Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample15.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify165.0ms (7.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

prune2.0ms (0.1%)

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: 13.4b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) 1)
13.4b	(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite15.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
9×	`times-frac_binary64_1461`
4×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
3×	`associate-/r_binary64_1399` `associate-/l_binary64_1400`
2×	`associate-/r/_binary64_1401` `flip-+_binary64_1429` `pow1_binary64_1516` `flip3-+_binary64_1458`
1×	`div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

2 → 40

Calls

2 calls:

7.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
5.0ms	(+.f64 (*.f64 x x) 1)

series106.0ms (5%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
49.0ms	(+.f64 (*.f64 x x) 1)

simplify68.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4989	689
1	4989	689

prune112.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	3	47

Merged error: 0b

Counts

47 → 3

Compiler

Compiled 1740 to 1069 computations (38.6% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
13.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.3b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite68.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_1477`
76×	`times-frac_binary64_1461`
53×	`*-un-lft-identity_binary64_1455`
47×	`sqrt-prod_binary64_1471` `add-cube-cbrt_binary64_1490`
28×	`add-exp-log_binary64_1493`
24×	`associate-r_binary64_1395` `associate-l_binary64_1396`
18×	`add-cbrt-cube_binary64_1491`
15×	`unswap-sqr_binary64_1423`
10×	`sqrt-div_binary64_1472`
9×	`div-exp_binary64_1506`
8×	`prod-exp_binary64_1504` `pow1_binary64_1516`
6×	`associate-/r/_binary64_1401` `associate-/r*_binary64_1399`
5×	`flip-+_binary64_1429` `cbrt-undiv_binary64_1489` `flip3-+_binary64_1458`
4×	`add-log-exp_binary64_1494` `cbrt-unprod_binary64_1488`
3×	`associate-/l*_binary64_1400` `div-inv_binary64_1452`
2×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `1-exp_binary64_1499` `pow1/2_binary64_1535` `rec-exp_binary64_1505`
1×	`associate-r/_binary64_1397` `clear-num_binary64_1454` `frac-times_binary64_1465` `-commutative_binary64_1386` `frac-2neg_binary64_1466` `associate-*l/_binary64_1398` `pow-prod-down_binary64_1526`

Counts

4 → 158

Calls

4 calls:

33.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series208.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
60.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
42.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
35.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify100.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4965	3380
1	4965	3380

prune192.0ms (9.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	170	3	173

Merged error: 0b

Counts

173 → 3

Compiler

Compiled 3855 to 2338 computations (39.4% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 1 (pow.f64 x 5))
0.3b	(pow.f64 (/.f64 1 x) 3)
16.1b	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))

rewrite79.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64_1477`
61×	`times-frac_binary64_1461` `*-un-lft-identity_binary64_1455`
49×	`add-cube-cbrt_binary64_1490`
41×	`unpow-prod-down_binary64_1534`
32×	`cancel-sign-sub-inv_binary64_1421`
29×	`cube-prod_binary64_1483`
17×	`add-exp-log_binary64_1493`
9×	`div-inv_binary64_1452`
8×	`difference-of-squares_binary64_1424` `div-exp_binary64_1506` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491`
7×	`associate-/r*_binary64_1399` `sqr-pow_binary64_1427` `pow-exp_binary64_1523`
5×	`distribute-lft-out--_binary64_1407` `pow1_binary64_1516`
4×	`distribute-lft-out_binary64_1406` `cube-div_binary64_1484` `1-exp_binary64_1499` `pow-to-exp_binary64_1524` `rec-exp_binary64_1505`
3×	`pow-pow_binary64_1527` `associate-/l*_binary64_1400` `frac-sub_binary64_1464` `pow-unpow_binary64_1532`
2×	`inv-pow_binary64_1540` `cube-mult_binary64_1485` `unpow3_binary64_1521` `pow-flip_binary64_1529` `cbrt-undiv_binary64_1489` `rem-cube-cbrt_binary64_1478` `diff-log_binary64_1547`
1×	`flip-+_binary64_1429` `clear-num_binary64_1454` `flip--_binary64_1430` `associate--l+_binary64_1392` `frac-2neg_binary64_1466` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `sum-log_binary64_1546` `frac-add_binary64_1463` `flip3--_binary64_1459`

Counts

3 → 164

Calls

3 calls:

51.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))
6.0ms	(pow.f64 (/.f64 1 x) 3)
5.0ms	(/.f64 1 (pow.f64 x 5))

series149.0ms (7.1%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(/.f64 1 (pow.f64 x 5))
49.0ms	(pow.f64 (/.f64 1 x) 3)
39.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))

simplify94.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4855	2535
1	4855	2535

prune212.0ms (10.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	173	3	176

Merged error: 0b

Counts

176 → 3

Compiler

Compiled 3464 to 2742 computations (20.8% saved)

regimes41.0ms (2%)

Compiler: Compiled 94 to 72 computations (23.4% saved)

bsearch29.0ms (1.4%)

Steps

Iters	Range		Point
8	0.8300690620861652	768.6789257213327	699.7906104029425
9	-48960445435.83525	-27878.189113504326	-1270641095.991968

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	46
1	36	46

end0.0ms (0%)

sample414.0ms (19.8%)

Algorithm

1×

intervals

Results

182.0ms

8000×

body

128

valid

Compiler

Compiled 85 to 67 computations (21.2% saved)

Details

analyze1.0ms (0.1%)

sample15.0ms (0.7%)

simplify165.0ms (7.9%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite15.0ms (0.7%)

series106.0ms (5%)

simplify68.0ms (3.2%)

prune112.0ms (5.3%)

localize8.0ms (0.4%)

rewrite68.0ms (3.3%)

series208.0ms (9.9%)

simplify100.0ms (4.8%)

prune192.0ms (9.1%)

localize9.0ms (0.4%)

rewrite79.0ms (3.8%)

series149.0ms (7.1%)

simplify94.0ms (4.5%)

prune212.0ms (10.1%)

regimes41.0ms (2%)

bsearch29.0ms (1.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample414.0ms (19.8%)

Profiling