Details

analyze1.9s (11%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5362	451
0	5	5
1	5	5

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%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample129.0ms (0.7%)

Algorithm

1×

intervals

Results

42.0ms	256×	body	128	valid
34.0ms	261×	body	128	nan
18.0ms	124×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify35.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5205	41

prune5.0ms (0%)

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

Error

26.0b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
9.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
11.7b	(sqrt.f64 (/.f64 d h))
14.1b	(sqrt.f64 (/.f64 d l))

rewrite52.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_1480`
41×	`prod-exp_binary64_1491`
32×	`add-sqr-sqrt_binary64_1464`
29×	`times-frac_binary64_1448`
26×	`sqrt-prod_binary64_1458` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
21×	`add-cbrt-cube_binary64_1478`
16×	`associate-r_binary64_1382` `div-exp_binary64_1493`
14×	`sqrt-div_binary64_1459`
13×	`pow1_binary64_1503`
10×	`pow-exp_binary64_1510`
9×	`cbrt-unprod_binary64_1475` `frac-times_binary64_1452`
6×	`associate-r/_binary64_1384` `associate-l/_binary64_1385`
4×	`rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `add-log-exp_binary64_1481` `flip--_binary64_1417`
3×	`div-inv_binary64_1439`
2×	`sqrt-pow1_binary64_1460` `cbrt-undiv_binary64_1476` `cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `associate-l_binary64_1383` `*-commutative_binary64_1373` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow1/2_binary64_1522` `pow-to-exp_binary64_1511`

Counts

4 → 127

Calls

4 calls:

16.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

series482.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

305.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
93.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
44.0ms	(sqrt.f64 (/.f64 d l))
40.0ms	(sqrt.f64 (/.f64 d h))

simplify86.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5007	3595

prune266.0ms (1.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	123	16	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	16	140

Error

9.9b

Counts

140 → 16

Compiler

Compiled 5251 to 2570 computations (51.1% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.7b	(/.f64 (.f64 M D) (.f64 d 2))
4.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
9.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
14.1b	(sqrt.f64 (/.f64 d l))

rewrite65.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log_binary64_1480`
48×	`prod-exp_binary64_1491`
37×	`add-cbrt-cube_binary64_1478`
22×	`add-sqr-sqrt_binary64_1464`
20×	`times-frac_binary64_1448` `div-exp_binary64_1493`
19×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
16×	`associate-r_binary64_1382` `cbrt-unprod_binary64_1475` `pow1_binary64_1503`
13×	`sqrt-div_binary64_1459` `sqrt-prod_binary64_1458`
12×	`associate-*r/_binary64_1384`
10×	`pow-exp_binary64_1510`
9×	`frac-times_binary64_1452`
7×	`pow-prod-down_binary64_1513`
6×	`cbrt-undiv_binary64_1476` `associate-*l/_binary64_1385`
4×	`flip3--_binary64_1446` `add-log-exp_binary64_1481` `flip--_binary64_1417`
3×	`div-inv_binary64_1439`
2×	`cancel-sign-sub-inv_binary64_1408` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `associate-l_binary64_1383` `*-commutative_binary64_1373` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow-to-exp_binary64_1511`
1×	`sqrt-pow1_binary64_1460` `associate-/r_binary64_1386` `clear-num_binary64_1441` `associate-/l_binary64_1387` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`

Counts

4 → 126

Calls

4 calls:

22.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
15.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

series1.2s (7.2%)

Counts

4 → 12

Calls

4 calls:

1.1s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
92.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
41.0ms	(sqrt.f64 (/.f64 d l))
22.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5089	4485

prune269.0ms (1.6%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	128	10	138
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	130	24	154

Error

8.9b

Counts

154 → 24

Compiler

Compiled 6985 to 2824 computations (59.6% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.3b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
3.7b	(/.f64 (.f64 M D) (.f64 d 2))
4.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
9.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite74.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_1480`
55×	`prod-exp_binary64_1491`
46×	`add-cbrt-cube_binary64_1478`
30×	`times-frac_binary64_1448` `add-sqr-sqrt_binary64_1464`
25×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
23×	`cbrt-unprod_binary64_1475`
22×	`sqrt-prod_binary64_1458`
20×	`div-exp_binary64_1493`
18×	`associate-*r/_binary64_1384`
16×	`associate-r_binary64_1382`
14×	`pow-prod-down_binary64_1513`
13×	`sqrt-div_binary64_1459`
10×	`pow-exp_binary64_1510` `cbrt-prod_binary64_1473`
9×	`frac-times_binary64_1452`
6×	`cbrt-undiv_binary64_1476` `associate-*l/_binary64_1385`
4×	`flip3--_binary64_1446` `add-log-exp_binary64_1481` `flip--_binary64_1417`
3×	`rem-sqrt-square_binary64_1455` `div-inv_binary64_1439`
2×	`cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `associate-l_binary64_1383` `*-commutative_binary64_1373` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow-to-exp_binary64_1511`
1×	`sqrt-pow1_binary64_1460` `associate-/r_binary64_1386` `clear-num_binary64_1441` `associate-/l_binary64_1387` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`

Counts

4 → 142

Calls

4 calls:

26.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
8.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))

series1.7s (9.9%)

Counts

4 → 12

Calls

4 calls:

1.5s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
108.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
92.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
25.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify119.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4959	5759
1	4959	5759

prune317.0ms (1.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	148	6	154
Fresh	4	19	23
Picked	1	0	1
Done	0	0	0
Total	153	25	178

Error

5.6b

Counts

178 → 25

Compiler

Compiled 8638 to 3267 computations (62.2% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.7b	(/.f64 (.f64 M D) (.f64 d 2))
4.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
4.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
4.7b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)

rewrite77.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`add-exp-log_binary64_1480`
55×	`prod-exp_binary64_1491`
48×	`add-cbrt-cube_binary64_1478`
24×	`pow1_binary64_1503`
23×	`cbrt-unprod_binary64_1475`
21×	`div-exp_binary64_1493`
17×	`associate-*r/_binary64_1384`
15×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
14×	`cancel-sign-sub-inv_binary64_1408` `pow-prod-down_binary64_1513`
12×	`sqrt-div_binary64_1459` `add-cube-cbrt_binary64_1477`
10×	`pow-exp_binary64_1510` `times-frac_binary64_1448`
9×	`associate-r_binary64_1382` `frac-times_binary64_1452`
8×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
7×	`cbrt-undiv_binary64_1476`
6×	`associate-*l/_binary64_1385`
4×	`associate-/r*_binary64_1386` `div-inv_binary64_1439` `flip3--_binary64_1446` `add-log-exp_binary64_1481` `flip--_binary64_1417`
2×	`sub-neg_binary64_1435` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-l_binary64_1383` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `difference-of-squares_binary64_1411` `pow-to-exp_binary64_1511`
1×	`distribute-lft-out--_binary64_1394`

Counts

4 → 130

Calls

4 calls:

32.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
10.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
8.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))

series1.6s (9.6%)

Counts

4 → 12

Calls

4 calls:

1.5s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
95.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
78.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
22.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify112.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4939	6636
1	4939	6636

prune250.0ms (1.5%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	3	21	24
Picked	1	0	1
Done	0	0	0
Total	142	25	167

Error

4.6b

Counts

167 → 25

Compiler

Compiled 7156 to 2314 computations (67.7% saved)

regimes1.6s (9.2%)

Accuracy

Total 6.4b remaining (41.2%)

Threshold costs 0b (0%)

Compiler

Compiled 24804 to 17387 computations (29.9% saved)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	66
1	86	66

Compiler

Compiled 82 to 58 computations (29.3% saved)

end0.0ms (0%)

sample6.6s (38.3%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.2s	8657×	body	128	nan
706.0ms	4722×	body	128	invalid

Compiler

Compiled 3593 to 2518 computations (29.9% saved)

Details

analyze1.9s (11%)

sample129.0ms (0.7%)

simplify35.0ms (0.2%)

prune5.0ms (0%)

localize22.0ms (0.1%)

rewrite52.0ms (0.3%)

series482.0ms (2.8%)

simplify86.0ms (0.5%)

prune266.0ms (1.5%)

localize29.0ms (0.2%)

rewrite65.0ms (0.4%)

series1.2s (7.2%)

simplify99.0ms (0.6%)

prune269.0ms (1.6%)

localize32.0ms (0.2%)

rewrite74.0ms (0.4%)

series1.7s (9.9%)

simplify119.0ms (0.7%)

prune317.0ms (1.8%)

localize31.0ms (0.2%)

rewrite77.0ms (0.4%)

series1.6s (9.6%)

simplify112.0ms (0.7%)

prune250.0ms (1.5%)

regimes1.6s (9.2%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample6.6s (38.3%)

Profiling