Details

analyze1.5s (13.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample72.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	196×	body	128	valid
12.0ms	23×	body	2048	valid
9.0ms	256×	pre	128	true
8.0ms	12×	body	4096	valid
6.0ms	15×	body	1024	valid
1.0ms	4×	body	512	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify300.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune5.0ms (0.1%)

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: 12.3b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
1.4b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
15.7b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite115.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_1442`
21×	`add-sqr-sqrt_binary64_1464`
20×	`add-cube-cbrt_binary64_1477`
18×	`times-frac_binary64_1448`
16×	`sqrt-prod_binary64_1458`
8×	`pow1_binary64_1503`
6×	`associate-/r*_binary64_1386` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
4×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`sqrt-pow1_binary64_1460` `associate-/l*_binary64_1387`
2×	`associate-*r/_binary64_1384` `associate-/r/_binary64_1388` `pow1/2_binary64_1522`
1×	`cbrt-undiv_binary64_1476` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

4 → 81

Calls

4 calls:

32.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
30.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
19.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
12.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series761.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
156.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
125.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
101.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify191.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	4986	2228
1	4986	2228

prune274.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Merged error: 12.0b

Counts

94 → 11

Compiler

Compiled 2573 to 1691 computations (34.3% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
15.7b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.7b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
15.7b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite76.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1464`
9×	`sqrt-prod_binary64_1458` `*-un-lft-identity_binary64_1442`
7×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
6×	`sqrt-div_binary64_1459` `add-log-exp_binary64_1481`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `pow1/2_binary64_1522`
1×	`sum-log_binary64_1533` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393`

Counts

4 → 57

Calls

4 calls:

26.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
11.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
11.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
10.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series453.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
102.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
98.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
91.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify127.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4897	1276
1	4897	1276

prune343.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	69	11	80

Merged error: 12.0b

Counts

80 → 11

Compiler

Compiled 4559 to 3138 computations (31.2% saved)

localize40.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
7.4b	(+.f64 1 (/.f64 (/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))
16.4b	(cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
16.4b	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite130.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_1442`
14×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
9×	`times-frac_binary64_1448`
6×	`add-cbrt-cube_binary64_1478` `cbrt-prod_binary64_1473` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
4×	`cbrt-div_binary64_1474` `pow1_binary64_1503`
3×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`pow1/3_binary64_1524`
1×	`cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

4 → 65

Calls

4 calls:

84.0ms	(+.f64 1 (/.f64 (/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))
12.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
11.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
6.0ms	(/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))

series1.2s (11.1%)

Counts

4 → 12

Calls

4 calls:

490.0ms	(+.f64 1 (/.f64 (/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))
328.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
230.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
114.0ms	(/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))

simplify133.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4901	2362
1	4901	2362

prune311.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 12.0b

Counts

88 → 11

Compiler

Compiled 3478 to 2280 computations (34.4% saved)

localize51.0ms (0.5%)

Local error

Found 4 expressions with local error:

7.4b	(+.f64 1 (/.f64 (cbrt.f64 (pow.f64 (/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))) 3)) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))
13.6b	(cbrt.f64 (pow.f64 (/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))
16.4b	(cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
16.4b	(cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

rewrite214.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`cbrt-prod_binary64_1473`
23×	`*-un-lft-identity_binary64_1442`
21×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
18×	`times-frac_binary64_1448`
13×	`cube-prod_binary64_1470` `unpow-prod-down_binary64_1521`
6×	`add-log-exp_binary64_1481`
5×	`cbrt-div_binary64_1474`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/3_binary64_1524`
2×	`div-inv_binary64_1439`
1×	`cube-mult_binary64_1472` `sum-log_binary64_1533` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `cube-div_binary64_1471` `rem-cbrt-cube_binary64_1466`

Counts

4 → 80

Calls

4 calls:

161.0ms	(+.f64 1 (/.f64 (cbrt.f64 (pow.f64 (/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))) 3)) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))
12.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
12.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
11.0ms	(cbrt.f64 (pow.f64 (/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))

series882.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

398.0ms	(+.f64 1 (/.f64 (cbrt.f64 (pow.f64 (/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))) 3)) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))
197.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
189.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
99.0ms	(cbrt.f64 (pow.f64 (/.f64 x (fabs.f64 (cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x))))) 3))

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4972	2955
1	4972	2955

prune194.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	92	11	103

Merged error: 12.0b

Counts

103 → 11

Compiler

Compiled 3754 to 2463 computations (34.4% saved)

regimes670.0ms (6.4%)

Compiler: Compiled 9099 to 6755 computations (25.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	26
1	21	26

end0.0ms (0%)

sample2.4s (22.7%)

Algorithm

1×

intervals

Results

347.0ms	6063×	body	128	valid
239.0ms	800×	body	2048	valid
164.0ms	8000×	pre	128	true
113.0ms	505×	body	1024	valid
98.0ms	256×	body	4096	valid
45.0ms	258×	body	512	valid
13.0ms	118×	body	256	valid

Compiler

Compiled 1334 to 996 computations (25.3% saved)

Details

analyze1.5s (13.9%)

sample72.0ms (0.7%)

simplify300.0ms (2.9%)

prune5.0ms (0.1%)

localize24.0ms (0.2%)

rewrite115.0ms (1.1%)

series761.0ms (7.2%)

simplify191.0ms (1.8%)

prune274.0ms (2.6%)

localize32.0ms (0.3%)

rewrite76.0ms (0.7%)

series453.0ms (4.3%)

simplify127.0ms (1.2%)

prune343.0ms (3.3%)

localize40.0ms (0.4%)

rewrite130.0ms (1.2%)

series1.2s (11.1%)

simplify133.0ms (1.3%)

prune311.0ms (3%)

localize51.0ms (0.5%)

rewrite214.0ms (2%)

series882.0ms (8.4%)

simplify96.0ms (0.9%)

prune194.0ms (1.8%)

regimes670.0ms (6.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (22.7%)

Profiling