Details

analyze392.0ms (10.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Symmetry

Compiler

Compiled 8 to 6 computations (25% saved)

sample28.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	93×	body	1024	valid
3.0ms	43×	body	512	valid
2.0ms	98×	body	128	valid
1.0ms	6×	body	2048	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

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

Error

41.3b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.3b	(-.f64 (exp.f64 x) 1)

rewrite84.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

41.3b

Rules

35×	`add-sqr-sqrt_binary64_1464`
30×	`*-un-lft-identity_binary64_1442`
21×	`times-frac_binary64_1448`
15×	`add-cube-cbrt_binary64_1477`
10×	`difference-of-squares_binary64_1411`
7×	`associate-/r*_binary64_1386`
5×	`difference-of-sqr-1_binary64_1412` `distribute-lft-out--_binary64_1394`
4×	`add-log-exp_binary64_1481` `add-cbrt-cube_binary64_1478`
3×	`add-exp-log_binary64_1480` `cancel-sign-sub-inv_binary64_1408` `associate-/l*_binary64_1387`
2×	`pow1_binary64_1503` `flip3--_binary64_1446` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 977 to 489 computations (49.9% saved)

series78.0ms (2%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

45.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
17.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 252 to 184 computations (27% saved)

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5105	1195

prune61.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	4	76

Error

0.0b

Counts

76 → 4

Compiler

Compiled 1025 to 517 computations (49.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))))
0.0b	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
0.3b	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
0.3b	(*.f64 1/24 x)

rewrite138.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`add-sqr-sqrt_binary64_1464`
17×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
15×	`add-cbrt-cube_binary64_1478`
14×	`add-exp-log_binary64_1480`
13×	`pow1_binary64_1503`
9×	`associate-r_binary64_1382` `times-frac_binary64_1448`
7×	`associate-l_binary64_1383`
5×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
4×	`add-log-exp_binary64_1481` `associate-*r/_binary64_1384`
3×	`unswap-sqr_binary64_1410` `-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/l_binary64_1387` `associate-/r*_binary64_1386`
2×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-/r/_binary64_1388`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439`

Counts

4 → 92

Calls

4 calls:

8.0ms	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
6.0ms	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
6.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))))
4.0ms	(*.f64 1/24 x)

Compiler

Compiled 2689 to 1626 computations (39.5% saved)

series161.0ms (4.2%)

Error

0.0b

Counts

4 → 19

Calls

4 calls:

54.0ms	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
41.0ms	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
34.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))))
19.0ms	(*.f64 1/24 x)

Compiler

Compiled 739 to 532 computations (28% saved)

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5001	2236

prune123.0ms (3.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	110	5	115

Error

0.0b

Counts

115 → 5

Compiler

Compiled 2754 to 1721 computations (37.5% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 1/24 x) 1/6)
0.0b	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 1/24 x) 1/6)) 1/2))
0.3b	(.f64 x (+.f64 (.f64 1/24 x) 1/6))
0.3b	(*.f64 1/24 x)

rewrite127.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`add-sqr-sqrt_binary64_1464`
10×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`associate-l_binary64_1383` `associate-r_binary64_1382`
6×	`add-log-exp_binary64_1481`
4×	`associate-*r/_binary64_1384`
3×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`
1×	`sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 73

Calls

4 calls:

12.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 1/24 x) 1/6)) 1/2))
7.0ms	(.f64 x (+.f64 (.f64 1/24 x) 1/6))
5.0ms	(+.f64 (*.f64 1/24 x) 1/6)
4.0ms	(*.f64 1/24 x)

Compiler

Compiled 2015 to 1457 computations (27.7% saved)

series155.0ms (4%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

50.0ms	(.f64 x (+.f64 (.f64 1/24 x) 1/6))
35.0ms	(.f64 x (+.f64 (.f64 x (+.f64 (*.f64 1/24 x) 1/6)) 1/2))
34.0ms	(+.f64 (*.f64 1/24 x) 1/6)
19.0ms	(*.f64 1/24 x)

Compiler

Compiled 994 to 772 computations (22.3% saved)

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4923	1083
1	4923	1083

prune107.0ms (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	93	5	98

Error

0.0b

Counts

98 → 5

Compiler

Compiled 2272 to 1630 computations (28.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.1b	(*.f64 (pow.f64 x 3) 1/720)
0.3b	(*.f64 x 1/12)

rewrite136.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

19×	`add-sqr-sqrt_binary64_1464`
18×	`add-log-exp_binary64_1481`
15×	`associate-l_binary64_1383`
11×	`add-exp-log_binary64_1480`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`add-cbrt-cube_binary64_1478`
6×	`pow1_binary64_1503` `associate-r_binary64_1382` `sum-log_binary64_1533`
5×	`unswap-sqr_binary64_1410`
4×	`prod-exp_binary64_1491` `unpow-prod-down_binary64_1521` `cube-prod_binary64_1470`
3×	`diff-log_binary64_1534`
2×	`cbrt-unprod_binary64_1475` `*-commutative_binary64_1373` `sqr-pow_binary64_1414`
1×	`pow-prod-down_binary64_1513` `pow-to-exp_binary64_1511` `pow-exp_binary64_1510` `unpow3_binary64_1508` `cube-mult_binary64_1472` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-+l+_binary64_1375` `+-commutative_binary64_1372` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `cancel-sign-sub-inv_binary64_1408` `associate--l+_binary64_1379`

Counts

4 → 77

Calls

4 calls:

13.0ms	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
10.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
8.0ms	(*.f64 (pow.f64 x 3) 1/720)
4.0ms	(*.f64 x 1/12)

Compiler

Compiled 1744 to 1403 computations (19.6% saved)

series152.0ms (3.9%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

43.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
36.0ms	(-.f64 (+.f64 (+.f64 1/2 (/.f64 1 x)) (.f64 x 1/12)) (.f64 (pow.f64 x 3) 1/720))
34.0ms	(*.f64 (pow.f64 x 3) 1/720)
20.0ms	(*.f64 x 1/12)

Compiler

Compiled 749 to 635 computations (15.2% saved)

simplify77.0ms (2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4946	1364
1	4946	1364

prune108.0ms (2.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	104	5	109

Error

0.0b

Counts

109 → 5

Compiler

Compiled 1905 to 1520 computations (20.2% saved)

regimes200.0ms (5.2%)

Accuracy

Total 0.9b remaining (99.5%)

Threshold costs 0.9b (99.5%)

Compiler

Compiled 2319 to 1645 computations (29.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	67
1	74	67

Removed

()

end0.0ms (0%)

sample1.5s (38.4%)

Algorithm

1×

intervals

Results

360.0ms	2669×	body	1024	valid
104.0ms	1316×	body	512	valid
74.0ms	3108×	body	128	valid
48.0ms	274×	body	2048	valid
30.0ms	633×	body	256	valid

Compiler

Compiled 713 to 512 computations (28.2% saved)

Details

analyze392.0ms (10.1%)

sample28.0ms (0.7%)

simplify7.0ms (0.2%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite84.0ms (2.2%)

series78.0ms (2%)

simplify64.0ms (1.7%)

prune61.0ms (1.6%)

localize11.0ms (0.3%)

rewrite138.0ms (3.6%)

series161.0ms (4.2%)

simplify62.0ms (1.6%)

prune123.0ms (3.2%)

localize15.0ms (0.4%)

rewrite127.0ms (3.3%)

series155.0ms (4%)

simplify80.0ms (2.1%)

prune107.0ms (2.8%)

localize9.0ms (0.2%)

rewrite136.0ms (3.5%)

series152.0ms (3.9%)

simplify77.0ms (2%)

prune108.0ms (2.8%)

regimes200.0ms (5.2%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (38.4%)

Profiling