Details

analyze83.0ms (0.1%)

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)

sample42.0ms (0%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
10.0ms	256×	pre	128	true

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify329.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4836	17
1	4836	17

prune13.0ms (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: 13.8b

Counts

2 → 2

Compiler

Compiled 35 to 26 computations (25.7% saved)

localize20.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
0.0b	(-.f64 (.f64 a a) (.f64 b b))
13.4b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite28.0ms (0%)

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:

13.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
7.0ms	(-.f64 (.f64 a a) (.f64 b b))
2.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

series205.0ms (0.1%)

Counts

3 → 9

Calls

3 calls:

91.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
68.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
46.0ms	(-.f64 (.f64 a a) (.f64 b b))

simplify168.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	5039	1000

prune543.0ms (0.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	42	19	61
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	44	19	63

Merged error: 0.0b

Counts

63 → 19

Compiler

Compiled 1491 to 586 computations (60.7% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite57.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_1464`
21×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
19×	`times-frac_binary64_1448`
13×	`associate-r_binary64_1382`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
7×	`pow1_binary64_1503`
6×	`add-log-exp_binary64_1481`
3×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `associate-l_binary64_1383` `sqrt-prod_binary64_1458`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417` `prod-exp_binary64_1491` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `pow1/2_binary64_1522` `div-sub_binary64_1447`

Counts

4 → 87

Calls

4 calls:

16.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
14.0ms	(*.f64 b (/.f64 b a))
7.0ms	(-.f64 a (*.f64 b (/.f64 b a)))
3.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))

series195.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
61.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
39.0ms	(-.f64 a (*.f64 b (/.f64 b a)))
27.0ms	(*.f64 b (/.f64 b a))

simplify152.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4967	1505
1	4967	1505

prune1.1s (0.7%)

Pruning

38 alts after pruning (38 fresh and 0 done)

	Pruned	Kept	Total
New	69	30	99
Fresh	10	8	18
Picked	1	0	1
Done	0	0	0
Total	80	38	118

Merged error: 0b

Counts

118 → 38

Compiler

Compiled 2546 to 1002 computations (60.6% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite121.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`add-sqr-sqrt_binary64_1464`
80×	`times-frac_binary64_1448`
74×	`*-un-lft-identity_binary64_1442`
69×	`add-cube-cbrt_binary64_1477`
36×	`swap-sqr_binary64_1409`
34×	`associate-r_binary64_1382` `associate-l_binary64_1383` `pow1_binary64_1503`
31×	`sqrt-prod_binary64_1458`
30×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
14×	`sqrt-div_binary64_1459`
12×	`unswap-sqr_binary64_1410`
10×	`difference-of-squares_binary64_1411`
9×	`sqrt-pow1_binary64_1460` `cbrt-unprod_binary64_1475` `pow1/2_binary64_1522` `prod-exp_binary64_1491`
8×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `div-exp_binary64_1493`
7×	`flip3--_binary64_1446` `flip--_binary64_1417` `pow-prod-up_binary64_1512`
6×	`frac-times_binary64_1452`
5×	`pow-prod-down_binary64_1513` `pow-sqr_binary64_1415`
4×	`associate-r/_binary64_1384` `add-log-exp_binary64_1481` `associate-l/_binary64_1385`
3×	`pow2_binary64_1523` `rem-sqrt-square_binary64_1455` `pow-plus_binary64_1505` `*-commutative_binary64_1373`
1×	`sqr-abs_binary64_1457` `sqrt-unprod_binary64_1462` `rem-square-sqrt_binary64_1454`

Counts

4 → 215

Calls

4 calls:

25.0ms	(.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 b a) (/.f64 b a)))) (sqrt.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
22.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
22.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
6.0ms	(sqrt.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))))

series189.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))))
48.0ms	(.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 b a) (/.f64 b a)))) (sqrt.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
43.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
35.0ms	(*.f64 (/.f64 b a) (/.f64 b a))

simplify148.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5349	3061

prune6.5s (4.1%)

Pruning

58 alts after pruning (57 fresh and 1 done)

	Pruned	Kept	Total
New	189	38	227
Fresh	18	19	37
Picked	0	1	1
Done	0	0	0
Total	207	58	265

Merged error: 0b

Counts

265 → 58

Compiler

Compiled 7192 to 3753 computations (47.8% saved)

localize97.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (/.f64 b a) (/.f64 b a))
0.4b	(*.f64 (/.f64 b a) (/.f64 b a))
0.4b	(pow.f64 (/.f64 b a) 6)
0.7b	(pow.f64 (sqrt.f64 (/.f64 b a)) 4)

rewrite269.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`add-sqr-sqrt_binary64_1464`
98×	`times-frac_binary64_1448`
77×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
32×	`add-exp-log_binary64_1480`
29×	`unpow-prod-down_binary64_1521`
28×	`add-cbrt-cube_binary64_1478`
26×	`associate-r_binary64_1382` `swap-sqr_binary64_1409` `associate-l_binary64_1383`
21×	`pow1_binary64_1503`
13×	`sqrt-prod_binary64_1458`
10×	`div-inv_binary64_1439`
9×	`div-exp_binary64_1493`
8×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
6×	`pow-unpow_binary64_1519`
4×	`add-log-exp_binary64_1481` `pow-pow_binary64_1514`
3×	`pow-exp_binary64_1510`
2×	`pow2_binary64_1523` `associate-r/_binary64_1384` `pow-plus_binary64_1505` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `pow-sqr_binary64_1415` `frac-times_binary64_1452` `sqr-pow_binary64_1414` `pow-prod-up_binary64_1512` `associate-*l/_binary64_1385` `pow-to-exp_binary64_1511`
1×	`sqrt-pow1_binary64_1460` `pow1/2_binary64_1522` `sqrt-pow2_binary64_1461`

Counts

4 → 195

Calls

4 calls:

47.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
41.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
18.0ms	(pow.f64 (sqrt.f64 (/.f64 b a)) 4)
17.0ms	(pow.f64 (/.f64 b a) 6)

series798.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

534.0ms	(pow.f64 (sqrt.f64 (/.f64 b a)) 4)
130.0ms	(pow.f64 (/.f64 b a) 6)
72.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
60.0ms	(*.f64 (/.f64 b a) (/.f64 b a))

simplify287.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (168.0ms)

Iter	Nodes	Cost
0	5748	2230

prune9.6s (6%)

Pruning

80 alts after pruning (78 fresh and 2 done)

	Pruned	Kept	Total
New	185	22	207
Fresh	0	56	56
Picked	0	1	1
Done	0	1	1
Total	185	80	265

Merged error: 0b

Counts

265 → 80

Compiler

Compiled 11284 to 5130 computations (54.5% saved)

regimes17.2s (10.7%)

Compiler: Compiled 91449 to 56322 computations (38.4% saved)

bsearch1.5min (56.8%)

simplify20.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	75
1	47	75

end0.0ms (0%)

sample30.9s (19.4%)

Algorithm

1×

intervals

Results

510.0ms	8000×	body	128	valid
288.0ms	8000×	pre	128	true
5.0ms	129×	pre	128	false

Compiler

Compiled 13115 to 8069 computations (38.5% saved)

Pareto

0.1901082012494141

Details

analyze83.0ms (0.1%)

sample42.0ms (0%)

simplify329.0ms (0.2%)

prune13.0ms (0%)

localize20.0ms (0%)

rewrite28.0ms (0%)

series205.0ms (0.1%)

simplify168.0ms (0.1%)

prune543.0ms (0.3%)

localize16.0ms (0%)

rewrite57.0ms (0%)

series195.0ms (0.1%)

simplify152.0ms (0.1%)

prune1.1s (0.7%)

localize25.0ms (0%)

rewrite121.0ms (0.1%)

series189.0ms (0.1%)

simplify148.0ms (0.1%)

prune6.5s (4.1%)

localize97.0ms (0.1%)

rewrite269.0ms (0.2%)

series798.0ms (0.5%)

simplify287.0ms (0.2%)

prune9.6s (6%)

regimes17.2s (10.7%)

bsearch1.5min (56.8%)

simplify20.0ms (0%)

end0.0ms (0%)

sample30.9s (19.4%)

Profiling