Details

analyze1.7s (9.6%)

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)

sample53.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
4.0ms	102×	body	128	invalid

Compiler

Compiled 27 to 32 computations (-18.5% saved)

simplify467.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (461.0ms)

Iter	Nodes	Cost
0	4162	19
1	4162	19

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

Error

8.2b

Counts

2 → 1

Compiler

Compiled 26 to 26 computations (0% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 z 9) t)
0.4b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
7.7b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

rewrite87.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

8.0b

Rules

13×	`add-exp-log_binary64_21599` `add-cbrt-cube_binary64_21597`
8×	`pow1_binary64_21622`
6×	`add-cube-cbrt_binary64_21596` `add-sqr-sqrt_binary64_21583` `*-un-lft-identity_binary64_21561`
5×	`add-log-exp_binary64_21600`
4×	`prod-exp_binary64_21610` `cbrt-unprod_binary64_21594`
3×	`times-frac_binary64_21567` `associate-/l_binary64_21506` `pow-prod-down_binary64_21632` `associate-r*_binary64_21501`
2×	`div-exp_binary64_21612` `cbrt-undiv_binary64_21595` `flip3--_binary64_21565` `associate-/l/_binary64_21508` `flip--_binary64_21536`
1×	`frac-2neg_binary64_21572` `div-sub_binary64_21566` `clear-num_binary64_21560` `div-inv_binary64_21558` `associate-/r_binary64_21505` `diff-log_binary64_21653` `sub-neg_binary64_21554` `cancel-sign-sub-inv_binary64_21527` `associate-l_binary64_21502` `-commutative_binary64_21492`

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 1206 to 698 computations (42.1% saved)

series713.0ms (4%)

Error

7.9b

Counts

3 → 57

Calls

3 calls:

428.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
193.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
55.0ms	(.f64 (.f64 z 9) t)

Compiler

Compiled 1725 to 1383 computations (19.8% saved)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5092	1631

prune104.0ms (0.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	9	112

Error

7.8b

Counts

112 → 9

Compiler

Compiled 1825 to 958 computations (47.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 z 9) t)
0.4b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
7.8b	(.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (/.f64 1/2 a))

rewrite99.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

17×	`add-sqr-sqrt_binary64_21583`
16×	`associate-r_binary64_21501`
13×	`add-exp-log_binary64_21599` `add-cbrt-cube_binary64_21597`
12×	`add-cube-cbrt_binary64_21596` `*-un-lft-identity_binary64_21561`
10×	`pow1_binary64_21622` `times-frac_binary64_21567`
5×	`prod-exp_binary64_21610` `add-log-exp_binary64_21600` `cbrt-unprod_binary64_21594`
4×	`pow-prod-down_binary64_21632` `associate-l_binary64_21502`
3×	`flip3--_binary64_21565` `flip--_binary64_21536`
2×	`frac-times_binary64_21571` `unswap-sqr_binary64_21529` `associate-l/_binary64_21504` `-commutative_binary64_21492`
1×	`div-exp_binary64_21612` `cbrt-undiv_binary64_21595` `associate-*r/_binary64_21503` `div-inv_binary64_21558` `diff-log_binary64_21653` `sub-neg_binary64_21554` `cancel-sign-sub-inv_binary64_21527`

Counts

3 → 66

Calls

3 calls:

9.0ms	(.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (/.f64 1/2 a))
5.0ms	(.f64 (.f64 z 9) t)
4.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

Compiler

Compiled 1508 to 876 computations (41.9% saved)

series680.0ms (3.8%)

Error

7.8b

Counts

3 → 57

Calls

3 calls:

407.0ms	(.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (/.f64 1/2 a))
186.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
52.0ms	(.f64 (.f64 z 9) t)

Compiler

Compiled 1725 to 1383 computations (19.8% saved)

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5292	1963

prune109.0ms (0.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	121	11	132

Error

7.8b

Counts

132 → 11

Compiler

Compiled 2129 to 1129 computations (47% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 t z) 9)
0.4b	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))
0.6b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))
7.5b	(/.f64 a (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2))

rewrite623.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

471×	`times-frac_binary64_21567`
232×	`add-cube-cbrt_binary64_21596` `add-sqr-sqrt_binary64_21583` `*-un-lft-identity_binary64_21561`
57×	`associate-/r*_binary64_21505`
35×	`add-exp-log_binary64_21599`
23×	`add-cbrt-cube_binary64_21597`
22×	`div-inv_binary64_21558`
18×	`div-exp_binary64_21612`
10×	`pow1_binary64_21622`
9×	`cbrt-undiv_binary64_21595`
6×	`add-log-exp_binary64_21600` `associate-/r/_binary64_21507` `associate-/l*_binary64_21506`
3×	`1-exp_binary64_21605` `rec-exp_binary64_21611` `pow-prod-down_binary64_21632` `prod-exp_binary64_21610` `cbrt-unprod_binary64_21594` `associate-r_binary64_21501`
2×	`frac-2neg_binary64_21572` `clear-num_binary64_21560`
1×	`inv-pow_binary64_21646` `pow-flip_binary64_21635` `diff-log_binary64_21653` `flip3--_binary64_21565` `sub-neg_binary64_21554` `flip--_binary64_21536` `cancel-sign-sub-inv_binary64_21527` `associate-l_binary64_21502` `*-commutative_binary64_21492`

Counts

4 → 304

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))
8.0ms	(/.f64 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 9926 to 5742 computations (42.2% saved)

series981.0ms (5.5%)

Error

7.8b

Counts

4 → 78

Calls

4 calls:

412.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))
274.0ms	(/.f64 a (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2))
184.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))
56.0ms	(.f64 (.f64 t z) 9)

Compiler

Compiled 2958 to 2407 computations (18.6% saved)

simplify156.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

382 → 382

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4959	12076
1	4959	12076

prune543.0ms (3.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	376	6	382
Fresh	5	3	8
Picked	1	0	1
Done	0	2	2
Total	382	11	393

Error

7.8b

Counts

393 → 11

Compiler

Compiled 9910 to 5341 computations (46.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 t z) 9)
0.4b	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))
0.4b	(/.f64 1 (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2))
7.5b	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))

rewrite2.9s (16.2%)

Algorithm

1×	rewrite-expression-head

Error

7.8b

Rules

1976×	`times-frac_binary64_21567`
852×	`add-cube-cbrt_binary64_21596` `add-sqr-sqrt_binary64_21583` `*-un-lft-identity_binary64_21561`
107×	`div-inv_binary64_21558`
103×	`add-exp-log_binary64_21599`
77×	`div-exp_binary64_21612`
57×	`associate-/r*_binary64_21505`
35×	`add-cbrt-cube_binary64_21597`
18×	`cbrt-undiv_binary64_21595`
17×	`1-exp_binary64_21605` `rec-exp_binary64_21611`
16×	`associate-/r/_binary64_21507` `associate-/l*_binary64_21506`
10×	`pow1_binary64_21622`
6×	`add-log-exp_binary64_21600`
3×	`pow-prod-down_binary64_21632` `prod-exp_binary64_21610` `cbrt-unprod_binary64_21594` `associate-r_binary64_21501`
2×	`frac-2neg_binary64_21572` `clear-num_binary64_21560`
1×	`associate-/l/_binary64_21508` `inv-pow_binary64_21646` `pow-flip_binary64_21635` `diff-log_binary64_21653` `flip3--_binary64_21565` `sub-neg_binary64_21554` `flip--_binary64_21536` `cancel-sign-sub-inv_binary64_21527` `associate-l_binary64_21502` `*-commutative_binary64_21492`

Counts

4 → 781

Calls

4 calls:

28.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))
12.0ms	(/.f64 1 (/.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 30773 to 20116 computations (34.6% saved)

series889.0ms (5%)

Error

7.8b

Counts

4 → 75

Calls

4 calls:

445.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2)))
204.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 t z) 9))
130.0ms	(/.f64 1 (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 t z) 9)) 2))
54.0ms	(.f64 (.f64 t z) 9)

Compiler

Compiled 2967 to 2487 computations (16.2% saved)

simplify374.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

856 → 856

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4965	36322
1	4965	36322

prune2.1s (11.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	853	3	856
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	856	11	867

Error

7.8b

Counts

867 → 11

Compiler

Compiled 26296 to 15358 computations (41.6% saved)

regimes2.0s (11.6%)

Accuracy

Total 0.4b remaining (5.5%)

Threshold costs 0.4b (5.5%)

Compiler

Compiled 25495 to 22097 computations (13.3% saved)

bsearch0.0ms (0%)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	22
1	68	22

Remove

(sort z t)

(sort x y)

Compiler

Compiled 60 to 56 computations (6.7% saved)

end0.0ms (0%)

sample2.9s (16.5%)

Algorithm

1×

intervals

Results

575.0ms	8000×	body	128	valid
141.0ms	3134×	body	128	invalid

Compiler

Compiled 2128 to 1849 computations (13.1% saved)

Details

analyze1.7s (9.6%)

sample53.0ms (0.3%)

simplify467.0ms (2.6%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite87.0ms (0.5%)

series713.0ms (4%)

simplify56.0ms (0.3%)

prune104.0ms (0.6%)

localize10.0ms (0.1%)

rewrite99.0ms (0.6%)

series680.0ms (3.8%)

simplify77.0ms (0.4%)

prune109.0ms (0.6%)

localize11.0ms (0.1%)

rewrite623.0ms (3.5%)

series981.0ms (5.5%)

simplify156.0ms (0.9%)

prune543.0ms (3.1%)

localize12.0ms (0.1%)

rewrite2.9s (16.2%)

series889.0ms (5%)

simplify374.0ms (2.1%)

prune2.1s (11.9%)

regimes2.0s (11.6%)

bsearch0.0ms (0%)

simplify23.0ms (0.1%)

end0.0ms (0%)

sample2.9s (16.5%)

Profiling