`
24×	`div-exp_binary64_20248`
22×	`associate-r_binary64_20137`
21×	`unswap-sqr_binary64_20165`
17×	`div-inv_binary64_20194`
16×	`associate-/l*_binary64_20142`
13×	`cbrt-undiv_binary64_20231`
12×	`associate-/r*_binary64_20141`
10×	`prod-exp_binary64_20246`
6×	`pow1_binary64_20258` `add-log-exp_binary64_20236` `cbrt-unprod_binary64_20230`
3×	`1-exp_binary64_20241` `rec-exp_binary64_20247` `associate-/l/_binary64_20144`
2×	`frac-2neg_binary64_20208` `clear-num_binary64_20196` `flip3--_binary64_20201` `flip--_binary64_20172`
1×	`pow-prod-down_binary64_20268` `frac-times_binary64_20207` `associate-l/_binary64_20140` `associate-r/_binary64_20139` `*-commutative_binary64_20128` `div-sub_binary64_20202` `diff-log_binary64_20289` `sub-neg_binary64_20190` `cancel-sign-sub-inv_binary64_20163`

Counts

4 → 321

Calls

4 calls:

48.0ms	(.f64 (/.f64 (/.f64 1 a) (sqrt.f64 2)) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) (sqrt.f64 2)))
8.0ms	(/.f64 (/.f64 1 a) (sqrt.f64 2))
7.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) (sqrt.f64 2))
4.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))

Compiler

Compiled 8342 to 5649 computations (32.3% saved)

series2.3s (6.8%)

Error

6.6b

Counts

4 → 78

Calls

4 calls:

1.3s	(.f64 (/.f64 (/.f64 1 a) (sqrt.f64 2)) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 t z) 9)) (sqrt.f64 2)))
587.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) (sqrt.f64 2))
310.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))
63.0ms	(/.f64 (/.f64 1 a) (sqrt.f64 2))

Compiler

Compiled 2378 to 2377 computations (0% saved)

simplify118.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

399 → 399

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5914	9993

prune543.0ms (1.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	390	9	399
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	401	12	413

Error

6.6b

Counts

413 → 12

Compiler

Compiled 6218 to 4195 computations (32.5% saved)

localize12.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 9 (.f64 t z))
0.3b	(-.f64 (.f64 x y) (.f64 9 (*.f64 t z)))
6.8b	(/.f64 (-.f64 (.f64 x y) (.f64 9 (.f64 t z))) (.f64 a 2))

rewrite142.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

13×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
8×	`pow1_binary64_20258`
6×	`add-cube-cbrt_binary64_20232` `add-sqr-sqrt_binary64_20219` `*-un-lft-identity_binary64_20197`
5×	`add-log-exp_binary64_20236`
4×	`prod-exp_binary64_20246` `cbrt-unprod_binary64_20230`
3×	`times-frac_binary64_20203` `associate-/l_binary64_20142` `pow-prod-down_binary64_20268` `associate-l*_binary64_20138`
2×	`div-exp_binary64_20248` `cbrt-undiv_binary64_20231` `flip3--_binary64_20201` `associate-/l/_binary64_20144` `flip--_binary64_20172`
1×	`frac-2neg_binary64_20208` `div-sub_binary64_20202` `clear-num_binary64_20196` `div-inv_binary64_20194` `associate-/r_binary64_20141` `diff-log_binary64_20289` `sub-neg_binary64_20190` `cancel-sign-sub-inv_binary64_20163` `associate-r_binary64_20137` `-commutative_binary64_20128`

Counts

3 → 54

Calls

3 calls:

9.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 9 (.f64 t z))) (.f64 a 2))
5.0ms	(.f64 9 (.f64 t z))
4.0ms	(-.f64 (.f64 x y) (.f64 9 (*.f64 t z)))

Compiler

Compiled 1246 to 688 computations (44.8% saved)

series1.1s (3.1%)

Error

6.6b

Counts

3 → 57

Calls

3 calls:

674.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 9 (.f64 t z))) (.f64 a 2))
288.0ms	(-.f64 (.f64 x y) (.f64 9 (*.f64 t z)))
74.0ms	(.f64 9 (.f64 t z))

Compiler

Compiled 1387 to 1364 computations (1.7% saved)

simplify67.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4994	1627
1	4994	1627

prune106.0ms (0.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	111	12	123

Error

6.6b

Counts

123 → 12

Compiler

Compiled 1019 to 561 computations (44.9% saved)

regimes22.2s (65.5%)

Accuracy

Total 0.6b remaining (7.4%)

Threshold costs 0.6b (7.4%)

Compiler

Compiled 204866 to 186588 computations (8.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	19
1	55	19

end32.0ms (0.1%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 65 to 65 computations (0% saved)

sample1.3s (3.8%)

Algorithm

1×

intervals

Results

342.0ms	8000×	body	128	valid
130.0ms	3121×	body	128	invalid

Compiler

Compiled 313 to 304 computations (2.9% saved)

Details

analyze1.8s (5.2%)

sample43.0ms (0.1%)

simplify445.0ms (1.3%)

prune3.0ms (0%)

localize10.0ms (0%)

rewrite128.0ms (0.4%)

series1.1s (3.1%)

simplify53.0ms (0.2%)

prune104.0ms (0.3%)

localize11.0ms (0%)

rewrite200.0ms (0.6%)

series1.1s (3.2%)

simplify64.0ms (0.2%)

prune158.0ms (0.5%)

localize13.0ms (0%)

rewrite903.0ms (2.7%)

series2.3s (6.8%)

simplify118.0ms (0.3%)

prune543.0ms (1.6%)

localize12.0ms (0%)

rewrite142.0ms (0.4%)

series1.1s (3.1%)

simplify67.0ms (0.2%)

prune106.0ms (0.3%)

regimes22.2s (65.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end32.0ms (0.1%)

sample1.3s (3.8%)

Profiling