Details

analyze80.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample33.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify226.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	497	18
1	497	18

prune8.0ms (0.1%)

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: 0.1b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(*.f64 3 (sqrt.f64 x))
0.3b	(/.f64 1/9 x)

rewrite77.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_11353`
31×	`*-un-lft-identity_binary64_11331`
26×	`add-cube-cbrt_binary64_11366`
24×	`times-frac_binary64_11337`
20×	`cancel-sign-sub-inv_binary64_11297`
14×	`associate--l+_binary64_11268`
13×	`add-exp-log_binary64_11369` `add-cbrt-cube_binary64_11367`
9×	`add-log-exp_binary64_11370`
6×	`pow1_binary64_11392` `associate-/l_binary64_11276` `associate-r*_binary64_11271`
4×	`div-inv_binary64_11328` `associate-/r*_binary64_11275` `sqrt-prod_binary64_11347`
3×	`distribute-lft-out--_binary64_11283` `div-exp_binary64_11382` `cbrt-undiv_binary64_11365` `associate-l_binary64_11272` `diff-log_binary64_11423`
2×	`cbrt-unprod_binary64_11364` `frac-sub_binary64_11340` `sub-neg_binary64_11324` `unswap-sqr_binary64_11299` `frac-2neg_binary64_11342` `flip3--_binary64_11335` `prod-exp_binary64_11380` `clear-num_binary64_11330` `flip--_binary64_11306`
1×	`*-commutative_binary64_11262` `difference-of-squares_binary64_11300` `associate--l-_binary64_11269` `pow-prod-down_binary64_11402`

Counts

4 → 109

Calls

4 calls:

33.0ms	(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
11.0ms	(*.f64 3 (sqrt.f64 x))
10.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
6.0ms	(/.f64 1/9 x)

series172.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
48.0ms	(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
34.0ms	(*.f64 3 (sqrt.f64 x))
21.0ms	(/.f64 1/9 x)

simplify122.0ms (2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4913	1720
1	4913	1720

prune239.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Merged error: 0.0b

Counts

123 → 10

Compiler

Compiled 2168 to 1499 computations (30.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(*.f64 3 (sqrt.f64 x))
0.5b	(/.f64 1 (*.f64 x 9))

rewrite64.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64_11369` `*-un-lft-identity_binary64_11331`
21×	`add-sqr-sqrt_binary64_11353`
16×	`add-cbrt-cube_binary64_11367`
15×	`add-cube-cbrt_binary64_11366`
14×	`cancel-sign-sub-inv_binary64_11297`
12×	`times-frac_binary64_11337`
9×	`pow1_binary64_11392` `add-log-exp_binary64_11370`
8×	`associate--l+_binary64_11268`
6×	`div-exp_binary64_11382` `associate-/l_binary64_11276` `associate-r*_binary64_11271`
5×	`distribute-lft-out--_binary64_11283` `div-inv_binary64_11328` `prod-exp_binary64_11380`
4×	`cbrt-undiv_binary64_11365` `sqrt-prod_binary64_11347`
3×	`cbrt-unprod_binary64_11364` `associate-l_binary64_11272` `diff-log_binary64_11423`
2×	`1-exp_binary64_11375` `frac-sub_binary64_11340` `sub-neg_binary64_11324` `pow-flip_binary64_11405` `rec-exp_binary64_11381` `unswap-sqr_binary64_11299` `frac-2neg_binary64_11342` `associate-/r*_binary64_11275` `flip3--_binary64_11335` `pow-prod-down_binary64_11402` `clear-num_binary64_11330` `flip--_binary64_11306`
1×	`*-commutative_binary64_11262` `difference-of-squares_binary64_11300` `associate--l-_binary64_11269` `inv-pow_binary64_11416`

Counts

4 → 105

Calls

4 calls:

25.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
9.0ms	(*.f64 3 (sqrt.f64 x))
8.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
8.0ms	(/.f64 1 (*.f64 x 9))

series170.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
56.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
26.0ms	(*.f64 3 (sqrt.f64 x))
24.0ms	(/.f64 1 (*.f64 x 9))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5119	1611

prune226.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	117	10	127

Merged error: 0.0b

Counts

127 → 10

Compiler

Compiled 2211 to 1585 computations (28.3% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(/.f64 (/.f64 1 x) 9)
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite140.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

147×	`times-frac_binary64_11337`
94×	`add-sqr-sqrt_binary64_11353`
93×	`*-un-lft-identity_binary64_11331`
88×	`add-cube-cbrt_binary64_11366`
50×	`cancel-sign-sub-inv_binary64_11297`
44×	`associate--l+_binary64_11268`
20×	`add-exp-log_binary64_11369`
16×	`associate-/l*_binary64_11276` `add-cbrt-cube_binary64_11367`
11×	`div-inv_binary64_11328`
9×	`add-log-exp_binary64_11370`
8×	`div-exp_binary64_11382`
6×	`pow1_binary64_11392` `associate-r_binary64_11271`
5×	`cbrt-undiv_binary64_11365`
4×	`associate-/r*_binary64_11275` `sqrt-prod_binary64_11347`
3×	`distribute-lft-out--_binary64_11283` `associate-l_binary64_11272` `diff-log_binary64_11423`
2×	`cbrt-unprod_binary64_11364` `frac-sub_binary64_11340` `sub-neg_binary64_11324` `unswap-sqr_binary64_11299` `frac-2neg_binary64_11342` `flip3--_binary64_11335` `prod-exp_binary64_11380` `clear-num_binary64_11330` `flip--_binary64_11306`
1×	`*-commutative_binary64_11262` `difference-of-squares_binary64_11300` `associate-/l/_binary64_11278` `1-exp_binary64_11375` `associate--l-_binary64_11269` `rec-exp_binary64_11381` `pow-prod-down_binary64_11402`

Counts

4 → 184

Calls

4 calls:

65.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
15.0ms	(*.f64 3 (sqrt.f64 x))
13.0ms	(/.f64 (/.f64 1 x) 9)
10.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))

series180.0ms (3%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
50.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
30.0ms	(*.f64 3 (sqrt.f64 x))
21.0ms	(/.f64 (/.f64 1 x) 9)

simplify164.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4933	3290
1	4933	3290

prune413.0ms (6.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	198	8	206

Merged error: 0.0b

Counts

206 → 8

Compiler

Compiled 3809 to 2699 computations (29.1% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
0.3b	(/.f64 (/.f64 y 3) (sqrt.f64 x))
0.3b	(/.f64 1/9 x)

rewrite194.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

297×	`times-frac_binary64_11337`
180×	`add-sqr-sqrt_binary64_11353`
169×	`*-un-lft-identity_binary64_11331`
164×	`add-cube-cbrt_binary64_11366`
95×	`cancel-sign-sub-inv_binary64_11297`
83×	`sqrt-prod_binary64_11347`
17×	`div-inv_binary64_11328`
16×	`associate-/l*_binary64_11276`
14×	`associate--l+_binary64_11268`
10×	`add-exp-log_binary64_11369` `add-cbrt-cube_binary64_11367`
9×	`associate-/r*_binary64_11275`
8×	`add-log-exp_binary64_11370`
5×	`difference-of-squares_binary64_11300`
4×	`div-exp_binary64_11382` `cbrt-undiv_binary64_11365`
3×	`distribute-lft-out--_binary64_11283` `pow1_binary64_11392` `diff-log_binary64_11423`
2×	`frac-sub_binary64_11340` `sub-neg_binary64_11324` `frac-2neg_binary64_11342` `flip3--_binary64_11335` `clear-num_binary64_11330` `flip--_binary64_11306`
1×	`associate-/l/_binary64_11278` `associate--l-_binary64_11269`

Counts

3 → 257

Calls

3 calls:

114.0ms	(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
16.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
6.0ms	(/.f64 1/9 x)

series164.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

78.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
65.0ms	(-.f64 (-.f64 1 (/.f64 1/9 x)) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
21.0ms	(/.f64 1/9 x)

simplify199.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4946	5826
1	4946	5826

prune500.0ms (8.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	265	1	266
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	265	9	274

Merged error: 0b

Counts

274 → 9

Compiler

Compiled 5418 to 3346 computations (38.2% saved)

regimes311.0ms (5.2%)

Compiler: Compiled 1694 to 1465 computations (13.5% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	18
1	45	18

end0.0ms (0%)

sample2.2s (36.1%)

Algorithm

1×

intervals

Results

685.0ms	8000×	body	128	valid
8.0ms	99×	body	128	invalid

Compiler

Compiled 595 to 517 computations (13.1% saved)

Details

analyze80.0ms (1.3%)

sample33.0ms (0.5%)

simplify226.0ms (3.8%)

prune8.0ms (0.1%)

localize17.0ms (0.3%)

rewrite77.0ms (1.3%)

series172.0ms (2.8%)

simplify122.0ms (2%)

prune239.0ms (4%)

localize18.0ms (0.3%)

rewrite64.0ms (1.1%)

series170.0ms (2.8%)

simplify91.0ms (1.5%)

prune226.0ms (3.7%)

localize19.0ms (0.3%)

rewrite140.0ms (2.3%)

series180.0ms (3%)

simplify164.0ms (2.7%)

prune413.0ms (6.9%)

localize18.0ms (0.3%)

rewrite194.0ms (3.2%)

series164.0ms (2.7%)

simplify199.0ms (3.3%)

prune500.0ms (8.3%)

regimes311.0ms (5.2%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.2s (36.1%)

Profiling