Details

analyze1.6s (6.3%)

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)

sample130.0ms (0.5%)

Algorithm

1×

intervals

Results

39.0ms	256×	body	128	valid
34.0ms	286×	body	128	nan
21.0ms	156×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify130.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

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

26.2b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(.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))))
10.9b	(sqrt.f64 (/.f64 d h))
11.5b	(sqrt.f64 (/.f64 d l))
15.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite302.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

13.5b

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

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.6s (6.2%)

Error

18.6b

Counts

4 → 50

Calls

4 calls:

882.0ms	(.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))))
552.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
42.0ms	(sqrt.f64 (/.f64 d h))
40.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune289.0ms (1.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	158	19	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	19	178

Error

11.1b

Counts

178 → 19

Compiler

Compiled 6123 to 2870 computations (53.1% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.9b	(/.f64 (.f64 M D) (.f64 d 2))
4.9b	(.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))))
11.5b	(sqrt.f64 (/.f64 d l))
15.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite289.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

9.9b

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:

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 (9.6%)

Error

11.0b

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))))
552.0ms	(.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))
47.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6088 to 4435 computations (27.2% saved)

simplify139.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4947	5747
1	4947	5747

prune309.0ms (1.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	170	7	177
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	174	22	196

Error

10.1b

Counts

196 → 22

Compiler

Compiled 8097 to 3184 computations (60.7% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.8b	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
2.9b	(/.f64 (.f64 M D) (.f64 d 2))
4.9b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.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))))
15.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite433.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

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×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119`

Counts

4 → 154

Calls

4 calls:

41.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.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))))
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 d (cbrt.f64 l)))

Compiler

Compiled 9641 to 3786 computations (60.7% saved)

series2.6s (10%)

Error

8.9b

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)))) (.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))))
552.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
137.0ms	(sqrt.f64 (/.f64 d (cbrt.f64 l)))
134.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 7079 to 5065 computations (28.5% saved)

simplify123.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4971	8326
1	4971	8326

prune497.0ms (1.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	198	7	205
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	202	25	227

Error

8.4b

Counts

227 → 25

Compiler

Compiled 11690 to 4794 computations (59% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.9b	(/.f64 (.f64 M D) (.f64 2 d))
4.9b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.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)))
5.7b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
7.6b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)

rewrite474.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

8.0b

Rules

104×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
48×	`add-cbrt-cube_binary64_1137`
36×	`sqrt-div_binary64_1118`
29×	`frac-times_binary64_1111` `associate-*r/_binary64_1043`
24×	`pow1_binary64_1162`
23×	`cbrt-unprod_binary64_1134`
21×	`div-exp_binary64_1152`
16×	`associate-*l/_binary64_1044`
15×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
14×	`pow-prod-down_binary64_1172` `cancel-sign-sub-inv_binary64_1067`
12×	`add-cube-cbrt_binary64_1136`
10×	`pow-exp_binary64_1169` `times-frac_binary64_1107`
8×	`flip3--_binary64_1105` `flip--_binary64_1076` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`
7×	`cbrt-undiv_binary64_1135` `associate-r_binary64_1041`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `associate-/r_binary64_1045` `associate-l*_binary64_1042`
2×	`pow-to-exp_binary64_1170` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `-commutative_binary64_1032` `sub-neg_binary64_1094` `difference-of-squares_binary64_1070`
1×	`distribute-lft-out--_binary64_1053`

Counts

4 → 142

Calls

4 calls:

44.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.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)
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 9417 to 3919 computations (58.4% saved)

series2.8s (11.1%)

Error

8.4b

Counts

4 → 57

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)))) (.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)))
554.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
379.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
138.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 7879 to 5538 computations (29.7% saved)

simplify138.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4973	9707
1	4973	9707

prune367.0ms (1.4%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	2	22	24
Picked	0	1	1
Done	0	0	0
Total	198	26	224

Error

7.5b

Counts

224 → 26

Compiler

Compiled 10524 to 4033 computations (61.7% saved)

regimes2.7s (10.7%)

Accuracy

Total 4.9b remaining (37.5%)

Threshold costs 0b (0%)

Compiler

Compiled 39391 to 28803 computations (26.9% saved)

bsearch11.0ms (0%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	146	321
1	146	321

end0.0ms (0%)

sample7.9s (31%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.0s	8423×	body	128	nan
906.0ms	4906×	body	128	invalid

Compiler

Compiled 5854 to 4241 computations (27.6% saved)

Details

analyze1.6s (6.3%)

sample130.0ms (0.5%)

simplify130.0ms (0.5%)

prune5.0ms (0%)

localize24.0ms (0.1%)

rewrite302.0ms (1.2%)

series1.6s (6.2%)

simplify91.0ms (0.4%)

prune289.0ms (1.1%)

localize26.0ms (0.1%)

rewrite289.0ms (1.1%)

series2.5s (9.6%)

simplify139.0ms (0.5%)

prune309.0ms (1.2%)

localize34.0ms (0.1%)

rewrite433.0ms (1.7%)

series2.6s (10%)

simplify123.0ms (0.5%)

prune497.0ms (1.9%)

localize36.0ms (0.1%)

rewrite474.0ms (1.9%)

series2.8s (11.1%)

simplify138.0ms (0.5%)

prune367.0ms (1.4%)

regimes2.7s (10.7%)

bsearch11.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample7.9s (31%)

Profiling