Details

analyze1.7s (6.7%)

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%	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)

sample121.0ms (0.5%)

Algorithm

1×

intervals

Results

35.0ms	256×	body	128	valid
29.0ms	235×	body	128	nan
19.0ms	137×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify132.0ms (0.5%)

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

23.4b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.8b	(.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))))
8.0b	(sqrt.f64 (/.f64 d l))
9.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
10.7b	(sqrt.f64 (/.f64 d h))

rewrite290.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

11.9b

Rules

77×	`add-exp-log_binary64_1480`
41×	`prod-exp_binary64_1491`
32×	`add-sqr-sqrt_binary64_1464`
29×	`times-frac_binary64_1448`
26×	`add-cube-cbrt_binary64_1477` `sqrt-prod_binary64_1458` `*-un-lft-identity_binary64_1442`
21×	`add-cbrt-cube_binary64_1478`
16×	`div-exp_binary64_1493` `associate-r_binary64_1382`
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×	`add-log-exp_binary64_1481` `rem-sqrt-square_binary64_1455` `pow-prod-down_binary64_1513` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`div-inv_binary64_1439`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `pow-to-exp_binary64_1511` `cbrt-undiv_binary64_1476` `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`

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

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.6s (6.2%)

Error

17.2b

Counts

4 → 50

Calls

4 calls:

892.0ms	(.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))))
543.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
40.0ms	(sqrt.f64 (/.f64 d l))
39.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune275.0ms (1.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	163	14	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	14	178

Error

10.2b

Counts

178 → 14

Compiler

Compiled 5936 to 2734 computations (53.9% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(/.f64 (.f64 M D) (.f64 d 2))
6.8b	(.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))))
8.0b	(sqrt.f64 (/.f64 d l))
9.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite284.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

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))))
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))

Compiler

Compiled 6223 to 2306 computations (62.9% saved)

series2.5s (9.8%)

Error

10.2b

Counts

4 → 51

Calls

4 calls:

1.7s	(.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))))
544.0ms	(.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))
45.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6088 to 4435 computations (27.2% saved)

simplify124.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4947	5747
1	4947	5747

prune305.0ms (1.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	169	8	177
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	172	19	191

Error

9.7b

Counts

191 → 19

Compiler

Compiled 8016 to 3116 computations (61.1% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.4b	(sqrt.f64 (/.f64 (cbrt.f64 d) l))
4.7b	(/.f64 (.f64 M D) (.f64 d 2))
6.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (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))))
9.2b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite344.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

8.5b

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:

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))))
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))
4.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 7884 to 2640 computations (66.5% saved)

series2.7s (10.8%)

Error

9.2b

Counts

4 → 51

Calls

4 calls:

1.8s	(.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))))
553.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
148.0ms	(/.f64 (.f64 M D) (.f64 d 2))
144.0ms	(sqrt.f64 (/.f64 (cbrt.f64 d) l))

Compiler

Compiled 6949 to 4919 computations (29.2% saved)

simplify133.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4965	6948
1	4965	6948

prune358.0ms (1.4%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	191	21	212

Error

8.9b

Counts

212 → 21

Compiler

Compiled 9859 to 3528 computations (64.2% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.2b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
4.7b	(/.f64 (.f64 M D) (.f64 2 d))
5.0b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
6.8b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (cbrt.f64 d)) (sqrt.f64 (/.f64 (cbrt.f64 d) l)))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))

rewrite322.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

8.7b

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×	`times-frac_binary64_1448` `pow-exp_binary64_1510`
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` `flip3--_binary64_1446` `flip--_binary64_1417` `div-inv_binary64_1439` `associate-l_binary64_1383` `associate-/r*_binary64_1386`
2×	`sub-neg_binary64_1435` `difference-of-squares_binary64_1411` `-commutative_binary64_1373` `pow-to-exp_binary64_1511` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l_binary64_1387`
1×	`distribute-lft-out--_binary64_1394`

Counts

4 → 130

Calls

4 calls:

27.0ms	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
9.0ms	(/.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 7660 to 2672 computations (65.1% saved)

series2.9s (11.6%)

Error

8.9b

Counts

4 → 57

Calls

4 calls:

1.8s	(.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 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
543.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
363.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
136.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 7671 to 5317 computations (30.7% saved)

simplify116.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5047	8167

prune300.0ms (1.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	19	20
Picked	0	1	1
Done	0	0	0
Total	186	22	208

Error

8.9b

Counts

208 → 22

Compiler

Compiled 8922 to 2797 computations (68.7% saved)

regimes2.7s (10.7%)

Accuracy

Total 4.6b remaining (33.4%)

Threshold costs 0b (0%)

Compiler

Compiled 38922 to 28481 computations (26.8% saved)

bsearch13.0ms (0.1%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	129	190
1	129	190

end0.0ms (0%)

sample7.8s (30.9%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.1s	8300×	body	128	nan
666.0ms	4678×	body	128	invalid

Compiler

Compiled 5703 to 4157 computations (27.1% saved)

Details

analyze1.7s (6.7%)

sample121.0ms (0.5%)

simplify132.0ms (0.5%)

prune5.0ms (0%)

localize20.0ms (0.1%)

rewrite290.0ms (1.2%)

series1.6s (6.2%)

simplify91.0ms (0.4%)

prune275.0ms (1.1%)

localize25.0ms (0.1%)

rewrite284.0ms (1.1%)

series2.5s (9.8%)

simplify124.0ms (0.5%)

prune305.0ms (1.2%)

localize28.0ms (0.1%)

rewrite344.0ms (1.4%)

series2.7s (10.8%)

simplify133.0ms (0.5%)

prune358.0ms (1.4%)

localize30.0ms (0.1%)

rewrite322.0ms (1.3%)

series2.9s (11.6%)

simplify116.0ms (0.5%)

prune300.0ms (1.2%)

regimes2.7s (10.7%)

bsearch13.0ms (0.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.8s (30.9%)

Profiling