Details

analyze1.9s (5.4%)

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)

sample157.0ms (0.5%)

Algorithm

1×

intervals

Results

36.0ms	256×	body	128	valid
33.0ms	255×	body	128	nan
29.0ms	162×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify43.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5205	41

prune6.0ms (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

26.2b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(/.f64 (.f64 M D) (.f64 d 2))
8.8b	(sqrt.f64 (/.f64 d h))
13.3b	(sqrt.f64 (/.f64 d l))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite274.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

12.6b

Rules

84×	`add-exp-log_binary64_1480`
42×	`prod-exp_binary64_1491`
31×	`add-sqr-sqrt_binary64_1464`
30×	`times-frac_binary64_1448`
28×	`add-cbrt-cube_binary64_1478`
26×	`sqrt-prod_binary64_1458`
25×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
20×	`div-exp_binary64_1493`
13×	`associate-r_binary64_1382`
10×	`pow-exp_binary64_1510` `cbrt-unprod_binary64_1475`
8×	`pow1_binary64_1503`
6×	`cbrt-undiv_binary64_1476`
4×	`add-log-exp_binary64_1481` `div-inv_binary64_1439` `rem-sqrt-square_binary64_1455`
2×	`pow-to-exp_binary64_1511` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `sqrt-div_binary64_1459`
1×	`pow-prod-down_binary64_1513` `associate-r/_binary64_1384` `associate-l_binary64_1383` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-/r_binary64_1386`

Counts

4 → 115

Calls

4 calls:

12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
11.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3980 to 1816 computations (54.4% saved)

series803.0ms (2.3%)

Error

24.7b

Counts

4 → 36

Calls

4 calls:

546.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
132.0ms	(/.f64 (.f64 M D) (.f64 d 2))
42.0ms	(sqrt.f64 (/.f64 d h))
40.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3146 to 2306 computations (26.7% saved)

simplify77.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5039	2413

prune276.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	133	18	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	18	152

Error

12.8b

Counts

152 → 18

Compiler

Compiled 5237 to 2439 computations (53.4% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.3b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
5.4b	(/.f64 (.f64 M D) (.f64 d 2))
8.8b	(sqrt.f64 (/.f64 d h))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite312.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

9.1b

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×	`div-exp_binary64_1493` `times-frac_binary64_1448`
19×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
16×	`pow1_binary64_1503` `cbrt-unprod_binary64_1475` `associate-r_binary64_1382`
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×	`add-log-exp_binary64_1481` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`div-inv_binary64_1439`
2×	`pow-to-exp_binary64_1511` `associate-l_binary64_1383` `*-commutative_binary64_1373` `rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `distribute-rgt-in_binary64_1392` `cancel-sign-sub-inv_binary64_1408` `distribute-lft-in_binary64_1391`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-/r_binary64_1386`

Counts

4 → 126

Calls

4 calls:

26.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 6223 to 2306 computations (62.9% saved)

series3.2s (9.4%)

Error

10.6b

Counts

4 → 55

Calls

4 calls:

2.4s	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
561.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
144.0ms	(/.f64 (.f64 M D) (.f64 d 2))
43.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 6480 to 4729 computations (27% saved)

simplify123.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4953	6056
1	4953	6056

prune334.0ms (1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	169	12	181
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	174	25	199

Error

9.7b

Counts

199 → 25

Compiler

Compiled 8524 to 3397 computations (60.1% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.8b	(sqrt.f64 (/.f64 d (cbrt.f64 h)))
4.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
5.4b	(/.f64 (.f64 M D) (.f64 d 2))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite382.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

8.2b

Rules

102×	`add-exp-log_binary64_1480`
55×	`prod-exp_binary64_1491`
46×	`add-cbrt-cube_binary64_1478`
30×	`add-sqr-sqrt_binary64_1464` `times-frac_binary64_1448`
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×	`add-log-exp_binary64_1481` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`div-inv_binary64_1439` `rem-sqrt-square_binary64_1455`
2×	`pow-to-exp_binary64_1511` `associate-l_binary64_1383` `*-commutative_binary64_1373` `sub-neg_binary64_1435` `distribute-rgt-in_binary64_1392` `cancel-sign-sub-inv_binary64_1408` `distribute-lft-in_binary64_1391`
1×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-/r_binary64_1386` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460`

Counts

4 → 142

Calls

4 calls:

27.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 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))
9.0ms	(/.f64 (.f64 M D) (.f64 d 2))
4.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 h)))

Compiler

Compiled 8206 to 3354 computations (59.1% saved)

series3.2s (9.3%)

Error

9.7b

Counts

4 → 54

Calls

4 calls:

2.3s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
574.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
147.0ms	(/.f64 (.f64 M D) (.f64 d 2))
147.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 h)))

Compiler

Compiled 7731 to 5737 computations (25.8% saved)

simplify159.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4948	7543
1	4948	7543

prune480.0ms (1.4%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	187	9	196
Fresh	4	20	24
Picked	1	0	1
Done	0	0	0
Total	192	29	221

Error

9.0b

Counts

221 → 29

Compiler

Compiled 10851 to 4797 computations (55.8% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.9b	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
4.3b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
6.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))

rewrite1.2s (3.4%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

Rules

801×	`add-exp-log_binary64_1480`
480×	`prod-exp_binary64_1491`
201×	`div-exp_binary64_1493`
122×	`add-cbrt-cube_binary64_1478`
108×	`cbrt-unprod_binary64_1475`
75×	`pow-exp_binary64_1510`
48×	`associate-r_binary64_1382`
39×	`cbrt-undiv_binary64_1476`
38×	`times-frac_binary64_1448`
36×	`cbrt-prod_binary64_1473`
31×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
29×	`pow1_binary64_1503`
21×	`associate-*r/_binary64_1384`
17×	`pow-prod-down_binary64_1513`
15×	`pow-to-exp_binary64_1511`
12×	`sqrt-div_binary64_1459`
10×	`frac-times_binary64_1452`
7×	`associate-*l/_binary64_1385`
4×	`add-log-exp_binary64_1481` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`associate-l_binary64_1383` `div-inv_binary64_1439` `*-commutative_binary64_1373`
2×	`sub-neg_binary64_1435` `distribute-rgt-in_binary64_1392` `cancel-sign-sub-inv_binary64_1408` `distribute-lft-in_binary64_1391`
1×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387` `associate-/r_binary64_1386`

Counts

4 → 287

Calls

4 calls:

35.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
31.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
18.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 21310 to 6853 computations (67.8% saved)

series4.5s (12.9%)

Error

9.0b

Counts

4 → 63

Calls

4 calls:

2.3s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
1.2s	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
663.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
149.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 9958 to 7039 computations (29.3% saved)

simplify189.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5138	13559

prune956.0ms (2.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	348	2	350
Fresh	2	26	28
Picked	1	0	1
Done	0	0	0
Total	351	28	379

Error

8.8b

Counts

379 → 28

Compiler

Compiled 19012 to 6969 computations (63.3% saved)

regimes4.9s (14.2%)

Accuracy

Total 6.6b remaining (44.1%)

Threshold costs 0b (0%)

Compiler

Compiled 69310 to 50026 computations (27.8% saved)

bsearch0.0ms (0%)

simplify15.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	93
1	117	93

Compiler

Compiled 114 to 72 computations (36.8% saved)

end0.0ms (0%)

sample11.0s (31.8%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.1s	8365×	body	128	nan
685.0ms	4690×	body	128	invalid

Compiler

Compiled 8891 to 6419 computations (27.8% saved)

Details

analyze1.9s (5.4%)

sample157.0ms (0.5%)

simplify43.0ms (0.1%)

prune6.0ms (0%)

localize21.0ms (0.1%)

rewrite274.0ms (0.8%)

series803.0ms (2.3%)

simplify77.0ms (0.2%)

prune276.0ms (0.8%)

localize26.0ms (0.1%)

rewrite312.0ms (0.9%)

series3.2s (9.4%)

simplify123.0ms (0.4%)

prune334.0ms (1%)

localize33.0ms (0.1%)

rewrite382.0ms (1.1%)

series3.2s (9.3%)

simplify159.0ms (0.5%)

prune480.0ms (1.4%)

localize41.0ms (0.1%)

rewrite1.2s (3.4%)

series4.5s (12.9%)

simplify189.0ms (0.5%)

prune956.0ms (2.8%)

regimes4.9s (14.2%)

bsearch0.0ms (0%)

simplify15.0ms (0%)

end0.0ms (0%)

sample11.0s (31.8%)

Profiling