Details

analyze513.0ms (10.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample21.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify163.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune2.0ms (0.1%)

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

Merged error: 27.2b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.4b	(+.f64 (.f64 a c) (.f64 b d))
26.7b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
9×	`times-frac_binary64_1461`
4×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
3×	`flip-+_binary64_1429` `associate-/r_binary64_1399` `associate-/l_binary64_1400` `flip3-+_binary64_1458`
2×	`associate-/r/_binary64_1401` `pow1_binary64_1516` `associate-/l/_binary64_1402`
1×	`div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

2 → 42

Calls

2 calls:

10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series260.0ms (5.4%)

Counts

2 → 6

Calls

2 calls:

184.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
75.0ms	(+.f64 (.f64 a c) (.f64 b d))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5447	1227

prune346.0ms (7.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	9	49

Merged error: 26.4b

Counts

49 → 9

Compiler

Compiled 8589 to 3626 computations (57.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 a c) (.f64 b d))
17.5b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1477`
21×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
18×	`sqrt-prod_binary64_1471` `times-frac_binary64_1461`
6×	`sqrt-div_binary64_1472` `pow1_binary64_1516` `associate-/r*_binary64_1399` `add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
5×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
3×	`associate-/l*_binary64_1400`
2×	`sqrt-pow1_binary64_1473` `associate-/r/_binary64_1401` `rem-sqrt-square_binary64_1468` `associate-/l/_binary64_1402` `pow1/2_binary64_1535`
1×	`div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

4 → 84

Calls

4 calls:

12.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
5.0ms	(+.f64 (.f64 a c) (.f64 b d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series422.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

246.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
76.0ms	(+.f64 (.f64 a c) (.f64 b d))
50.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
50.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify72.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5228	2326

prune200.0ms (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Merged error: 25.5b

Counts

105 → 10

Compiler

Compiled 5603 to 1636 computations (70.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

17.5b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1477`
22×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
21×	`sqrt-prod_binary64_1471`
18×	`times-frac_binary64_1461`
8×	`sqrt-div_binary64_1472`
7×	`pow1_binary64_1516`
6×	`associate-/r*_binary64_1399` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
5×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
4×	`add-log-exp_binary64_1494`
3×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `associate-/l*_binary64_1400` `pow1/2_binary64_1535`
2×	`associate-/r/_binary64_1401` `associate-/l/_binary64_1402`
1×	`div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `div-inv_binary64_1452`

Counts

4 → 88

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
5.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series391.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
52.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
49.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
40.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify80.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5041	2368

prune138.0ms (2.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	99	11	110

Merged error: 25.5b

Counts

110 → 11

Compiler

Compiled 5001 to 781 computations (84.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

13.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
29.3b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.3b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.3b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite74.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-exp-log_binary64_1493`
43×	`add-sqr-sqrt_binary64_1477`
33×	`times-frac_binary64_1461`
25×	`*-un-lft-identity_binary64_1455`
24×	`associate-r_binary64_1395`
22×	`add-cube-cbrt_binary64_1490`
21×	`cbrt-prod_binary64_1486`
20×	`prod-exp_binary64_1504` `cbrt-div_binary64_1487`
18×	`add-cbrt-cube_binary64_1491`
15×	`div-exp_binary64_1506` `associate-l_binary64_1396`
10×	`associate-/r/_binary64_1401` `flip-+_binary64_1429` `flip3-+_binary64_1458`
9×	`unswap-sqr_binary64_1423`
8×	`cbrt-unprod_binary64_1488`
7×	`cbrt-undiv_binary64_1489`
6×	`pow1_binary64_1516`
5×	`frac-times_binary64_1465`
4×	`1-exp_binary64_1499` `add-log-exp_binary64_1494` `rec-exp_binary64_1505`
3×	`associate-r/_binary64_1397` `pow1/3_binary64_1537` `associate-l/_binary64_1398`
2×	`div-inv_binary64_1452`
1×	`*-commutative_binary64_1386` `pow-prod-down_binary64_1526`

Counts

4 → 119

Calls

4 calls:

40.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series691.0ms (14.4%)

Counts

4 → 12

Calls

4 calls:

282.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
140.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
139.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
129.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify129.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4924	4114
1	4924	4114

prune156.0ms (3.2%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	131	11	142

Merged error: 25.5b

Counts

142 → 11

Compiler

Compiled 5364 to 976 computations (81.8% saved)

regimes132.0ms (2.7%)

Compiler: Compiled 1284 to 752 computations (41.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	80
1	24	80

end0.0ms (0%)

sample810.0ms (16.8%)

Algorithm

1×

intervals

Results

341.0ms	8000×	body	128	valid
17.0ms	425×	body	128	invalid

Compiler

Compiled 345 to 186 computations (46.1% saved)

Details

analyze513.0ms (10.7%)

sample21.0ms (0.4%)

simplify163.0ms (3.4%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite18.0ms (0.4%)

series260.0ms (5.4%)

simplify62.0ms (1.3%)

prune346.0ms (7.2%)

localize12.0ms (0.3%)

rewrite35.0ms (0.7%)

series422.0ms (8.8%)

simplify72.0ms (1.5%)

prune200.0ms (4.2%)

localize15.0ms (0.3%)

rewrite37.0ms (0.8%)

series391.0ms (8.1%)

simplify80.0ms (1.7%)

prune138.0ms (2.9%)

localize16.0ms (0.3%)

rewrite74.0ms (1.5%)

series691.0ms (14.4%)

simplify129.0ms (2.7%)

prune156.0ms (3.2%)

regimes132.0ms (2.7%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample810.0ms (16.8%)

Profiling