Details

analyze2.0s (5%)

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)

sample160.0ms (0.4%)

Algorithm

1×

intervals

Results

45.0ms	256×	body	128	valid
43.0ms	272×	body	128	nan
30.0ms	138×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify158.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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

28.7b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize28.0ms (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))))
11.4b	(sqrt.f64 (/.f64 d h))
12.5b	(sqrt.f64 (/.f64 d l))
14.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite352.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

14.7b

Rules

77×	`add-exp-log_binary64_1139`
41×	`prod-exp_binary64_1150`
32×	`add-sqr-sqrt_binary64_1123`
29×	`times-frac_binary64_1107`
26×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117`
21×	`add-cbrt-cube_binary64_1137`
16×	`div-exp_binary64_1152` `associate-r_binary64_1041`
14×	`sqrt-div_binary64_1118`
13×	`pow1_binary64_1162`
10×	`pow-exp_binary64_1169`
9×	`cbrt-unprod_binary64_1134` `frac-times_binary64_1111`
6×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
4×	`pow-prod-down_binary64_1172` `add-log-exp_binary64_1140` `rem-sqrt-square_binary64_1114` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `cbrt-undiv_binary64_1135` `associate-l_binary64_1042` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`

Counts

4 → 127

Calls

4 calls:

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

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.8s (4.7%)

Error

21.0b

Counts

4 → 50

Calls

4 calls:

1.0s	(.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))))
658.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
61.0ms	(sqrt.f64 (/.f64 d l))
43.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify133.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune360.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	160	17	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	17	178

Error

14.0b

Counts

178 → 17

Compiler

Compiled 6026 to 2803 computations (53.5% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.5b	(/.f64 (.f64 M D) (.f64 d 2))
7.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.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))))
12.5b	(sqrt.f64 (/.f64 d l))
14.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite396.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

11.9b

Rules

93×	`add-exp-log_binary64_1139`
48×	`prod-exp_binary64_1150`
37×	`add-cbrt-cube_binary64_1137`
22×	`add-sqr-sqrt_binary64_1123`
20×	`div-exp_binary64_1152` `times-frac_binary64_1107`
19×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
16×	`pow1_binary64_1162` `cbrt-unprod_binary64_1134` `associate-r_binary64_1041`
13×	`sqrt-div_binary64_1118` `sqrt-prod_binary64_1117`
12×	`associate-*r/_binary64_1043`
10×	`pow-exp_binary64_1169`
9×	`frac-times_binary64_1111`
7×	`pow-prod-down_binary64_1172`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042` `*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

Counts

4 → 126

Calls

4 calls:

23.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
19.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.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))))
9.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 5941 to 2966 computations (50.1% saved)

series3.2s (8.1%)

Error

14.0b

Counts

4 → 56

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.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))))
648.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
171.0ms	(/.f64 (.f64 M D) (.f64 d 2))
42.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6028 to 4814 computations (20.1% saved)

simplify127.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5113	5785

prune413.0ms (1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	172	10	182
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	177	22	199

Error

12.9b

Counts

199 → 22

Compiler

Compiled 7909 to 4210 computations (46.8% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.5b	(/.f64 (.f64 M D) (.f64 d 2))
3.9b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
7.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
14.0b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite593.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

Rules

102×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
46×	`add-cbrt-cube_binary64_1137`
37×	`sqrt-div_binary64_1118`
30×	`add-sqr-sqrt_binary64_1123` `associate-*r/_binary64_1043` `times-frac_binary64_1107`
29×	`frac-times_binary64_1111`
25×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
23×	`cbrt-unprod_binary64_1134`
22×	`sqrt-prod_binary64_1117`
20×	`div-exp_binary64_1152`
16×	`associate-r_binary64_1041` `associate-*l/_binary64_1044`
14×	`pow-prod-down_binary64_1172`
10×	`pow-exp_binary64_1169` `cbrt-prod_binary64_1132`
8×	`flip3--_binary64_1105` `flip--_binary64_1076`
6×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140`
3×	`div-inv_binary64_1098` `rem-sqrt-square_binary64_1114`
2×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042` `*-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

Counts

4 → 154

Calls

4 calls:

56.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
21.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.0ms	(/.f64 (.f64 M D) (.f64 d 2))
4.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))

Compiler

Compiled 9295 to 4474 computations (51.9% saved)

series3.4s (8.7%)

Error

12.4b

Counts

4 → 56

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
711.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
197.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
155.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 6974 to 5374 computations (22.9% saved)

simplify178.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5016	8277

prune664.0ms (1.7%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	203	7	210
Fresh	0	21	21
Picked	1	0	1
Done	0	0	0
Total	204	28	232

Error

12.1b

Counts

232 → 28

Compiler

Compiled 11458 to 5863 computations (48.8% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.9b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
5.2b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
6.8b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
7.2b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))) l)))

rewrite683.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

10.3b

Rules

92×	`add-exp-log_binary64_1139`
51×	`prod-exp_binary64_1150`
37×	`sqrt-div_binary64_1118`
36×	`add-cbrt-cube_binary64_1137`
33×	`add-sqr-sqrt_binary64_1123`
29×	`frac-times_binary64_1111` `associate-*r/_binary64_1043` `times-frac_binary64_1107`
28×	`*-un-lft-identity_binary64_1101`
25×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
22×	`sqrt-prod_binary64_1117`
19×	`cbrt-unprod_binary64_1134`
17×	`div-exp_binary64_1152`
16×	`associate-*l/_binary64_1044`
14×	`pow-prod-down_binary64_1172` `cancel-sign-sub-inv_binary64_1067`
10×	`pow-exp_binary64_1169` `cbrt-prod_binary64_1132`
8×	`flip3--_binary64_1105` `flip--_binary64_1076` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
7×	`associate-r_binary64_1041`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `associate-l_binary64_1042`
3×	`cbrt-undiv_binary64_1135` `associate-/r*_binary64_1045` `rem-sqrt-square_binary64_1114`
2×	`sub-neg_binary64_1094` `difference-of-squares_binary64_1070` `*-commutative_binary64_1032` `pow-to-exp_binary64_1170`
1×	`distribute-lft-out--_binary64_1053` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119`

Counts

4 → 156

Calls

4 calls:

69.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.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)
9.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
4.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))

Compiler

Compiled 9817 to 4944 computations (49.6% saved)

series3.7s (9.4%)

Error

11.6b

Counts

4 → 59

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 1 (cbrt.f64 h))) (sqrt.f64 (/.f64 d (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 d (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))) l)))
686.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
455.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
196.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))

Compiler

Compiled 7442 to 5747 computations (22.8% saved)

simplify177.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4943	9860
1	4943	9860

prune641.0ms (1.6%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	207	8	215
Fresh	6	21	27
Picked	1	0	1
Done	0	0	0
Total	214	29	243

Error

11.5b

Counts

243 → 29

Compiler

Compiled 10932 to 5388 computations (50.7% saved)

regimes6.0s (15.2%)

Accuracy

Total 5.4b remaining (39.2%)

Threshold costs 0b (0%)

Compiler

Compiled 72893 to 54486 computations (25.3% saved)

bsearch22.0ms (0.1%)

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

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	195	332
1	195	332

end0.0ms (0%)

sample14.1s (35.7%)

Algorithm

1×

intervals

Results

1.4s	8000×	body	128	valid
1.3s	8334×	body	128	nan
869.0ms	4819×	body	128	invalid

Compiler

Compiled 10648 to 7927 computations (25.6% saved)

Details

analyze2.0s (5%)

sample160.0ms (0.4%)

simplify158.0ms (0.4%)

prune5.0ms (0%)

localize28.0ms (0.1%)

rewrite352.0ms (0.9%)

series1.8s (4.7%)

simplify133.0ms (0.3%)

prune360.0ms (0.9%)

localize40.0ms (0.1%)

rewrite396.0ms (1%)

series3.2s (8.1%)

simplify127.0ms (0.3%)

prune413.0ms (1%)

localize47.0ms (0.1%)

rewrite593.0ms (1.5%)

series3.4s (8.7%)

simplify178.0ms (0.5%)

prune664.0ms (1.7%)

localize35.0ms (0.1%)

rewrite683.0ms (1.7%)

series3.7s (9.4%)

simplify177.0ms (0.4%)

prune641.0ms (1.6%)

regimes6.0s (15.2%)

bsearch22.0ms (0.1%)

simplify7.0ms (0%)

end0.0ms (0%)

sample14.1s (35.7%)

Profiling