Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	62×	body	1024	valid
4.0ms	142×	body	128	valid
2.0ms	28×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify172.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune6.0ms (0.2%)

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: 28.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_1471`
14×	`add-sqr-sqrt_binary64_1477` `*-un-lft-identity_binary64_1455`
6×	`cancel-sign-sub-inv_binary64_1421`
5×	`add-cube-cbrt_binary64_1490`
4×	`difference-of-squares_binary64_1424` `add-log-exp_binary64_1494`
3×	`distribute-lft-out--_binary64_1407` `pow1_binary64_1516`
2×	`distribute-lft-out_binary64_1406` `sqrt-div_binary64_1472` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
1×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `flip-+_binary64_1429` `flip--_binary64_1430` `diff-log_binary64_1547` `sub-neg_binary64_1448` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `flip3--_binary64_1459`

Counts

2 → 40

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series97.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

70.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify62.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5005	794

prune104.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Merged error: 0.1b

Counts

47 → 4

Compiler

Compiled 1376 to 1013 computations (26.4% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1455`
24×	`sqrt-prod_binary64_1471`
21×	`distribute-lft-out_binary64_1406`
18×	`times-frac_binary64_1461`
16×	`add-sqr-sqrt_binary64_1477`
15×	`add-cube-cbrt_binary64_1490`
7×	`add-exp-log_binary64_1493`
6×	`associate-/r*_binary64_1399`
5×	`pow1_binary64_1516` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491`
3×	`flip-+_binary64_1429` `associate-/l*_binary64_1400` `flip3-+_binary64_1458`
2×	`associate-/r/_binary64_1401` `sqrt-div_binary64_1472` `div-exp_binary64_1506`
1×	`sqrt-pow1_binary64_1473` `inv-pow_binary64_1540` `rem-sqrt-square_binary64_1468` `1-exp_binary64_1499` `clear-num_binary64_1454` `pow-flip_binary64_1529` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `pow1/2_binary64_1535` `div-inv_binary64_1452` `sum-log_binary64_1546` `rec-exp_binary64_1505` `+-commutative_binary64_1385`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
11.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series129.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

62.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
40.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify67.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4944	1516
1	4944	1516

prune246.0ms (6.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Merged error: 0.0b

Counts

88 → 8

Compiler

Compiled 3858 to 2979 computations (22.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

rewrite70.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`sqrt-prod_binary64_1471`
70×	`add-sqr-sqrt_binary64_1477`
46×	`*-un-lft-identity_binary64_1455`
40×	`sqrt-pow1_binary64_1473`
32×	`sqrt-div_binary64_1472` `pow1_binary64_1516`
28×	`add-cube-cbrt_binary64_1490`
20×	`pow1/2_binary64_1535`
18×	`swap-sqr_binary64_1422`
12×	`rem-sqrt-square_binary64_1468`
10×	`associate-r_binary64_1395` `associate-l_binary64_1396` `add-exp-log_binary64_1493`
9×	`flip-+_binary64_1429` `flip3-+_binary64_1458` `times-frac_binary64_1461` `pow-prod-up_binary64_1525` `unswap-sqr_binary64_1423`
8×	`distribute-lft-out_binary64_1406` `add-cbrt-cube_binary64_1491`
5×	`pow-prod-down_binary64_1526` `pow-sqr_binary64_1428`
4×	`add-log-exp_binary64_1494` `frac-times_binary64_1465` `sqr-abs_binary64_1470`
3×	`associate-/r_binary64_1399` `associate-/l_binary64_1400`
2×	`associate-r/_binary64_1397` `associate-/r/_binary64_1401` `div-exp_binary64_1506` `associate-l/_binary64_1398`
1×	`prod-exp_binary64_1504` `inv-pow_binary64_1540` `pow-plus_binary64_1518` `1-exp_binary64_1499` `clear-num_binary64_1454` `pow-flip_binary64_1529` `*-commutative_binary64_1386` `sqrt-unprod_binary64_1475` `cbrt-undiv_binary64_1489` `pow2_binary64_1536` `frac-2neg_binary64_1466` `cbrt-unprod_binary64_1488` `div-inv_binary64_1452` `rec-exp_binary64_1505` `rem-square-sqrt_binary64_1467`

Counts

4 → 169

Calls

4 calls:

22.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
19.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

series184.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
46.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
42.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
30.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify72.0ms (2%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4969	2509
1	4969	2509

prune256.0ms (7.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	180	9	189

Merged error: 0.0b

Counts

189 → 9

Compiler

Compiled 4110 to 3119 computations (24.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.2b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1477` `*-un-lft-identity_binary64_1455`
18×	`add-cube-cbrt_binary64_1490`
13×	`cbrt-prod_binary64_1486`
10×	`associate-r_binary64_1395` `add-exp-log_binary64_1493`
9×	`sqrt-prod_binary64_1471` `times-frac_binary64_1461`
8×	`add-cbrt-cube_binary64_1491`
7×	`pow1_binary64_1516`
6×	`cbrt-div_binary64_1487`
4×	`flip-+_binary64_1429` `add-log-exp_binary64_1494` `flip3-+_binary64_1458`
3×	`distribute-lft-out_binary64_1406` `associate-/r_binary64_1399` `associate-/l_binary64_1400` `associate-l_binary64_1396` `unswap-sqr_binary64_1423`
2×	`associate-*r/_binary64_1397` `associate-/r/_binary64_1401` `sqrt-div_binary64_1472` `pow1/3_binary64_1537` `div-exp_binary64_1506`
1×	`prod-exp_binary64_1504` `inv-pow_binary64_1540` `1-exp_binary64_1499` `clear-num_binary64_1454` `pow-flip_binary64_1529` `*-commutative_binary64_1386` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `cbrt-unprod_binary64_1488` `div-inv_binary64_1452` `rec-exp_binary64_1505` `pow-prod-down_binary64_1526`

Counts

4 → 90

Calls

4 calls:

14.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series773.0ms (21.6%)

Counts

4 → 12

Calls

4 calls:

599.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
79.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
50.0ms	(cbrt.f64 (+.f64 1 x))
44.0ms	(cbrt.f64 (+.f64 1 x))

simplify94.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4869	3063
1	4869	3063

prune226.0ms (6.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	102	9	111

Merged error: 0.0b

Counts

111 → 9

Compiler

Compiled 3935 to 3078 computations (21.8% saved)

regimes26.0ms (0.7%)

Compiler: Compiled 248 to 202 computations (18.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample856.0ms (23.9%)

Algorithm

1×

intervals

Results

198.0ms	1934×	body	1024	valid
124.0ms	4310×	body	128	valid
85.0ms	1007×	body	512	valid
32.0ms	246×	body	2048	valid
29.0ms	503×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 272 to 224 computations (17.6% saved)

Details

analyze3.0ms (0.1%)

sample19.0ms (0.5%)

simplify172.0ms (4.8%)

prune6.0ms (0.2%)

localize5.0ms (0.1%)

rewrite17.0ms (0.5%)

series97.0ms (2.7%)

simplify62.0ms (1.7%)

prune104.0ms (2.9%)

localize6.0ms (0.2%)

rewrite32.0ms (0.9%)

series129.0ms (3.6%)

simplify67.0ms (1.9%)

prune246.0ms (6.9%)

localize8.0ms (0.2%)

rewrite70.0ms (1.9%)

series184.0ms (5.1%)

simplify72.0ms (2%)

prune256.0ms (7.2%)

localize9.0ms (0.3%)

rewrite41.0ms (1.1%)

series773.0ms (21.6%)

simplify94.0ms (2.6%)

prune226.0ms (6.3%)

regimes26.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample856.0ms (23.9%)

Profiling