Details

analyze1.9s (7.1%)

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

Symmetry

(sort M D)

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample160.0ms (0.6%)

Algorithm

1×

intervals

Results

45.0ms	314×	body	128	nan
35.0ms	256×	body	128	valid
23.0ms	178×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify35.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

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

28.3b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b	(/.f64 (.f64 M D) (.f64 d 2))
12.3b	(sqrt.f64 (/.f64 d h))
12.5b	(sqrt.f64 (/.f64 d l))
15.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite245.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

14.7b

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:

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 l))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3980 to 1816 computations (54.4% saved)

series800.0ms (3%)

Error

26.6b

Counts

4 → 36

Calls

4 calls:

541.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
138.0ms	(/.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)

simplify69.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5039	2413

prune262.0ms (1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	130	21	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	21	152

Error

14.0b

Counts

152 → 21

Compiler

Compiled 5318 to 2516 computations (52.7% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.8b	(.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))))
6.2b	(/.f64 (.f64 M D) (.f64 d 2))
12.5b	(sqrt.f64 (/.f64 d l))
15.4b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite295.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

12.0b

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:

21.0ms	(.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))))
13.0ms	(.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 l))

Compiler

Compiled 6223 to 2306 computations (62.9% saved)

series2.5s (9.2%)

Error

13.6b

Counts

4 → 51

Calls

4 calls:

1.6s	(.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))))
555.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
142.0ms	(/.f64 (.f64 M D) (.f64 d 2))
43.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6088 to 4435 computations (27.2% saved)

simplify126.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4947	5747
1	4947	5747

prune320.0ms (1.2%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	165	12	177
Fresh	5	15	20
Picked	1	0	1
Done	0	0	0
Total	171	27	198

Error

11.5b

Counts

198 → 27

Compiler

Compiled 8403 to 3369 computations (59.9% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b	(/.f64 (.f64 M D) (.f64 2 d))
6.3b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
6.3b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
12.5b	(sqrt.f64 (/.f64 d l))

rewrite191.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

10.0b

Rules

86×	`add-exp-log_binary64_1480`
42×	`prod-exp_binary64_1491`
30×	`add-cbrt-cube_binary64_1478`
21×	`div-exp_binary64_1493`
17×	`add-sqr-sqrt_binary64_1464`
14×	`add-cube-cbrt_binary64_1477` `times-frac_binary64_1448` `*-un-lft-identity_binary64_1442`
13×	`sqrt-prod_binary64_1458`
10×	`pow-exp_binary64_1510` `cbrt-unprod_binary64_1475`
7×	`pow1_binary64_1503` `cbrt-undiv_binary64_1476`
4×	`add-log-exp_binary64_1481` `associate-/r*_binary64_1386`
3×	`div-inv_binary64_1439` `associate-l_binary64_1383`
2×	`rem-sqrt-square_binary64_1455` `pow-to-exp_binary64_1511` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l*_binary64_1387`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `sqrt-div_binary64_1459` `pow-prod-down_binary64_1513` `associate-r_binary64_1382` `*-commutative_binary64_1373`

Counts

4 → 98

Calls

4 calls:

10.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
8.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 4302 to 1677 computations (61% saved)

series1.1s (4.1%)

Error

11.5b

Counts

4 → 42

Calls

4 calls:

530.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
349.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
132.0ms	(/.f64 (.f64 M D) (.f64 2 d))
42.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 4768 to 3034 computations (36.4% saved)

simplify67.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5170	2467

prune244.0ms (0.9%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	131	9	140
Fresh	5	21	26
Picked	1	0	1
Done	0	0	0
Total	137	30	167

Error

10.0b

Counts

167 → 30

Compiler

Compiled 6715 to 2678 computations (60.1% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
6.3b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
6.3b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))

rewrite349.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

9.5b

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×	`pow-prod-down_binary64_1513` `cancel-sign-sub-inv_binary64_1408`
12×	`add-cube-cbrt_binary64_1477` `sqrt-div_binary64_1459`
10×	`pow-exp_binary64_1510` `times-frac_binary64_1448`
9×	`frac-times_binary64_1452`
8×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`
7×	`associate-r_binary64_1382` `cbrt-undiv_binary64_1476`
6×	`associate-*l/_binary64_1385`
4×	`add-log-exp_binary64_1481` `associate-l_binary64_1383` `div-inv_binary64_1439` `associate-/r*_binary64_1386` `flip3--_binary64_1446` `flip--_binary64_1417`
2×	`pow-to-exp_binary64_1511` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387` `sub-neg_binary64_1435` `difference-of-squares_binary64_1411`
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 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
10.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
8.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 8304 to 2673 computations (67.8% saved)

series3.4s (12.8%)

Error

9.9b

Counts

4 → 60

Calls

4 calls:

2.3s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
536.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
362.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
143.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 8609 to 5644 computations (34.4% saved)

simplify126.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4963	9026
1	4963	9026

prune315.0ms (1.2%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	182	8	190
Fresh	6	23	29
Picked	1	0	1
Done	0	0	0
Total	189	31	220

Error

9.6b

Counts

220 → 31

Compiler

Compiled 9880 to 2781 computations (71.9% saved)

regimes4.2s (15.5%)

Accuracy

Total 5.6b remaining (40%)

Threshold costs 0b (0%)

Compiler

Compiled 65544 to 46013 computations (29.8% saved)

bsearch16.0ms (0.1%)

Compiler: Compiled 35 to 31 computations (11.4% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	156	195
1	156	195

Compiler

Compiled 246 to 144 computations (41.5% saved)

end0.0ms (0%)

sample10.0s (37.3%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.1s	8678×	body	128	nan
670.0ms	4854×	body	128	invalid

Compiler

Compiled 8424 to 5907 computations (29.9% saved)

Details

analyze1.9s (7.1%)

sample160.0ms (0.6%)

simplify35.0ms (0.1%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite245.0ms (0.9%)

series800.0ms (3%)

simplify69.0ms (0.3%)

prune262.0ms (1%)

localize24.0ms (0.1%)

rewrite295.0ms (1.1%)

series2.5s (9.2%)

simplify126.0ms (0.5%)

prune320.0ms (1.2%)

localize27.0ms (0.1%)

rewrite191.0ms (0.7%)

series1.1s (4.1%)

simplify67.0ms (0.2%)

prune244.0ms (0.9%)

localize31.0ms (0.1%)

rewrite349.0ms (1.3%)

series3.4s (12.8%)

simplify126.0ms (0.5%)

prune315.0ms (1.2%)

regimes4.2s (15.5%)

bsearch16.0ms (0.1%)

simplify19.0ms (0.1%)

end0.0ms (0%)

sample10.0s (37.3%)

Profiling