Details

analyze483.0ms (6.6%)

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%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Compiler

Compiled 9 to 9 computations (0% saved)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	78×	body	128	nan
1.0ms	24×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify100.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

prune2.0ms (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

17.8b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.4b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.3b	(/.f64 A (*.f64 V l))
14.1b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1464`
15×	`sqrt-prod_binary64_1458`
11×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
10×	`associate-r_binary64_1382` `add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
9×	`times-frac_binary64_1448`
6×	`pow1_binary64_1503`
3×	`div-inv_binary64_1439` `associate-/l_binary64_1387` `associate-l*_binary64_1383` `add-log-exp_binary64_1481`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sqrt-div_binary64_1459` `prod-exp_binary64_1491` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`

Counts

3 → 66

Calls

3 calls:

8.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
4.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

series113.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
33.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))
18.0ms	(/.f64 A (*.f64 V l))

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4793	857
1	4793	857

prune81.0ms (1.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	57	18	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	18	76

Error

6.1b

Counts

76 → 18

Compiler

Compiled 1130 to 407 computations (64% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
2.1b	(/.f64 V (/.f64 (cbrt.f64 A) l))
2.9b	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
14.1b	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

rewrite145.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

849×	`times-frac_binary64_1448`
358×	`add-sqr-sqrt_binary64_1464`
331×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
157×	`sqrt-prod_binary64_1458`
146×	`cbrt-prod_binary64_1473`
93×	`associate-/r*_binary64_1386`
79×	`associate-r_binary64_1382`
32×	`add-exp-log_binary64_1480`
24×	`div-inv_binary64_1439`
23×	`add-cbrt-cube_binary64_1478`
15×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
8×	`associate-/r/_binary64_1388`
7×	`pow1_binary64_1503`
6×	`unswap-sqr_binary64_1410`
5×	`rem-sqrt-square_binary64_1455`
4×	`cbrt-unprod_binary64_1475` `associate-/l*_binary64_1387` `add-log-exp_binary64_1481` `prod-exp_binary64_1491`
3×	`associate-l_binary64_1383`
2×	`clear-num_binary64_1441` `sqrt-div_binary64_1459` `frac-2neg_binary64_1453`
1×	`sqrt-pow1_binary64_1460` `associate-r/_binary64_1384` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `pow1/2_binary64_1522`

Counts

4 → 463

Calls

4 calls:

40.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
18.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
18.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))
7.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))

series270.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
79.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))
58.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))
48.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))

simplify186.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4982	12244
1	4982	12244

prune421.0ms (5.8%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	461	14	475
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	470	23	493

Error

2.3b

Counts

493 → 23

Compiler

Compiled 11820 to 2251 computations (81% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
1.4b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))))
1.9b	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
4.6b	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464`
13×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
12×	`times-frac_binary64_1448` `cbrt-prod_binary64_1473`
11×	`add-cbrt-cube_binary64_1478`
10×	`sqrt-prod_binary64_1458` `pow1_binary64_1503`
6×	`associate-/l*_binary64_1387`
4×	`cbrt-unprod_binary64_1475` `add-log-exp_binary64_1481` `prod-exp_binary64_1491`
3×	`associate-l_binary64_1383` `pow-prod-down_binary64_1513`
2×	`associate-*r/_binary64_1384` `cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `sqrt-div_binary64_1459` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-r_binary64_1382` `associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `pow1/3_binary64_1524` `pow1/2_binary64_1522`

Counts

4 → 78

Calls

4 calls:

13.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))))
5.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))
5.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
1.0ms	(cbrt.f64 A)

series507.0ms (7%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))))
135.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V))))
83.0ms	(cbrt.f64 A)
71.0ms	(/.f64 (cbrt.f64 A) (*.f64 l (cbrt.f64 V)))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4942	1674
1	4942	1674

prune112.0ms (1.5%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	3	19	22
Picked	1	0	1
Done	0	0	0
Total	88	25	113

Error

1.3b

Counts

113 → 25

Compiler

Compiled 2451 to 831 computations (66.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
1.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) l) (/.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 V)))
1.4b	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) l) (/.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 V))))))
4.6b	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) l) (/.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 V))))

rewrite80.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`cbrt-prod_binary64_1473`
85×	`add-sqr-sqrt_binary64_1464`
76×	`times-frac_binary64_1448`
59×	`associate-r_binary64_1382`
45×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
30×	`add-exp-log_binary64_1480`
20×	`add-cbrt-cube_binary64_1478`
14×	`pow1_binary64_1503` `unswap-sqr_binary64_1410`
11×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
10×	`associate-l_binary64_1383`
9×	`associate-*r/_binary64_1384`
7×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
6×	`sqrt-div_binary64_1459`
5×	`pow-prod-down_binary64_1513`
4×	`add-log-exp_binary64_1481`
3×	`frac-times_binary64_1452` `associate-*l/_binary64_1385`
2×	`sqrt-pow1_binary64_1460` `div-inv_binary64_1439` `*-commutative_binary64_1373`
1×	`sqrt-prod_binary64_1458` `pow1/3_binary64_1524` `pow1/2_binary64_1522`

Counts

4 → 149

Calls

4 calls:

26.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) l) (/.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 V)))
17.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) l) (/.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 V))))))
15.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) l) (/.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 V))))
1.0ms	(cbrt.f64 A)

series517.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(.f64 c0 (.f64 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V))) (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) l) (/.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 V))))))
147.0ms	(sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) l) (/.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 V))))
80.0ms	(cbrt.f64 A)
73.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) l) (/.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 V)))

simplify97.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4988	3725
1	4988	3725

prune168.0ms (2.3%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	1	23	24
Picked	0	1	1
Done	0	0	0
Total	158	28	186

Error

0.8b

Counts

186 → 28

Compiler

Compiled 4696 to 1347 computations (71.3% saved)

regimes1.5s (20.9%)

Accuracy

Total 4.0b remaining (86.1%)

Threshold costs 0b (0%)

Compiler

Compiled 14669 to 10241 computations (30.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	19	31

end0.0ms (0%)

sample2.2s (29.9%)

Algorithm

1×

intervals

Results

300.0ms	8000×	body	128	valid
110.0ms	2932×	body	128	nan
32.0ms	873×	body	128	invalid

Compiler

Compiled 1760 to 1225 computations (30.4% saved)

Details

analyze483.0ms (6.6%)

sample25.0ms (0.3%)

simplify100.0ms (1.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite19.0ms (0.3%)

series113.0ms (1.6%)

simplify93.0ms (1.3%)

prune81.0ms (1.1%)

localize12.0ms (0.2%)

rewrite145.0ms (2%)

series270.0ms (3.7%)

simplify186.0ms (2.6%)

prune421.0ms (5.8%)

localize13.0ms (0.2%)

rewrite31.0ms (0.4%)

series507.0ms (7%)

simplify74.0ms (1%)

prune112.0ms (1.5%)

localize17.0ms (0.2%)

rewrite80.0ms (1.1%)

series517.0ms (7.1%)

simplify97.0ms (1.3%)

prune168.0ms (2.3%)

regimes1.5s (20.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (29.9%)

Profiling