Details

analyze477.0ms (4.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample100.0ms (1%)

Algorithm

1×

intervals

Results

40.0ms	131×	body	2048	nan
20.0ms	256×	body	128	valid
13.0ms	54×	body	1024	nan
7.0ms	38×	body	512	nan
2.0ms	13×	body	256	nan
1.0ms	16×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify449.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (276.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

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: 28.4b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
26.3b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1442`
7×	`add-sqr-sqrt_binary64_1464`
6×	`sqrt-prod_binary64_1458`
5×	`add-log-exp_binary64_1481` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
4×	`log-prod_binary64_1528` `add-exp-log_binary64_1480`
3×	`add-cbrt-cube_binary64_1478`
2×	`sqrt-div_binary64_1459` `distribute-lft-out_binary64_1393` `flip3-+_binary64_1445` `flip-+_binary64_1416` `log-div_binary64_1529` `difference-of-squares_binary64_1411`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `rem-log-exp_binary64_1483` `log-pow_binary64_1531` `flip3--_binary64_1446` `+-commutative_binary64_1372` `difference-of-sqr-1_binary64_1412` `flip--_binary64_1417` `pow1/2_binary64_1522`

Counts

3 → 45

Calls

3 calls:

13.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
12.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
10.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series164.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

81.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
50.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
33.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify115.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4931	923
1	4931	923

prune93.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Merged error: 0.0b

Counts

55 → 2

Compiler

Compiled 837 to 557 computations (33.5% saved)

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.2b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1464`
15×	`sqrt-prod_binary64_1458`
13×	`*-un-lft-identity_binary64_1442`
12×	`sqrt-div_binary64_1459`
10×	`associate-r_binary64_1382`
8×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
7×	`associate-l_binary64_1383`
6×	`add-exp-log_binary64_1480`
5×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `flip3-+_binary64_1445` `flip-+_binary64_1416`
4×	`frac-times_binary64_1452` `unswap-sqr_binary64_1410`
3×	`log-prod_binary64_1528` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `flip--_binary64_1417`
2×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `pow1/2_binary64_1522` `log-div_binary64_1529` `difference-of-squares_binary64_1411` `associate-l/_binary64_1385`
1×	`cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `rem-log-exp_binary64_1483` `log-pow_binary64_1531` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `difference-of-sqr-1_binary64_1412` `sqrt-unprod_binary64_1462` `distribute-lft-out_binary64_1393` `prod-exp_binary64_1491` `distribute-lft-out--_binary64_1394`

Counts

3 → 68

Calls

3 calls:

26.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
5.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
5.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

series203.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

81.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
64.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
56.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify136.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4977	1681
1	4977	1681

prune160.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	2	79

Merged error: 0.0b

Counts

79 → 2

Compiler

Compiled 1524 to 1157 computations (24.1% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
0.1b	(/.f64 3/32 (pow.f64 x 4))
0.1b	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
0.5b	(/.f64 1/4 (*.f64 x x))

rewrite95.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_1442`
32×	`add-sqr-sqrt_binary64_1464`
26×	`add-cube-cbrt_binary64_1477`
25×	`times-frac_binary64_1448`
16×	`distribute-lft-out--_binary64_1394`
14×	`add-exp-log_binary64_1480`
13×	`pow1_binary64_1503`
12×	`unpow-prod-down_binary64_1521`
11×	`add-cbrt-cube_binary64_1478`
10×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481`
9×	`log-pow_binary64_1531` `distribute-lft-out_binary64_1393`
8×	`associate-/r*_binary64_1386`
6×	`log-prod_binary64_1528` `associate-/l*_binary64_1387`
5×	`diff-log_binary64_1534` `div-exp_binary64_1493`
4×	`sqr-pow_binary64_1414` `associate--r+_binary64_1378`
3×	`associate--l+_binary64_1379` `cbrt-undiv_binary64_1476` `difference-of-squares_binary64_1411`
2×	`sum-log_binary64_1533` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `flip3--_binary64_1446` `flip--_binary64_1417` `frac-2neg_binary64_1453`
1×	`associate-+r-_binary64_1376` `cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `prod-exp_binary64_1491` `associate--r-_binary64_1381` `pow-to-exp_binary64_1511`

Counts

4 → 121

Calls

4 calls:

45.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
15.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
8.0ms	(/.f64 1/4 (*.f64 x x))
8.0ms	(/.f64 3/32 (pow.f64 x 4))

series360.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
89.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
43.0ms	(/.f64 3/32 (pow.f64 x 4))
34.0ms	(/.f64 1/4 (*.f64 x x))

simplify149.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4946	2312
1	4946	2312

prune274.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	132	3	135

Merged error: 0b

Counts

135 → 3

Compiler

Compiled 2992 to 2021 computations (32.5% saved)

localize39.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (.f64 x x)) (log.f64 x))))) (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))))
0.5b	(/.f64 1/4 (*.f64 x x))
0.5b	(/.f64 1/4 (*.f64 x x))
0.5b	(/.f64 1/4 (*.f64 x x))

rewrite250.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

434×	`*-un-lft-identity_binary64_1442`
240×	`distribute-lft-out--_binary64_1394`
196×	`cbrt-prod_binary64_1473`
131×	`pow1_binary64_1503`
120×	`log-pow_binary64_1531` `distribute-lft-out_binary64_1393`
87×	`swap-sqr_binary64_1409`
34×	`add-sqr-sqrt_binary64_1464`
21×	`add-exp-log_binary64_1480`
19×	`add-cbrt-cube_binary64_1478`
18×	`add-cube-cbrt_binary64_1477`
15×	`associate-r_binary64_1382` `associate-l_binary64_1383`
12×	`cbrt-div_binary64_1474`
9×	`times-frac_binary64_1448` `associate-/l*_binary64_1387`
6×	`cbrt-undiv_binary64_1476` `flip3--_binary64_1446` `flip--_binary64_1417` `pow1/3_binary64_1524` `div-exp_binary64_1493`
4×	`cbrt-unprod_binary64_1475` `add-log-exp_binary64_1481` `frac-times_binary64_1452` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411` `unswap-sqr_binary64_1410`
3×	`associate-/r*_binary64_1386` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453`
2×	`associate-r/_binary64_1384` `pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512` `associate-l/_binary64_1385`
1×	`pow2_binary64_1523` `pow-plus_binary64_1505` `*-commutative_binary64_1373`

Counts

4 → 210

Calls

4 calls:

123.0ms	(.f64 (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (.f64 x x)) (log.f64 x))))) (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))))
10.0ms	(/.f64 1/4 (*.f64 x x))
9.0ms	(/.f64 1/4 (*.f64 x x))
9.0ms	(/.f64 1/4 (*.f64 x x))

series1.1s (11.1%)

Counts

4 → 12

Calls

4 calls:

1.0s	(.f64 (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (.f64 x x)) (log.f64 x))))) (cbrt.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))))
33.0ms	(/.f64 1/4 (*.f64 x x))
29.0ms	(/.f64 1/4 (*.f64 x x))
28.0ms	(/.f64 1/4 (*.f64 x x))

simplify232.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5172	8237

prune1.7s (17.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	222	3	225

Merged error: 0b

Counts

225 → 3

Compiler

Compiled 12857 to 9181 computations (28.6% saved)

regimes108.0ms (1.1%)

Compiler: Compiled 477 to 367 computations (23.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample3.5s (35.6%)

Algorithm

1×

intervals

Results

1.3s	4059×	body	2048	nan
658.0ms	8000×	body	128	valid
481.0ms	1950×	body	1024	nan
189.0ms	1032×	body	512	nan
57.0ms	461×	body	256	nan
30.0ms	480×	body	128	nan
3.0ms	7×	body	4096	nan

Compiler

Compiled 169 to 132 computations (21.9% saved)

Details

analyze477.0ms (4.8%)

sample100.0ms (1%)

simplify449.0ms (4.5%)

prune4.0ms (0%)

localize15.0ms (0.2%)

rewrite40.0ms (0.4%)

series164.0ms (1.7%)

simplify115.0ms (1.2%)

prune93.0ms (0.9%)

localize20.0ms (0.2%)

rewrite49.0ms (0.5%)

series203.0ms (2.1%)

simplify136.0ms (1.4%)

prune160.0ms (1.6%)

localize27.0ms (0.3%)

rewrite95.0ms (1%)

series360.0ms (3.6%)

simplify149.0ms (1.5%)

prune274.0ms (2.8%)

localize39.0ms (0.4%)

rewrite250.0ms (2.5%)

series1.1s (11.1%)

simplify232.0ms (2.3%)

prune1.7s (17.2%)

regimes108.0ms (1.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.5s (35.6%)

Profiling