Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample30.0ms (0.1%)

Algorithm

1×

intervals

Results

13.0ms	58×	body	1024	valid
5.0ms	139×	body	128	valid
3.0ms	28×	body	512	valid
2.0ms	23×	body	256	valid
1.0ms	8×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify165.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune3.0ms (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

29.2b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.7b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite64.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64_1442`
76×	`times-frac_binary64_1448`
75×	`add-sqr-sqrt_binary64_1464`
34×	`cancel-sign-sub-inv_binary64_1408`
27×	`add-cube-cbrt_binary64_1477`
23×	`distribute-lft-out_binary64_1393`
22×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
9×	`difference-of-sqr-1_binary64_1412`
7×	`associate-/r*_binary64_1386`
4×	`add-cbrt-cube_binary64_1478` `associate-/r/_binary64_1388` `associate-/l*_binary64_1387` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
3×	`flip3--_binary64_1446` `flip--_binary64_1417`
2×	`associate-/l/_binary64_1389` `div-inv_binary64_1439` `pow1_binary64_1503`
1×	`cbrt-undiv_binary64_1476` `sub-neg_binary64_1435` `clear-num_binary64_1441` `frac-sub_binary64_1451` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `div-exp_binary64_1493`

Counts

2 → 114

Calls

2 calls:

44.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

series47.0ms (0.1%)

Counts

2 → 6

Calls

2 calls:

34.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
13.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify76.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5302	2309

prune152.0ms (0.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	5	121

Error

0.1b

Counts

121 → 5

Compiler

Compiled 2404 to 1713 computations (28.7% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 x 1) (*.f64 x x))
4.0b	(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
11.4b	(+.f64 (/.f64 x (+.f64 x 1)) (.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (.f64 x x))))
15.8b	(.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (.f64 x x)))

rewrite65.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64_1442`
49×	`add-sqr-sqrt_binary64_1464`
41×	`times-frac_binary64_1448`
26×	`associate-l_binary64_1383` `add-cube-cbrt_binary64_1477`
11×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `distribute-lft-out_binary64_1393`
9×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
8×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
6×	`pow1_binary64_1503`
5×	`associate-/l*_binary64_1387` `frac-add_binary64_1450`
4×	`associate-r/_binary64_1384` `associate-/r_binary64_1386` `sum-log_binary64_1533` `associate-/r/_binary64_1388` `frac-times_binary64_1452`
3×	`associate-r_binary64_1382`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `div-inv_binary64_1439` `+-commutative_binary64_1372` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `prod-exp_binary64_1491` `associate-+r+_binary64_1374` `associate-*l/_binary64_1385` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
1×	`associate-+l+_binary64_1375` `clear-num_binary64_1441` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `flip--_binary64_1417` `frac-2neg_binary64_1453` `div-sub_binary64_1447`

Counts

4 → 128

Calls

4 calls:

20.0ms	(.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (.f64 x x)))
14.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (.f64 x x))))
11.0ms	(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
6.0ms	(+.f64 (+.f64 x 1) (*.f64 x x))

series118.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (.f64 x x))))
25.0ms	(.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (.f64 x x)))
20.0ms	(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
9.0ms	(+.f64 (+.f64 x 1) (*.f64 x x))

simplify87.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4957	3861
1	4957	3861

prune223.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	141	4	145

Error

0.0b

Counts

145 → 4

Compiler

Compiled 4682 to 3243 computations (30.7% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
11.4b	(+.f64 (+.f64 (.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (*.f64 x x) (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))))
14.8b	(*.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 x 1))
15.8b	(.f64 (.f64 x x) (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))))

rewrite99.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`*-un-lft-identity_binary64_1442`
70×	`add-sqr-sqrt_binary64_1464`
62×	`times-frac_binary64_1448`
36×	`add-cube-cbrt_binary64_1477`
30×	`associate-r_binary64_1382`
27×	`associate-l_binary64_1383`
23×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
17×	`distribute-lft-out_binary64_1393`
13×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
12×	`associate-*r/_binary64_1384` `frac-add_binary64_1450`
11×	`pow1_binary64_1503`
9×	`add-log-exp_binary64_1481` `flip3-+_binary64_1445` `flip-+_binary64_1416`
8×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
6×	`associate-/r/_binary64_1388`
5×	`associate-/l*_binary64_1387`
4×	`cbrt-undiv_binary64_1476` `associate-/r*_binary64_1386` `pow-prod-down_binary64_1513` `frac-times_binary64_1452` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
3×	`sum-log_binary64_1533` `div-inv_binary64_1439`
2×	`associate-/l/_binary64_1389` `-commutative_binary64_1373` `associate-l/_binary64_1385`
1×	`associate-+l+_binary64_1375` `clear-num_binary64_1441` `flip3--_binary64_1446` `+-commutative_binary64_1372` `flip--_binary64_1417` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `div-sub_binary64_1447`

Counts

4 → 166

Calls

4 calls:

27.0ms	(+.f64 (+.f64 (.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (*.f64 x x) (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))))
21.0ms	(*.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 x 1))
18.0ms	(.f64 (.f64 x x) (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))))
11.0ms	(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))

series142.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(+.f64 (+.f64 (.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (*.f64 x x) (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))))
29.0ms	(.f64 (.f64 x x) (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))))
28.0ms	(*.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 x 1))
22.0ms	(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))

simplify123.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4936	5019
1	4936	5019

prune466.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	178	4	182

Error

0.0b

Counts

182 → 4

Compiler

Compiled 7814 to 5636 computations (27.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 -1 x) (+.f64 (.f64 x x) -1))
4.0b	(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
15.8b	(.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (.f64 x x) -1))
26.9b	(+.f64 (.f64 (+.f64 -1 (pow.f64 x 3)) (+.f64 (.f64 (+.f64 x 1) (.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (.f64 x x) -1))) (-.f64 (.f64 x x) x))) (.f64 (.f64 x x) (.f64 (-.f64 -1 x) (+.f64 (*.f64 x x) -1))))

rewrite902.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

1920×	`associate-*r/_binary64_1384`
1790×	`frac-times_binary64_1452`
1696×	`frac-add_binary64_1450`
1234×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
742×	`flip3--_binary64_1446` `flip--_binary64_1417`
479×	`associate-*l/_binary64_1385`
70×	`*-un-lft-identity_binary64_1442`
55×	`add-sqr-sqrt_binary64_1464`
41×	`times-frac_binary64_1448`
31×	`associate-l_binary64_1383`
28×	`add-cube-cbrt_binary64_1477`
13×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
11×	`distribute-lft-out_binary64_1393`
10×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
8×	`associate-r_binary64_1382` `pow1_binary64_1503`
7×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
6×	`add-log-exp_binary64_1481`
5×	`associate-/l*_binary64_1387`
4×	`associate-/r*_binary64_1386` `associate-/r/_binary64_1388` `associate-+r+_binary64_1374`
3×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
2×	`cbrt-undiv_binary64_1476` `associate-+l+_binary64_1375` `associate-/l/_binary64_1389` `div-inv_binary64_1439` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `difference-of-sqr--1_binary64_1413` `div-exp_binary64_1493`
1×	`sum-log_binary64_1533` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `div-sub_binary64_1447`

Counts

4 → 1026

Calls

4 calls:

73.0ms	(+.f64 (.f64 (+.f64 -1 (pow.f64 x 3)) (+.f64 (.f64 (+.f64 x 1) (.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (.f64 x x) -1))) (-.f64 (.f64 x x) x))) (.f64 (.f64 x x) (.f64 (-.f64 -1 x) (+.f64 (*.f64 x x) -1))))
19.0ms	(.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (.f64 x x) -1))
11.0ms	(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
10.0ms	(.f64 (-.f64 -1 x) (+.f64 (.f64 x x) -1))

series149.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(+.f64 (.f64 (+.f64 -1 (pow.f64 x 3)) (+.f64 (.f64 (+.f64 x 1) (.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (.f64 x x) -1))) (-.f64 (.f64 x x) x))) (.f64 (.f64 x x) (.f64 (-.f64 -1 x) (+.f64 (*.f64 x x) -1))))
25.0ms	(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
20.0ms	(.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (.f64 x x) -1))
13.0ms	(.f64 (-.f64 -1 x) (+.f64 (.f64 x x) -1))

simplify1.4s (3.5%)

Algorithm

1×	egg-herbie

Counts

1038 → 1038

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	6939	202041

prune33.8s (82.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	1035	3	1038
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	1037	5	1042

Error

0.0b

Counts

1042 → 5

Compiler

Compiled 154005 to 96577 computations (37.3% saved)

regimes338.0ms (0.8%)

Accuracy

Total 0.0b remaining (77.4%)

Threshold costs 0.0b (77.4%)

Compiler

Compiled 4812 to 3288 computations (31.7% saved)

bsearch60.0ms (0.1%)

Steps

Iters	Range		Point
7	2002.0971593067625	76411.77405661362	11950.400014151677
10	-3.210513510522684e+18	-237.0784643383779	-10352.2765048927

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	92	121
1	92	121

end0.0ms (0%)

sample2.3s (5.7%)

Algorithm

1×

intervals

Results

274.0ms	1983×	body	1024	valid
153.0ms	4229×	body	128	valid
108.0ms	1025×	body	512	valid
41.0ms	225×	body	2048	valid
37.0ms	538×	body	256	valid

Compiler

Compiled 2430 to 1655 computations (31.9% saved)

Details

analyze5.0ms (0%)

sample30.0ms (0.1%)

simplify165.0ms (0.4%)

prune3.0ms (0%)

localize7.0ms (0%)

rewrite64.0ms (0.2%)

series47.0ms (0.1%)

simplify76.0ms (0.2%)

prune152.0ms (0.4%)

localize18.0ms (0%)

rewrite65.0ms (0.2%)

series118.0ms (0.3%)

simplify87.0ms (0.2%)

prune223.0ms (0.5%)

localize16.0ms (0%)

rewrite99.0ms (0.2%)

series142.0ms (0.3%)

simplify123.0ms (0.3%)

prune466.0ms (1.1%)

localize23.0ms (0.1%)

rewrite902.0ms (2.2%)

series149.0ms (0.4%)

simplify1.4s (3.5%)

prune33.8s (82.6%)

regimes338.0ms (0.8%)

bsearch60.0ms (0.1%)

simplify5.0ms (0%)

end0.0ms (0%)

sample2.3s (5.7%)

Profiling