Details

analyze131.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 22 computations (31.3% saved)

sample24.0ms (0%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify149.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5029	46

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
14×	`add-cbrt-cube_binary64_1478`
10×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
8×	`add-cube-cbrt_binary64_1477`
7×	`associate-r_binary64_1382`
6×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `add-log-exp_binary64_1481` `prod-exp_binary64_1491`
4×	`associate-*r/_binary64_1384` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
3×	`pow-unpow_binary64_1519` `unpow-prod-down_binary64_1521`
2×	`cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `associate-l_binary64_1383` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-+r+_binary64_1374` `unswap-sqr_binary64_1410`
1×	`sum-log_binary64_1533` `pow-exp_binary64_1510` `unpow2_binary64_1507` `flip3--_binary64_1446` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `sqr-pow_binary64_1414` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 80

Calls

4 calls:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series177.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
40.0ms	(.f64 (.f64 a a) (+.f64 1 a))
31.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
31.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify47.0ms (0%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5227	1848

prune139.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	2	93

Merged error: 0.0b

Counts

93 → 2

Compiler

Compiled 3448 to 1857 computations (46.1% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
1.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
3.0b	(.f64 (.f64 b b) (*.f64 a a))

rewrite75.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_1503`
32×	`associate-*r/_binary64_1384`
26×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
20×	`pow-prod-down_binary64_1513` `frac-add_binary64_1450`
14×	`cbrt-unprod_binary64_1475` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491`
13×	`add-log-exp_binary64_1481`
8×	`associate-r_binary64_1382` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
6×	`sum-log_binary64_1533` `add-cube-cbrt_binary64_1477`
5×	`flip3--_binary64_1446` `flip--_binary64_1417`
4×	`pow-plus_binary64_1505` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow-prod-up_binary64_1512`
3×	`associate-l_binary64_1383` `*-commutative_binary64_1373` `unswap-sqr_binary64_1410`
2×	`pow2_binary64_1523` `cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `pow-sqr_binary64_1415` `associate-+r+_binary64_1374`
1×	`associate-+l+_binary64_1375` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393`

Counts

4 → 106

Calls

4 calls:

30.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))
8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series169.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
32.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
31.0ms	(.f64 (.f64 a a) (+.f64 1 a))
24.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5094	4777

prune298.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	117	3	120

Merged error: 0b

Counts

120 → 3

Compiler

Compiled 6732 to 4107 computations (39% saved)

localize43.0ms (0%)

Local error

Found 4 expressions with local error:

1.2b	(+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
1.5b	(.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (*.f64 b b) (-.f64 1 a)))
2.4b	(*.f64 (pow.f64 b 4) (pow.f64 a 4))
41.5b	(/.f64 (+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))

rewrite14.3s (9.5%)

Algorithm

1×	rewrite-expression-head

Rules

33584×	`associate-*r/_binary64_1384`
28080×	`frac-times_binary64_1452`
21940×	`flip3--_binary64_1446` `flip--_binary64_1417`
20384×	`frac-add_binary64_1450`
14040×	`associate-*l/_binary64_1385`
7511×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
5202×	`associate-/l/_binary64_1389`
34×	`add-exp-log_binary64_1480`
29×	`add-sqr-sqrt_binary64_1464`
26×	`associate-/r/_binary64_1388`
25×	`*-un-lft-identity_binary64_1442`
24×	`add-cbrt-cube_binary64_1478` `cancel-sign-sub-inv_binary64_1408` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
18×	`prod-exp_binary64_1491`
17×	`add-cube-cbrt_binary64_1477`
16×	`unpow-prod-down_binary64_1521`
13×	`pow1_binary64_1503`
12×	`associate-+r+_binary64_1374`
10×	`cbrt-unprod_binary64_1475` `associate-l_binary64_1383`
9×	`unswap-sqr_binary64_1410`
8×	`associate-r_binary64_1382` `sub-neg_binary64_1435` `sqr-pow_binary64_1414`
7×	`pow-prod-down_binary64_1513`
6×	`pow-exp_binary64_1510` `add-log-exp_binary64_1481` `pow-to-exp_binary64_1511`
4×	`associate-+l+_binary64_1375` `distribute-lft-out_binary64_1393`
3×	`cbrt-undiv_binary64_1476` `times-frac_binary64_1448` `associate-/l*_binary64_1387` `div-exp_binary64_1493`
2×	`*-commutative_binary64_1373`
1×	`associate-/r*_binary64_1386` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453`

Counts

4 → 10565

Calls

4 calls:

589.0ms	(/.f64 (+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
200.0ms	(+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
15.0ms	(.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (*.f64 b b) (-.f64 1 a)))
8.0ms	(*.f64 (pow.f64 b 4) (pow.f64 a 4))

series980.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

531.0ms	(+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
379.0ms	(/.f64 (+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
42.0ms	(*.f64 (pow.f64 b 4) (pow.f64 a 4))
29.0ms	(.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (*.f64 b b) (-.f64 1 a)))

simplify26.1s (17.4%)

Algorithm

1×	egg-herbie

Counts

10577 → 10577

Iterations

Useful iterations: 0 (578.0ms)

Iter	Nodes	Cost
0	27124	3860774

Details

analyze131.0ms (0.1%)

sample24.0ms (0%)

simplify149.0ms (0.1%)

prune6.0ms (0%)

localize16.0ms (0%)

rewrite40.0ms (0%)

series177.0ms (0.1%)

simplify47.0ms (0%)

prune139.0ms (0.1%)

localize20.0ms (0%)

rewrite75.0ms (0%)

series169.0ms (0.1%)

simplify87.0ms (0.1%)

prune298.0ms (0.2%)

localize43.0ms (0%)

rewrite14.3s (9.5%)

series980.0ms (0.7%)

simplify26.1s (17.4%)

prune1.8min (71.5%)

Profiling