Details

analyze475.0ms (6.8%)

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%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	172×	body	128	valid
8.0ms	29×	body	2048	valid
4.0ms	22×	body	1024	valid
4.0ms	11×	body	4096	valid
3.0ms	17×	body	512	valid
1.0ms	27×	body	128	nan
1.0ms	16×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify372.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (276.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 33.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 3 a) c)
0.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
1.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1464`
15×	`*-un-lft-identity_binary64_1442`
14×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
10×	`pow1_binary64_1503`
9×	`add-cube-cbrt_binary64_1477`
6×	`times-frac_binary64_1448` `associate-/l*_binary64_1387` `add-log-exp_binary64_1481` `sqrt-prod_binary64_1458` `difference-of-squares_binary64_1411`
4×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
3×	`associate-r_binary64_1382` `cancel-sign-sub-inv_binary64_1408` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `flip--_binary64_1417` `distribute-lft-out--_binary64_1394`
2×	`cbrt-undiv_binary64_1476` `associate-/l/_binary64_1389` `sqrt-div_binary64_1459` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `associate-l_binary64_1383` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `pow1/2_binary64_1522` `div-sub_binary64_1447`

Counts

4 → 80

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series258.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
16.0ms	(.f64 (.f64 3 a) c)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5038	1907

prune133.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Merged error: 5.6b

Counts

93 → 8

Compiler

Compiled 2199 to 1317 computations (40.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.4b	(.f64 (.f64 3 a) c)
1.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1464`
10×	`pow1_binary64_1503`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `*-un-lft-identity_binary64_1442`
8×	`add-log-exp_binary64_1481`
7×	`add-cube-cbrt_binary64_1477`
4×	`cancel-sign-sub-inv_binary64_1408` `sqrt-prod_binary64_1458`
3×	`associate-r_binary64_1382` `cbrt-unprod_binary64_1475` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `flip--_binary64_1417` `prod-exp_binary64_1491`
2×	`sub-neg_binary64_1435` `sqrt-div_binary64_1459` `diff-log_binary64_1534` `difference-of-squares_binary64_1411`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-l_binary64_1383` `*-commutative_binary64_1373` `pow1/2_binary64_1522` `distribute-lft-out--_binary64_1394`

Counts

4 → 62

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(.f64 (.f64 3 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series176.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
16.0ms	(.f64 (.f64 3 a) c)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4941	1226
1	4941	1226

prune80.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	73	9	82

Merged error: 5.5b

Counts

82 → 9

Compiler

Compiled 1732 to 1051 computations (39.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.1b	(/.f64 (/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3) a)
10.0b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite80.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`times-frac_binary64_1448`
140×	`*-un-lft-identity_binary64_1442`
111×	`add-sqr-sqrt_binary64_1464`
110×	`add-cube-cbrt_binary64_1477`
35×	`associate-/l*_binary64_1387`
33×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
26×	`associate-/r/_binary64_1388`
18×	`div-inv_binary64_1439`
15×	`cbrt-undiv_binary64_1476` `distribute-lft-out_binary64_1393` `div-exp_binary64_1493`
14×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
7×	`associate-/r*_binary64_1386`
6×	`cbrt-unprod_binary64_1475` `add-log-exp_binary64_1481` `prod-exp_binary64_1491`
5×	`pow1_binary64_1503`
3×	`sqrt-prod_binary64_1458`
2×	`clear-num_binary64_1441` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `associate-/l/_binary64_1389` `flip3--_binary64_1446` `+-commutative_binary64_1372` `flip--_binary64_1417` `pow1/2_binary64_1522`

Counts

4 → 214

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3) a)
12.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series486.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

207.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
155.0ms	(/.f64 (/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3) a)
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

simplify140.0ms (2%)

Algorithm

1×	egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5774	10154

prune436.0ms (6.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	225	10	235

Merged error: 5.4b

Counts

235 → 10

Compiler

Compiled 8475 to 5155 computations (39.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.1b	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (.f64 3 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (neg.f64 a))
10.1b	(/.f64 (.f64 (.f64 3 a) c) (.f64 3 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite61.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`times-frac_binary64_1448`
54×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
42×	`*-un-lft-identity_binary64_1442`
41×	`add-sqr-sqrt_binary64_1464`
40×	`add-cube-cbrt_binary64_1477`
24×	`associate-*r/_binary64_1384` `distribute-lft-neg-in_binary64_1399` `associate-/r/_binary64_1388` `distribute-rgt-neg-in_binary64_1400`
19×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
18×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
13×	`div-inv_binary64_1439` `flip3-+_binary64_1445` `flip-+_binary64_1416`
11×	`associate-/r*_binary64_1386`
8×	`associate-/l*_binary64_1387` `neg-mul-1_binary64_1438`
6×	`add-log-exp_binary64_1481`
5×	`pow1_binary64_1503`
3×	`sqrt-prod_binary64_1458`
2×	`clear-num_binary64_1441` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `associate-/l/_binary64_1389` `flip3--_binary64_1446` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `pow1/2_binary64_1522`

Counts

4 → 166

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (.f64 3 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (neg.f64 a))
12.0ms	(/.f64 (.f64 (.f64 3 a) c) (.f64 3 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series461.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(/.f64 (.f64 (.f64 3 a) c) (.f64 3 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
145.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (.f64 3 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (neg.f64 a))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

simplify108.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5100	6756

prune232.0ms (3.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	178	10	188

Merged error: 5.4b

Counts

188 → 10

Compiler

Compiled 5492 to 2859 computations (47.9% saved)

regimes1.0s (14.9%)

Compiler: Compiled 5215 to 4027 computations (22.8% saved)

bsearch123.0ms (1.7%)

Steps

Iters	Range		Point
9	2.394774756278425e+90	9.266040621085212e+95	1.1209799556123897e+93
10	4.505325403816651e-301	3.1952576883306086e-290	1.03289464838539e-299
9	-6.564386773984526e+133	-3.959911012611247e+125	-2.452019057043114e+129

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	123	95
1	123	95

end0.0ms (0%)

sample2.0s (29.2%)

Algorithm

1×

intervals

Results

290.0ms	5244×	body	128	valid
284.0ms	1069×	body	2048	valid
156.0ms	744×	body	1024	valid
129.0ms	392×	body	4096	valid
57.0ms	345×	body	512	valid
35.0ms	684×	body	128	nan
21.0ms	206×	body	256	valid
19.0ms	347×	body	128	invalid

Compiler

Compiled 1034 to 790 computations (23.6% saved)

Details

analyze475.0ms (6.8%)

sample40.0ms (0.6%)

simplify372.0ms (5.3%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite37.0ms (0.5%)

series258.0ms (3.7%)

simplify65.0ms (0.9%)

prune133.0ms (1.9%)

localize14.0ms (0.2%)

rewrite27.0ms (0.4%)

series176.0ms (2.5%)

simplify71.0ms (1%)

prune80.0ms (1.1%)

localize18.0ms (0.3%)

rewrite80.0ms (1.1%)

series486.0ms (6.9%)

simplify140.0ms (2%)

prune436.0ms (6.2%)

localize14.0ms (0.2%)

rewrite61.0ms (0.9%)

series461.0ms (6.6%)

simplify108.0ms (1.5%)

prune232.0ms (3.3%)

regimes1.0s (14.9%)

bsearch123.0ms (1.7%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.0s (29.2%)

Profiling