Details

analyze1.0ms (0%)

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)

sample10.0ms (0%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify95.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

prune1.0ms (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

Error

14.5b

Counts

2 → 1

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

14.5b	(/.f64 x (+.f64 (*.f64 x x) 1))
14.5b	(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`times-frac_binary64_1448` `add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
3×	`associate-/r_binary64_1386` `add-cbrt-cube_binary64_1478` `associate-/l_binary64_1387` `add-exp-log_binary64_1480`
2×	`associate-/r/_binary64_1388`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503` `div-exp_binary64_1493`

Counts

1 → 29

Calls

2 calls:

6.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
0.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))

series55.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

55.0ms

(/.f64 x (+.f64 (*.f64 x x) 1))

Compiler

Compiled 124 to 106 computations (14.5% saved)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5088	673

prune165.0ms (0.2%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	10	31	41
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	10	32	42

Error

Counts

42 → 32

Compiler

Compiled 903 to 558 computations (38.2% saved)

localize7.0ms (0%)

Local error

Found 8 expressions with local error:

14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
0.0b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite67.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_1448`
164×	`add-sqr-sqrt_binary64_1464`
162×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
156×	`sqrt-prod_binary64_1458`
27×	`associate-/l*_binary64_1387`
22×	`sqrt-div_binary64_1459`
18×	`associate-/r/_binary64_1388`
12×	`associate-/r*_binary64_1386`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `flip3-+_binary64_1445` `flip-+_binary64_1416`
9×	`div-inv_binary64_1439`
6×	`pow1_binary64_1503`
4×	`cbrt-undiv_binary64_1476` `add-log-exp_binary64_1481` `div-exp_binary64_1493`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`
1×	`associate-/l/_binary64_1389`

Counts

4 → 262

Calls

8 calls:

19.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
7.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))

series224.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

71.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
57.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
52.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
44.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 838 to 686 computations (18.1% saved)

simplify148.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4913	9010
1	4913	9010

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

19.9b	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))
2.7b	(/.f64 x (+.f64 (pow.f64 x 4) -1))
2.7b	(/.f64 x (+.f64 (pow.f64 x 4) -1))
19.9b	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))

rewrite36.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_1464`
43×	`times-frac_binary64_1448` `*-un-lft-identity_binary64_1442`
28×	`add-cube-cbrt_binary64_1477`
27×	`associate-l_binary64_1383`
21×	`difference-of-sqr--1_binary64_1413`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
7×	`associate-/r*_binary64_1386` `distribute-lft-out_binary64_1393` `sqr-pow_binary64_1414` `unpow-prod-down_binary64_1521`
6×	`associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408`
4×	`associate-/r/_binary64_1388` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow1_binary64_1503`
3×	`associate-/l*_binary64_1387`
2×	`associate-*r/_binary64_1384` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `sub-neg_binary64_1435` `flip3--_binary64_1446` `add-log-exp_binary64_1481` `flip--_binary64_1417` `frac-times_binary64_1452` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
1×	`clear-num_binary64_1441` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `difference-of-sqr-1_binary64_1412` `frac-2neg_binary64_1453` `associate-l/_binary64_1385`

Counts

2 → 106

Calls

4 calls:

18.0ms	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))
7.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))
0.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))
0.0ms	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))

series230.0ms (0.3%)

Counts

2 → 23

Calls

2 calls:

143.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))
87.0ms	(.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)) (-.f64 (.f64 x x) 1))

Compiler

Compiled 341 to 281 computations (17.6% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4942	2202
1	4942	2202

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

5.9b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1)))
2.4b	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
2.4b	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
5.9b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1)))

rewrite31.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_1464`
40×	`times-frac_binary64_1448`
32×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
29×	`sqrt-prod_binary64_1458`
24×	`associate-r_binary64_1382`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
6×	`associate-/l_binary64_1387` `associate-l*_binary64_1383` `unswap-sqr_binary64_1410`
4×	`associate-/r/_binary64_1388` `pow1_binary64_1503`
3×	`associate-/r*_binary64_1386`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `add-log-exp_binary64_1481` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491` `div-exp_binary64_1493`
1×	`associate-r/_binary64_1384` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453`

Counts

2 → 91

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1)))
7.0ms	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
0.0ms	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
0.0ms	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1)))

series64.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

43.0ms	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1)))
20.0ms	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))

Compiler

Compiled 168 to 142 computations (15.5% saved)

simplify101.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4926	1886
1	4926	1886

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (/.f64 1 x) 3)
0.1b	(/.f64 1 (pow.f64 x 7))
0.0b	(/.f64 1 (pow.f64 x 5))
0.0b	(+.f64 (pow.f64 (/.f64 1 x) 3) (/.f64 1 (pow.f64 x 7)))
0.0b	(/.f64 1 (pow.f64 x 5))
0.1b	(/.f64 1 (pow.f64 x 7))
0.2b	(pow.f64 (/.f64 1 x) 3)
22.7b	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (+.f64 (pow.f64 (/.f64 1 x) 3) (/.f64 1 (pow.f64 x 7))))

rewrite110.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`*-un-lft-identity_binary64_1442`
60×	`times-frac_binary64_1448`
54×	`add-sqr-sqrt_binary64_1464`
52×	`add-cube-cbrt_binary64_1477`
37×	`unpow-prod-down_binary64_1521`
27×	`add-exp-log_binary64_1480`
24×	`distribute-lft-out_binary64_1393`
22×	`div-inv_binary64_1439`
16×	`add-log-exp_binary64_1481`
15×	`distribute-lft-out--_binary64_1394`
14×	`associate-/r*_binary64_1386` `div-exp_binary64_1493`
13×	`cube-prod_binary64_1470`
11×	`add-cbrt-cube_binary64_1478`
10×	`pow-exp_binary64_1510`
9×	`frac-sub_binary64_1451` `sqr-pow_binary64_1414`
7×	`1-exp_binary64_1486` `rec-exp_binary64_1492` `pow-to-exp_binary64_1511`
6×	`associate-/l*_binary64_1387` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503` `frac-add_binary64_1450`
5×	`cancel-sign-sub-inv_binary64_1408`
4×	`sum-log_binary64_1533` `diff-log_binary64_1534` `cube-div_binary64_1471`
3×	`inv-pow_binary64_1527` `cbrt-undiv_binary64_1476` `pow-unpow_binary64_1519` `pow-flip_binary64_1516` `pow-pow_binary64_1514`
2×	`clear-num_binary64_1441` `rem-cube-cbrt_binary64_1465` `frac-2neg_binary64_1453`
1×	`associate--l+_binary64_1379` `cube-mult_binary64_1472` `sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `unpow3_binary64_1508` `associate--r+_binary64_1378` `difference-of-squares_binary64_1411`

Counts

4 → 202

Calls

8 calls:

69.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (+.f64 (pow.f64 (/.f64 1 x) 3) (/.f64 1 (pow.f64 x 7))))
5.0ms	(pow.f64 (/.f64 1 x) 3)
5.0ms	(/.f64 1 (pow.f64 x 7))
5.0ms	(/.f64 1 (pow.f64 x 5))
0.0ms	(+.f64 (pow.f64 (/.f64 1 x) 3) (/.f64 1 (pow.f64 x 7)))

series158.0ms (0.2%)

Counts

4 → 19

Calls

4 calls:

46.0ms	(/.f64 1 (pow.f64 x 7))
44.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (+.f64 (pow.f64 (/.f64 1 x) 3) (/.f64 1 (pow.f64 x 7))))
35.0ms	(/.f64 1 (pow.f64 x 5))
32.0ms	(pow.f64 (/.f64 1 x) 3)

Compiler

Compiled 507 to 438 computations (13.6% saved)

simplify119.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4893	4192
1	4893	4192

prune8.4s (11.4%)

Pruning

277 alts after pruning (271 fresh and 6 done)

	Pruned	Kept	Total
New	511	252	763
Fresh	7	19	26
Picked	0	0	0
Done	0	6	6
Total	518	277	795

Error

Counts

795 → 277

Compiler

Compiled 17191 to 11717 computations (31.8% saved)

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))
0.0b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite52.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_1448`
100×	`add-sqr-sqrt_binary64_1464`
98×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
54×	`sqrt-prod_binary64_1458`
27×	`associate-/l*_binary64_1387`
14×	`sqrt-div_binary64_1459`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
10×	`associate-/r/_binary64_1388`
9×	`associate-/r*_binary64_1386`
7×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
6×	`div-inv_binary64_1439` `pow1_binary64_1503`
4×	`cbrt-undiv_binary64_1476` `add-log-exp_binary64_1481` `div-exp_binary64_1493`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`
1×	`associate-/l/_binary64_1389`

Counts

4 → 185

Calls

8 calls:

12.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))
7.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))

series337.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

165.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))
77.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
50.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
44.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 1134 to 960 computations (15.3% saved)

simplify137.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4914	6168
1	4914	6168

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

14.5b	(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))
14.5b	(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`times-frac_binary64_1448`
38×	`add-sqr-sqrt_binary64_1464`
27×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
15×	`distribute-lft-neg-in_binary64_1399` `distribute-rgt-neg-in_binary64_1400`
11×	`difference-of-squares_binary64_1411`
10×	`associate-/l*_binary64_1387`
5×	`neg-mul-1_binary64_1438`
4×	`associate-/r*_binary64_1386`
3×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
2×	`associate-/r/_binary64_1388`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `flip3--_binary64_1446` `add-log-exp_binary64_1481` `flip--_binary64_1417` `frac-2neg_binary64_1453` `distribute-frac-neg_binary64_1405` `pow1_binary64_1503` `div-sub_binary64_1447` `neg-sub0_binary64_1437` `div-exp_binary64_1493`

Counts

1 → 70

Calls

2 calls:

6.0ms	(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))
0.0ms	(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))

series54.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

54.0ms

(/.f64 (neg.f64 x) (-.f64 -1 (*.f64 x x)))

Compiler

Compiled 124 to 106 computations (14.5% saved)

simplify94.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4916	1643
1	4916	1643

localize10.0ms (0%)

Local error

Found 6 expressions with local error:

15.3b	(.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)))) (-.f64 (.f64 x x) 1))
4.7b	(log.f64 (exp.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1))))
2.7b	(/.f64 x (+.f64 (pow.f64 x 4) -1))
2.7b	(/.f64 x (+.f64 (pow.f64 x 4) -1))
4.7b	(log.f64 (exp.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1))))
15.3b	(.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)))) (-.f64 (.f64 x x) 1))

rewrite59.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`add-sqr-sqrt_binary64_1464`
63×	`times-frac_binary64_1448` `*-un-lft-identity_binary64_1442`
56×	`log-pow_binary64_1531`
54×	`exp-prod_binary64_1494`
42×	`add-cube-cbrt_binary64_1477`
31×	`associate-l_binary64_1383`
30×	`difference-of-sqr--1_binary64_1413`
10×	`distribute-lft-out_binary64_1393` `sqr-pow_binary64_1414` `unpow-prod-down_binary64_1521`
7×	`associate-/r*_binary64_1386` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
6×	`associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408` `associate-/r/_binary64_1388`
4×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
3×	`log-prod_binary64_1528` `div-inv_binary64_1439` `associate-/l*_binary64_1387` `add-log-exp_binary64_1481` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-*r/_binary64_1384` `sub-neg_binary64_1435` `difference-of-squares_binary64_1411`
1×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `clear-num_binary64_1441` `rem-log-exp_binary64_1483` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `difference-of-sqr-1_binary64_1412` `flip--_binary64_1417` `frac-2neg_binary64_1453` `prod-exp_binary64_1491` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`

Counts

3 → 143

Calls

6 calls:

26.0ms	(.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)))) (-.f64 (.f64 x x) 1))
11.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1))))
7.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))
0.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))
0.0ms	(.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)))) (-.f64 (.f64 x x) 1))

series1.3s (1.7%)

Counts

3 → 32

Calls

3 calls:

930.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1))))
198.0ms	(.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 (pow.f64 x 4) -1)))) (-.f64 (.f64 x x) 1))
136.0ms	(/.f64 x (+.f64 (pow.f64 x 4) -1))

Compiler

Compiled 582 to 480 computations (17.5% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4932	3023
1	4932	3023

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

5.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1)))))
2.4b	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
2.4b	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
0.2b	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))))
2.4b	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
5.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1)))))
6.0b	(sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1)))
6.0b	(sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1)))

rewrite69.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-prod_binary64_1458`
59×	`add-sqr-sqrt_binary64_1464`
58×	`times-frac_binary64_1448`
47×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
14×	`pow1_binary64_1503`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
7×	`pow-prod-down_binary64_1513`
6×	`rem-sqrt-square_binary64_1455` `associate-/r/_binary64_1388` `associate-/l_binary64_1387` `associate-l*_binary64_1383` `sqrt-div_binary64_1459`
5×	`sqrt-pow1_binary64_1460` `pow1/2_binary64_1522`
4×	`associate-*r/_binary64_1384` `add-log-exp_binary64_1481`
3×	`associate-/r*_binary64_1386` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491`
2×	`sqrt-unprod_binary64_1462` `unswap-sqr_binary64_1410`
1×	`associate-r_binary64_1382` `cbrt-undiv_binary64_1476` `clear-num_binary64_1441` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `frac-times_binary64_1452` `associate-l/_binary64_1385` `div-exp_binary64_1493`

Counts

4 → 144

Calls

8 calls:

25.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1)))))
8.0ms	(sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1)))
8.0ms	(sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1)))
7.0ms	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
0.0ms	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))))

series269.0ms (0.4%)

Counts

4 → 30

Calls

4 calls:

105.0ms	(sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1)))
98.0ms	(sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1)))
42.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1)))))
23.0ms	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))

Compiler

Compiled 844 to 666 computations (21.1% saved)

simplify110.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4893	3714
1	4893	3714

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1)))))
0.2b	(/.f64 (cbrt.f64 x) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) 1))))
0.2b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))
0.0b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.6b	(cbrt.f64 x)
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1464`
9×	`sqrt-prod_binary64_1458`
8×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
7×	`pow1_binary64_1503`
6×	`sqrt-div_binary64_1459`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
3×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `cbrt-prod_binary64_1473` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`
1×	`pow1/3_binary64_1524`

Counts

4 → 56

Calls

8 calls:

4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
1.0ms	(cbrt.f64 x)
0.0ms	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))

series236.0ms (0.3%)

Counts

4 → 39

Calls

4 calls:

75.0ms	(cbrt.f64 x)
55.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
53.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
52.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 1507 to 1039 computations (31.1% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4929	1119
1	4929	1119

prune21.2s (28.9%)

Pruning

452 alts after pruning (442 fresh and 10 done)

	Pruned	Kept	Total
New	536	223	759
Fresh	47	219	266
Picked	0	0	0
Done	1	10	11
Total	584	452	1036

Error

Counts

1036 → 452

Compiler

Compiled 26419 to 16595 computations (37.2% saved)

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))
0.0b	(-.f64 (/.f64 -1 x) x)
0.0b	(-.f64 (/.f64 -1 x) x)
0.1b	(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_1464`
72×	`times-frac_binary64_1448`
59×	`*-un-lft-identity_binary64_1442`
35×	`add-cube-cbrt_binary64_1477`
24×	`difference-of-squares_binary64_1411`
21×	`distribute-lft-neg-in_binary64_1399` `distribute-rgt-neg-in_binary64_1400`
12×	`distribute-lft-out--_binary64_1394`
10×	`associate-/l*_binary64_1387`
7×	`neg-mul-1_binary64_1438`
6×	`associate-/r*_binary64_1386`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `distribute-frac-neg_binary64_1405` `div-sub_binary64_1447` `neg-sub0_binary64_1437` `div-exp_binary64_1493`

Counts

2 → 109

Calls

4 calls:

11.0ms	(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))
7.0ms	(-.f64 (/.f64 -1 x) x)
0.0ms	(-.f64 (/.f64 -1 x) x)
0.0ms	(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))

series72.0ms (0.1%)

Counts

2 → 18

Calls

2 calls:

45.0ms	(/.f64 (neg.f64 1) (-.f64 (/.f64 -1 x) x))
27.0ms	(-.f64 (/.f64 -1 x) x)

Compiler

Compiled 196 to 172 computations (12.2% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4959	2384
1	4959	2384

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 x (/.f64 1 x)))
0.0b	(+.f64 x (/.f64 1 x))
0.0b	(+.f64 x (/.f64 1 x))
0.1b	(/.f64 1 (+.f64 x (/.f64 1 x)))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1442`
18×	`times-frac_binary64_1448`
16×	`add-exp-log_binary64_1480`
13×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
10×	`distribute-lft-out_binary64_1393`
6×	`associate-/r*_binary64_1386` `div-inv_binary64_1439` `rec-exp_binary64_1492`
5×	`cosh-undef_binary64_1636`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481`
3×	`associate-/l*_binary64_1387` `pow1_binary64_1503`
2×	`associate-/r/_binary64_1388` `flip3-+_binary64_1445` `flip-+_binary64_1416` `div-exp_binary64_1493`
1×	`inv-pow_binary64_1527` `cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `clear-num_binary64_1441` `1-exp_binary64_1486` `+-commutative_binary64_1372` `pow-flip_binary64_1516` `frac-2neg_binary64_1453`

Counts

2 → 59

Calls

4 calls:

9.0ms	(+.f64 x (/.f64 1 x))
8.0ms	(/.f64 1 (+.f64 x (/.f64 1 x)))
0.0ms	(+.f64 x (/.f64 1 x))
0.0ms	(/.f64 1 (+.f64 x (/.f64 1 x)))

series65.0ms (0.1%)

Counts

2 → 18

Calls

2 calls:

39.0ms	(/.f64 1 (+.f64 x (/.f64 1 x)))
26.0ms	(+.f64 x (/.f64 1 x))

Compiler

Compiled 177 to 153 computations (13.6% saved)

simplify91.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4899	953
1	4899	953

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1/16 (pow.f64 x 5))
0.0b	(/.f64 x (-.f64 (+.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 1/8 (pow.f64 x 3))))
0.0b	(+.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
0.0b	(/.f64 (/.f64 x (-.f64 (+.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 1/8 (pow.f64 x 3)))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(/.f64 1/16 (pow.f64 x 5))
0.3b	(/.f64 1/8 (pow.f64 x 3))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
20.3b	(-.f64 (+.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 1/8 (pow.f64 x 3)))

rewrite86.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary64_1448`
82×	`add-sqr-sqrt_binary64_1464`
77×	`*-un-lft-identity_binary64_1442`
68×	`add-cube-cbrt_binary64_1477`
40×	`cancel-sign-sub-inv_binary64_1408`
34×	`unpow-prod-down_binary64_1521`
22×	`cube-prod_binary64_1470`
19×	`associate-/r*_binary64_1386`
14×	`add-exp-log_binary64_1480`
13×	`add-log-exp_binary64_1481`
12×	`sqr-pow_binary64_1414`
8×	`add-cbrt-cube_binary64_1478`
7×	`cube-mult_binary64_1472` `unpow3_binary64_1508`
6×	`associate-/l*_binary64_1387` `div-exp_binary64_1493`
5×	`pow1_binary64_1503` `difference-of-squares_binary64_1411`
3×	`sum-log_binary64_1533` `div-inv_binary64_1439` `distribute-lft-out_binary64_1393` `diff-log_binary64_1534` `sqrt-prod_binary64_1458` `distribute-lft-out--_binary64_1394`
2×	`cbrt-undiv_binary64_1476` `pow-exp_binary64_1510` `clear-num_binary64_1441` `frac-sub_binary64_1451` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-to-exp_binary64_1511`
1×	`associate--l+_binary64_1379` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `pow1/2_binary64_1522`

Counts

4 → 189

Calls

8 calls:

41.0ms	(-.f64 (+.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 1/8 (pow.f64 x 3)))
5.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0ms	(/.f64 (/.f64 x (-.f64 (+.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 1/8 (pow.f64 x 3)))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))

series175.0ms (0.2%)

Counts

4 → 26

Calls

4 calls:

62.0ms	(-.f64 (+.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))) (/.f64 1/8 (pow.f64 x 3)))
39.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
38.0ms	(/.f64 1/16 (pow.f64 x 5))
36.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 873 to 688 computations (21.2% saved)

simplify106.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4956	3277
1	4956	3277

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

3.5b	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (-.f64 (pow.f64 x 1/4) (*.f64 1/2 (pow.f64 (pow.f64 x 9) 1/4))))
2.4b	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
0.1b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (-.f64 (pow.f64 x 1/4) (.f64 1/2 (pow.f64 (pow.f64 x 9) 1/4)))))
0.0b	(-.f64 (pow.f64 x 1/4) (*.f64 1/2 (pow.f64 (pow.f64 x 9) 1/4)))
2.4b	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
3.5b	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (-.f64 (pow.f64 x 1/4) (*.f64 1/2 (pow.f64 (pow.f64 x 9) 1/4))))
6.0b	(sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1)))
33.6b	(pow.f64 (pow.f64 x 9) 1/4)

rewrite56.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`sqrt-prod_binary64_1458`
65×	`add-sqr-sqrt_binary64_1464`
58×	`times-frac_binary64_1448`
50×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
27×	`associate-l_binary64_1383`
10×	`add-exp-log_binary64_1480` `unpow-prod-down_binary64_1521`
8×	`add-cbrt-cube_binary64_1478`
7×	`pow1_binary64_1503`
6×	`associate-/r/_binary64_1388` `associate-/l*_binary64_1387`
4×	`pow-exp_binary64_1510` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
3×	`associate-r_binary64_1382` `associate-/r*_binary64_1386` `rem-sqrt-square_binary64_1455` `div-inv_binary64_1439` `pow-unpow_binary64_1519` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-*r/_binary64_1384` `cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `distribute-lft-in_binary64_1391` `frac-times_binary64_1452` `sqr-pow_binary64_1414` `distribute-rgt-in_binary64_1392` `pow-to-exp_binary64_1511`
1×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `associate-l/_binary64_1385` `div-exp_binary64_1493` `pow-pow_binary64_1514`

Counts

4 → 155

Calls

8 calls:

20.0ms	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (-.f64 (pow.f64 x 1/4) (*.f64 1/2 (pow.f64 (pow.f64 x 9) 1/4))))
8.0ms	(sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1)))
7.0ms	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))
4.0ms	(pow.f64 (pow.f64 x 9) 1/4)
0.0ms	(-.f64 (pow.f64 x 1/4) (*.f64 1/2 (pow.f64 (pow.f64 x 9) 1/4)))

series373.0ms (0.5%)

Counts

4 → 16

Calls

4 calls:

178.0ms	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (.f64 x x) 1))) (-.f64 (pow.f64 x 1/4) (*.f64 1/2 (pow.f64 (pow.f64 x 9) 1/4))))
106.0ms	(pow.f64 (pow.f64 x 9) 1/4)
67.0ms	(sqrt.f64 (/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1)))
22.0ms	(/.f64 (sqrt.f64 x) (+.f64 (*.f64 x x) 1))

Compiler

Compiled 793 to 661 computations (16.6% saved)

simplify100.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4925	4347
1	4925	4347

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(/.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1)))) (cbrt.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))))) (cbrt.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1464` `sqrt-prod_binary64_1458`
8×	`sqrt-div_binary64_1459` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`sqrt-pow1_binary64_1460` `add-cbrt-cube_binary64_1478` `rem-sqrt-square_binary64_1455` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

4 → 60

Calls

8 calls:

5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1)))) (cbrt.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))))) (cbrt.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) 1))))) (fabs.f64 (sqrt.f64 (+.f64 (.f64 x x) 1))))

series218.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

57.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
55.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
53.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
52.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 2028 to 1444 computations (28.8% saved)

simplify112.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4865	1384
1	4865	1384

prune29.4s (40.1%)

Pruning

638 alts after pruning (623 fresh and 15 done)

	Pruned	Kept	Total
New	488	210	698
Fresh	24	413	437
Picked	0	0	0
Done	0	15	15
Total	512	638	1150

Error

Counts

1150 → 638

Compiler

Compiled 13599 to 9043 computations (33.5% saved)

simplify769.0ms (1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5106	53116

regimes6.1s (8.3%)

Compiler: Compiled 58325 to 41938 computations (28.1% saved)

bsearch0.0ms (0%)

regimes64.0ms (0.1%)

Compiler: Compiled 96 to 91 computations (5.2% saved)

bsearch27.0ms (0%)

Steps

Iters	Range		Point
10	47131.063510226086	1614589916290612.0	56166425.491830505
9	-5.2589740283259976e+23	-2053648057198059.5	-5.176580413214303e+23

Compiler

Compiled 1 to 1 computations (0% saved)

regimes26.0ms (0%)

Compiler: Compiled 23 to 26 computations (-13% saved)

bsearch20.0ms (0%)

Steps

Iters	Range		Point
8	0.04191749505049099	15.625426484059034	1.00048819294968
8	-122.59648859517979	-0.005481057407468642	-1.0278398150984853

Compiler

Compiled 1 to 1 computations (0% saved)

regimes9.0ms (0%)

Compiler: Compiled 6 to 9 computations (-50% saved)

bsearch3.0ms (0%)

Compiler: Compiled 44 to 33 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	58
1	40	58

end0.0ms (0%)

sample941.0ms (1.3%)

Algorithm

1×

intervals

Results

181.0ms

8000×

body

128

valid

Compiler

Compiled 29202 to 21003 computations (28.1% saved)