Details

analyze457.0ms (7.2%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	34×	body	2048	valid
9.0ms	177×	body	128	valid
4.0ms	23×	body	1024	valid
2.0ms	11×	body	512	valid
1.0ms	4×	body	4096	valid
1.0ms	18×	body	128	nan
1.0ms	14×	body	128	invalid
1.0ms	7×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify464.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (301.0ms)

Iter	Nodes	Cost
0	1706	24
1	1706	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: 36.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite30.0ms (0.5%)

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:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(.f64 (.f64 3 a) c)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series349.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
28.0ms	(.f64 (.f64 3 a) c)

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4842	1226
1	4842	1226

prune99.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	7	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	8	75

Merged error: 16.0b

Counts

75 → 8

Compiler

Compiled 1736 to 1050 computations (39.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.5b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
24.8b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
24.8b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_1481`
7×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`cbrt-prod_binary64_1473`
4×	`add-cbrt-cube_binary64_1478` `cancel-sign-sub-inv_binary64_1408` `cbrt-div_binary64_1474` `flip3--_binary64_1446` `add-exp-log_binary64_1480` `flip--_binary64_1417` `pow1_binary64_1503`
2×	`sub-neg_binary64_1435` `diff-log_binary64_1534` `pow1/3_binary64_1524`

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series572.0ms (9%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
154.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
153.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4879	1584
1	4879	1584

prune118.0ms (1.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	60	12	72

Merged error: 16.0b

Counts

72 → 12

Compiler

Compiled 2622 to 1634 computations (37.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464`
6×	`sqrt-prod_binary64_1458` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`add-cbrt-cube_binary64_1478` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `add-exp-log_binary64_1480` `flip--_binary64_1417`
2×	`sqrt-pow1_binary64_1460` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `diff-log_binary64_1534` `pow1/2_binary64_1522`

Counts

4 → 54

Calls

4 calls:

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

series360.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4930	1236
1	4930	1236

prune115.0ms (1.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	66	12	78

Merged error: 16.0b

Counts

78 → 12

Compiler

Compiled 2740 to 1667 computations (39.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

12.9b	(-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite53.0ms (0.8%)

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` `add-log-exp_binary64_1481`
4×	`add-cbrt-cube_binary64_1478` `flip3--_binary64_1446` `add-exp-log_binary64_1480` `flip--_binary64_1417`
3×	`sqrt-pow1_binary64_1460` `cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `pow1/2_binary64_1522`
1×	`sub-neg_binary64_1435` `diff-log_binary64_1534`

Counts

4 → 59

Calls

4 calls:

29.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series478.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
104.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5016	1313

prune125.0ms (2%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	71	12	83

Merged error: 16.0b

Counts

83 → 12

Compiler

Compiled 3037 to 1803 computations (40.6% saved)

regimes699.0ms (11%)

Compiler: Compiled 4656 to 3499 computations (24.8% saved)

bsearch126.0ms (2%)

Steps

Iters	Range	Point
9	2.5114705838444347e+129	2.831801074286139e+135	8.100785156979165e+130
11	3.714320220403526e-128	6.808977649747393e-104	4.4072850734806817e-122
10	-5.370766603421699e+165	-1.6171936456930988e+154	-1.6422358087771794e+154

Iters

Range

Point

2.5114705838444347e+129

2.831801074286139e+135

8.100785156979165e+130

3.714320220403526e-128

6.808977649747393e-104

4.4072850734806817e-122

-5.370766603421699e+165

-1.6171936456930988e+154

-1.6422358087771794e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	113
1	100	113

end0.0ms (0%)

sample1.9s (29.6%)

Algorithm

1×

intervals

Results

282.0ms	1126×	body	2048	valid
275.0ms	5159×	body	128	valid
145.0ms	704×	body	1024	valid
140.0ms	444×	body	4096	valid
56.0ms	373×	body	512	valid
34.0ms	681×	body	128	nan
21.0ms	400×	body	128	invalid
19.0ms	194×	body	256	valid

Compiler

Compiled 894 to 664 computations (25.7% saved)

Details

analyze457.0ms (7.2%)

sample39.0ms (0.6%)

simplify464.0ms (7.3%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite30.0ms (0.5%)

series349.0ms (5.5%)

simplify80.0ms (1.3%)

prune99.0ms (1.6%)

localize14.0ms (0.2%)

rewrite31.0ms (0.5%)

series572.0ms (9%)

simplify71.0ms (1.1%)

prune118.0ms (1.9%)

localize13.0ms (0.2%)

rewrite26.0ms (0.4%)

series360.0ms (5.7%)

simplify58.0ms (0.9%)

prune115.0ms (1.8%)

localize17.0ms (0.3%)

rewrite53.0ms (0.8%)

series478.0ms (7.5%)

simplify67.0ms (1%)

prune125.0ms (2%)

regimes699.0ms (11%)

bsearch126.0ms (2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.9s (29.6%)

Profiling