Details

analyze461.0ms (5.7%)

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)

sample31.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 23 to 24 computations (-4.3% saved)

simplify154.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	111	16
1	111	16

prune4.0ms (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: 8.5b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

4.4b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
5.0b	(.f64 y (+.f64 1 (.f64 z z)))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64_8950`
26×	`add-exp-log_binary64_8982`
20×	`add-sqr-sqrt_binary64_8966`
18×	`add-cube-cbrt_binary64_8979` `*-un-lft-identity_binary64_8944`
16×	`add-cbrt-cube_binary64_8980`
13×	`associate-/l*_binary64_8889`
12×	`div-exp_binary64_8995`
6×	`cbrt-undiv_binary64_8978`
5×	`prod-exp_binary64_8993`
4×	`associate-*r/_binary64_8886` `pow1_binary64_9005`
3×	`associate-l_binary64_8885` `associate-r_binary64_8884` `div-inv_binary64_8941` `cbrt-unprod_binary64_8977`
2×	`flip3-+_binary64_8947` `associate-/r/_binary64_8890` `rec-exp_binary64_8994` `flip-+_binary64_8918` `add-log-exp_binary64_8983` `1-exp_binary64_8988`
1×	`distribute-rgt-in_binary64_8894` `clear-num_binary64_8943` `associate-/r_binary64_8888` `frac-2neg_binary64_8955` `-commutative_binary64_8875` `associate-/l/_binary64_8891` `unswap-sqr_binary64_8912` `pow-prod-down_binary64_9015` `distribute-lft-in_binary64_8893`

Counts

2 → 74

Calls

2 calls:

16.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
11.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series147.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

80.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
62.0ms	(.f64 y (+.f64 1 (.f64 z z)))

simplify121.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5190	1317

prune177.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	8	81

Merged error: 7.1b

Counts

81 → 8

Compiler

Compiled 1401 to 852 computations (39.2% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
4.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (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)))

rewrite92.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64_8982`
31×	`times-frac_binary64_8950`
30×	`add-cbrt-cube_binary64_8980`
28×	`sqrt-div_binary64_8961`
24×	`add-sqr-sqrt_binary64_8966`
22×	`add-cube-cbrt_binary64_8979` `*-un-lft-identity_binary64_8944`
18×	`div-exp_binary64_8995`
16×	`associate-*r/_binary64_8886`
15×	`prod-exp_binary64_8993`
14×	`flip3-+_binary64_8947` `flip-+_binary64_8918`
13×	`associate-/l*_binary64_8889`
11×	`pow1_binary64_9005`
9×	`cbrt-undiv_binary64_8978` `sqrt-prod_binary64_8960` `cbrt-unprod_binary64_8977`
8×	`associate-/r/_binary64_8890` `frac-times_binary64_8954`
6×	`associate-r_binary64_8884`
4×	`associate-*l/_binary64_8887` `add-log-exp_binary64_8983`
3×	`rec-exp_binary64_8994` `pow-prod-down_binary64_9015` `div-inv_binary64_8941` `1-exp_binary64_8988`
2×	`pow1/2_binary64_9024` `rem-sqrt-square_binary64_8957` `sqrt-pow1_binary64_8962`
1×	`associate-l_binary64_8885` `clear-num_binary64_8943` `associate-/r_binary64_8888` `frac-2neg_binary64_8955` `-commutative_binary64_8875` `associate-/l/_binary64_8891`

Counts

4 → 123

Calls

4 calls:

30.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
22.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
6.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series228.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
59.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
38.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
33.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify174.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4955	2530
1	4955	2530

prune255.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	136	7	143

Merged error: 7.1b

Counts

143 → 7

Compiler

Compiled 2994 to 1856 computations (38% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
0.8b	(.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (/.f64 (/.f64 1 x) (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)))

rewrite167.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`times-frac_binary64_8950`
145×	`add-exp-log_binary64_8982`
103×	`add-sqr-sqrt_binary64_8966`
84×	`associate-r_binary64_8884`
81×	`*-un-lft-identity_binary64_8944`
79×	`add-cube-cbrt_binary64_8979`
66×	`div-exp_binary64_8995`
53×	`prod-exp_binary64_8993`
48×	`sqrt-prod_binary64_8960`
45×	`add-cbrt-cube_binary64_8980`
19×	`rec-exp_binary64_8994` `1-exp_binary64_8988`
17×	`cbrt-undiv_binary64_8978`
13×	`cbrt-unprod_binary64_8977`
11×	`pow1_binary64_9005`
10×	`sqrt-div_binary64_8961`
9×	`associate-l_binary64_8885` `div-inv_binary64_8941`
7×	`unswap-sqr_binary64_8912`
6×	`associate-/r/_binary64_8890`
5×	`flip3-+_binary64_8947` `associate-*l/_binary64_8887` `flip-+_binary64_8918`
4×	`add-log-exp_binary64_8983`
3×	`associate-/l*_binary64_8889`
2×	`pow1/2_binary64_9024` `rem-sqrt-square_binary64_8957` `pow-prod-down_binary64_9015` `sqrt-pow1_binary64_8962` `pow-flip_binary64_9018`
1×	`inv-pow_binary64_9029` `associate-r/_binary64_8886` `frac-times_binary64_8954` `clear-num_binary64_8943` `associate-/r_binary64_8888` `frac-2neg_binary64_8955` `*-commutative_binary64_8875`

Counts

4 → 216

Calls

4 calls:

85.0ms	(.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))))
14.0ms	(/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series242.0ms (3%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
82.0ms	(.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))))
35.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
35.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify202.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4935	5475
1	4935	5475

prune593.0ms (7.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	229	6	235

Merged error: 7.1b

Counts

235 → 6

Compiler

Compiled 6062 to 3826 computations (36.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b	(/.f64 (/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x) (sqrt.f64 (+.f64 1 (*.f64 z z))))
1.7b	(/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x)
16.1b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
16.1b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite169.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

477×	`times-frac_binary64_8950`
202×	`add-sqr-sqrt_binary64_8966`
200×	`add-cube-cbrt_binary64_8979` `*-un-lft-identity_binary64_8944`
102×	`sqrt-prod_binary64_8960`
56×	`sqrt-div_binary64_8961`
52×	`associate-/r/_binary64_8890`
51×	`add-exp-log_binary64_8982`
50×	`associate-*l/_binary64_8887`
40×	`associate-/l*_binary64_8889`
34×	`div-inv_binary64_8941`
30×	`div-exp_binary64_8995`
28×	`flip3-+_binary64_8947` `flip-+_binary64_8918`
27×	`add-cbrt-cube_binary64_8980`
14×	`cbrt-undiv_binary64_8978`
9×	`associate-/r*_binary64_8888`
6×	`pow1_binary64_9005` `prod-exp_binary64_8993`
4×	`rec-exp_binary64_8994` `add-log-exp_binary64_8983` `1-exp_binary64_8988`
2×	`clear-num_binary64_8943` `frac-2neg_binary64_8955` `associate-/l/_binary64_8891` `pow1/2_binary64_9024` `rem-sqrt-square_binary64_8957` `sqrt-pow1_binary64_8962` `cbrt-unprod_binary64_8977`

Counts

4 → 338

Calls

4 calls:

44.0ms	(/.f64 (/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x) (sqrt.f64 (+.f64 1 (*.f64 z z))))
20.0ms	(/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x)
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series202.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x)
62.0ms	(/.f64 (/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x) (sqrt.f64 (+.f64 1 (*.f64 z z))))
40.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
31.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify323.0ms (4%)

Algorithm

1×	egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4955	14073
1	4955	14073

prune1.1s (13.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	350	6	356

Merged error: 7.1b

Counts

356 → 6

Compiler

Compiled 11024 to 6461 computations (41.4% saved)

regimes903.0ms (11.2%)

Compiler: Compiled 5439 to 4483 computations (17.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	32
1	17	32

end0.0ms (0%)

sample2.2s (27.4%)

Algorithm

1×

intervals

Results

556.0ms	8000×	body	128	valid
29.0ms	434×	body	128	invalid

Compiler

Compiled 718 to 583 computations (18.8% saved)

Details

analyze461.0ms (5.7%)

sample31.0ms (0.4%)

simplify154.0ms (1.9%)

prune4.0ms (0%)

localize14.0ms (0.2%)

rewrite38.0ms (0.5%)

series147.0ms (1.8%)

simplify121.0ms (1.5%)

prune177.0ms (2.2%)

localize20.0ms (0.3%)

rewrite92.0ms (1.1%)

series228.0ms (2.8%)

simplify174.0ms (2.2%)

prune255.0ms (3.1%)

localize22.0ms (0.3%)

rewrite167.0ms (2.1%)

series242.0ms (3%)

simplify202.0ms (2.5%)

prune593.0ms (7.3%)

localize20.0ms (0.2%)

rewrite169.0ms (2.1%)

series202.0ms (2.5%)

simplify323.0ms (4%)

prune1.1s (13.7%)

regimes903.0ms (11.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (27.4%)

Profiling