Details

analyze3.6s (7.3%)

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)

sample273.0ms (0.6%)

Algorithm

1×

intervals

Results

83.0ms	256×	body	128	valid
67.0ms	267×	body	128	nan
34.0ms	121×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify91.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5205	41

prune13.0ms (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

29.2b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.2b	(.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))))
11.5b	(sqrt.f64 (/.f64 d h))
12.2b	(sqrt.f64 (/.f64 d l))
13.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite107.0ms (0.2%)

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:

37.0ms	(.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))))
26.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
7.0ms	(sqrt.f64 (/.f64 d h))
7.0ms	(sqrt.f64 (/.f64 d l))

series3.0s (6.1%)

Counts

4 → 50

Calls

4 calls:

1.8s	(.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))))
1.1s	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
87.0ms	(sqrt.f64 (/.f64 d h))
81.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 2576 to 2255 computations (12.5% saved)

simplify226.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune799.0ms (1.6%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	152	25	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	25	178

Error

11.3b

Counts

178 → 25

Compiler

Compiled 6307 to 3014 computations (52.2% saved)

localize61.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(/.f64 (.f64 M D) (.f64 d 2))
7.2b	(.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))))
11.5b	(sqrt.f64 (/.f64 d h))
13.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite131.0ms (0.3%)

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:

48.0ms	(.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))))
26.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.0ms	(/.f64 (.f64 M D) (.f64 d 2))
6.0ms	(sqrt.f64 (/.f64 d h))

series5.9s (11.8%)

Counts

4 → 55

Calls

4 calls:

4.4s	(.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))))
1.1s	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
302.0ms	(/.f64 (.f64 M D) (.f64 d 2))
100.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4327 to 3539 computations (18.2% saved)

simplify287.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	4953	6056
1	4953	6056

prune806.0ms (1.6%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	169	12	181
Fresh	6	18	24
Picked	1	0	1
Done	0	0	0
Total	176	30	206

Error

9.5b

Counts

206 → 30

Compiler

Compiled 8671 to 3497 computations (59.7% saved)

localize72.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 d)
6.1b	(/.f64 (.f64 M D) (.f64 d 2))
7.2b	(.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 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
13.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite153.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_1480`
55×	`prod-exp_binary64_1491`
46×	`add-cbrt-cube_binary64_1478`
24×	`pow1_binary64_1503`
23×	`cbrt-unprod_binary64_1475`
20×	`div-exp_binary64_1493`
18×	`associate-*r/_binary64_1384`
16×	`associate-r_binary64_1382`
14×	`pow-prod-down_binary64_1513`
13×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
12×	`sqrt-div_binary64_1459`
10×	`pow-exp_binary64_1510` `times-frac_binary64_1448`
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×	`cbrt-prod_binary64_1473`
2×	`cancel-sign-sub-inv_binary64_1408` `div-inv_binary64_1439` `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×	`associate-/r_binary64_1386` `clear-num_binary64_1441` `associate-/l_binary64_1387` `frac-2neg_binary64_1453` `pow1/3_binary64_1524`

Counts

4 → 118

Calls

4 calls:

65.0ms	(.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 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
27.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
14.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(cbrt.f64 d)

series6.6s (13.3%)

Counts

4 → 54

Calls

4 calls:

5.0s	(.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 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
1.1s	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
287.0ms	(/.f64 (.f64 M D) (.f64 d 2))
166.0ms	(cbrt.f64 d)

Compiler

Compiled 5075 to 3854 computations (24.1% saved)

simplify305.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (169.0ms)

Iter	Nodes	Cost
0	5105	7370

prune835.0ms (1.7%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	167	5	172
Fresh	1	28	29
Picked	1	0	1
Done	0	0	0
Total	169	33	202

Error

8.9b

Counts

202 → 33

Compiler

Compiled 9963 to 3459 computations (65.3% saved)

localize75.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.7b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
6.1b	(/.f64 (.f64 M D) (.f64 d 2))
7.2b	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
7.3b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)

rewrite189.0ms (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:

75.0ms	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
23.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
20.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
14.0ms	(/.f64 (.f64 M D) (.f64 d 2))

series7.6s (15.4%)

Counts

4 → 63

Calls

4 calls:

5.5s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.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 d 2)) 2)) h) l)))
1.1s	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
792.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
289.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 5917 to 4414 computations (25.4% saved)

simplify261.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4938	9311
1	4938	9311

prune666.0ms (1.3%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	1	31	32
Picked	1	0	1
Done	0	0	0
Total	191	35	226

Error

8.7b

Counts

226 → 35

Compiler

Compiled 10058 to 2864 computations (71.5% saved)

regimes3.6s (7.3%)

Accuracy

Total 5.3b remaining (37.5%)

Threshold costs 0b (0%)

Compiler

Compiled 24621 to 18149 computations (26.3% saved)

bsearch548.0ms (1.1%)

Steps

Iters	Range		Point
4	1.8750340580379816e-177	2.9566362306286747e-177	2.0341561774685226e-177
8	-6.871369978331623e-52	-1.191052178232461e-55	-2.7129522053962947e-55

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify41.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	147	160
1	147	160

Compiler

Compiled 198 to 102 computations (48.5% saved)

end0.0ms (0%)

sample13.2s (26.7%)

Algorithm

1×

intervals

Results

2.1s	8000×	body	128	valid
1.9s	8241×	body	128	nan
1.3s	4751×	body	128	invalid

Compiler

Compiled 3640 to 2663 computations (26.8% saved)

Details

analyze3.6s (7.3%)

sample273.0ms (0.6%)

simplify91.0ms (0.2%)

prune13.0ms (0%)

localize57.0ms (0.1%)

rewrite107.0ms (0.2%)

series3.0s (6.1%)

simplify226.0ms (0.5%)

prune799.0ms (1.6%)

localize61.0ms (0.1%)

rewrite131.0ms (0.3%)

series5.9s (11.8%)

simplify287.0ms (0.6%)

prune806.0ms (1.6%)

localize72.0ms (0.1%)

rewrite153.0ms (0.3%)

series6.6s (13.3%)

simplify305.0ms (0.6%)

prune835.0ms (1.7%)

localize75.0ms (0.2%)

rewrite189.0ms (0.4%)

series7.6s (15.4%)

simplify261.0ms (0.5%)

prune666.0ms (1.3%)

regimes3.6s (7.3%)

bsearch548.0ms (1.1%)

simplify41.0ms (0.1%)

end0.0ms (0%)

sample13.2s (26.7%)

Profiling