Details

analyze41.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample22.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true
0.0ms	1×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify156.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4836	17
1	4836	17

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.4b

Counts

2 → 1

Compiler

Compiled 24 to 17 computations (29.2% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
14.0b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
7×	`add-sqr-sqrt_binary64_1464`
6×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
5×	`add-log-exp_binary64_1481`
4×	`times-frac_binary64_1448` `associate-/l*_binary64_1387` `pow1_binary64_1503`
3×	`sqrt-prod_binary64_1458` `difference-of-squares_binary64_1411`
2×	`cbrt-undiv_binary64_1476` `associate-/l/_binary64_1389` `flip3--_binary64_1446` `flip--_binary64_1417` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-/r*_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `div-sub_binary64_1447`

Counts

3 → 52

Calls

3 calls:

8.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
4.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

series89.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

35.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
33.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
21.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify69.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5039	1000

prune54.0ms (1.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Merged error: 0.0b

Counts

62 → 2

Compiler

Compiled 1075 to 364 computations (66.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 a b) a)
0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
0.0b	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))
0.0b	(/.f64 (-.f64 a b) a)

rewrite45.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64_1442`
68×	`add-sqr-sqrt_binary64_1464`
58×	`times-frac_binary64_1448`
41×	`add-cube-cbrt_binary64_1477`
20×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
19×	`associate-r_binary64_1382`
16×	`associate-l_binary64_1383`
9×	`associate-/l*_binary64_1387`
7×	`distribute-lft-out_binary64_1393` `pow1_binary64_1503` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
6×	`cbrt-undiv_binary64_1476` `associate-/r*_binary64_1386` `div-exp_binary64_1493`
4×	`cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `div-inv_binary64_1439` `add-log-exp_binary64_1481` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
3×	`sqrt-prod_binary64_1458`
2×	`clear-num_binary64_1441` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `flip--_binary64_1417` `frac-times_binary64_1452` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522` `div-sub_binary64_1447` `associate-*l/_binary64_1385`

Counts

4 → 143

Calls

4 calls:

18.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))
6.0ms	(/.f64 (-.f64 a b) a)
6.0ms	(/.f64 (+.f64 a b) a)
3.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))

series118.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))))
40.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 (-.f64 a b) a))
20.0ms	(/.f64 (-.f64 a b) a)
16.0ms	(/.f64 (+.f64 a b) a)

simplify54.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5294	2530

prune108.0ms (3.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	154	3	157

Merged error: 0b

Counts

157 → 3

Compiler

Compiled 3018 to 701 computations (76.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (-.f64 a b))
0.0b	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 1 (/.f64 a (-.f64 a b))))))
0.0b	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 1 (/.f64 a (-.f64 a b))))
0.1b	(/.f64 1 (/.f64 a (-.f64 a b)))

rewrite94.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

275×	`times-frac_binary64_1448`
214×	`add-sqr-sqrt_binary64_1464`
190×	`*-un-lft-identity_binary64_1442`
130×	`add-cube-cbrt_binary64_1477`
68×	`associate-r_binary64_1382`
62×	`add-exp-log_binary64_1480`
32×	`add-cbrt-cube_binary64_1478`
29×	`div-exp_binary64_1493`
26×	`associate-/r*_binary64_1386`
25×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
18×	`associate-/r/_binary64_1388`
16×	`associate-l_binary64_1383`
14×	`prod-exp_binary64_1491`
13×	`cbrt-undiv_binary64_1476`
11×	`div-inv_binary64_1439`
10×	`unswap-sqr_binary64_1410`
8×	`flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503`
6×	`cbrt-unprod_binary64_1475` `associate-/l*_binary64_1387` `1-exp_binary64_1486` `rec-exp_binary64_1492`
4×	`add-log-exp_binary64_1481`
3×	`distribute-lft-out_binary64_1393` `sqrt-prod_binary64_1458`
2×	`clear-num_binary64_1441` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `inv-pow_binary64_1527` `rem-sqrt-square_binary64_1455` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `pow-flip_binary64_1516` `frac-times_binary64_1452` `un-div-inv_binary64_1440` `pow1/2_binary64_1522` `associate-*l/_binary64_1385`

Counts

4 → 285

Calls

4 calls:

40.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 1 (/.f64 a (-.f64 a b))))
10.0ms	(/.f64 1 (/.f64 a (-.f64 a b)))
6.0ms	(/.f64 a (-.f64 a b))
1.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 1 (/.f64 a (-.f64 a b))))))

series127.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(sqrt.f64 (fabs.f64 (*.f64 (/.f64 (+.f64 a b) a) (/.f64 1 (/.f64 a (-.f64 a b))))))
41.0ms	(*.f64 (/.f64 (+.f64 a b) a) (/.f64 1 (/.f64 a (-.f64 a b))))
25.0ms	(/.f64 a (-.f64 a b))
20.0ms	(/.f64 1 (/.f64 a (-.f64 a b)))

simplify130.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4958	5476
1	4958	5476

prune247.0ms (8.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	297	3	300

Merged error: 0b

Counts

300 → 3

Compiler

Compiled 6496 to 2112 computations (67.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))))
0.0b	(sqrt.f64 (fabs.f64 (log.f64 (exp.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))))
0.0b	(log.f64 (exp.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
0.4b	(*.f64 (/.f64 b a) (/.f64 b a))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_1464`
40×	`times-frac_binary64_1448`
38×	`*-un-lft-identity_binary64_1442`
36×	`add-cube-cbrt_binary64_1477`
16×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
13×	`associate-r_binary64_1382` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `pow1_binary64_1503`
10×	`exp-prod_binary64_1494`
7×	`add-log-exp_binary64_1481`
6×	`log-pow_binary64_1531`
5×	`log-prod_binary64_1528`
4×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411` `div-exp_binary64_1493` `exp-sum_binary64_1488` `unswap-sqr_binary64_1410`
3×	`sqrt-prod_binary64_1458`
2×	`cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `rem-exp-log_binary64_1482` `exp-diff_binary64_1490`
1×	`pow2_binary64_1523` `sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `rem-sqrt-square_binary64_1455` `pow-plus_binary64_1505` `rem-log-exp_binary64_1483` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `pow-sqr_binary64_1415` `diff-log_binary64_1534` `frac-times_binary64_1452` `pow1/2_binary64_1522` `pow-prod-up_binary64_1512` `log-div_binary64_1529` `associate-*l/_binary64_1385`

Counts

4 → 117

Calls

4 calls:

11.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
5.0ms	(log.f64 (exp.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
5.0ms	(exp.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))))
1.0ms	(sqrt.f64 (fabs.f64 (log.f64 (exp.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))))

series132.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(log.f64 (exp.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
33.0ms	(sqrt.f64 (fabs.f64 (log.f64 (exp.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))))
26.0ms	(exp.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))))
19.0ms	(*.f64 (/.f64 b a) (/.f64 b a))

simplify95.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4982	1646
1	4982	1646

prune120.0ms (4.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	129	3	132

Merged error: 0b

Counts

132 → 3

Compiler

Compiled 2093 to 1217 computations (41.9% saved)

regimes211.0ms (7.3%)

Compiler: Compiled 2035 to 1440 computations (29.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	20
1	22	20

end0.0ms (0%)

sample870.0ms (30.2%)

Algorithm

1×

intervals

Results

275.0ms	8000×	body	128	valid
161.0ms	8000×	pre	128	true
2.0ms	122×	pre	128	false

Compiler

Compiled 271 to 193 computations (28.8% saved)

Details

analyze41.0ms (1.4%)

sample22.0ms (0.8%)

simplify156.0ms (5.4%)

prune4.0ms (0.1%)

localize7.0ms (0.3%)

rewrite20.0ms (0.7%)

series89.0ms (3.1%)

simplify69.0ms (2.4%)

prune54.0ms (1.9%)

localize9.0ms (0.3%)

rewrite45.0ms (1.6%)

series118.0ms (4.1%)

simplify54.0ms (1.9%)

prune108.0ms (3.8%)

localize12.0ms (0.4%)

rewrite94.0ms (3.3%)

series127.0ms (4.4%)

simplify130.0ms (4.5%)

prune247.0ms (8.6%)

localize9.0ms (0.3%)

rewrite32.0ms (1.1%)

series132.0ms (4.6%)

simplify95.0ms (3.3%)

prune120.0ms (4.2%)

regimes211.0ms (7.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample870.0ms (30.2%)

Profiling