Details

analyze1.7s (9.8%)

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)

sample122.0ms (0.7%)

Algorithm

1×

intervals

Results

35.0ms	255×	body	128	nan
35.0ms	256×	body	128	valid
22.0ms	152×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify133.0ms (0.8%)

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

26.1b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(.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))))
11.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
12.4b	(sqrt.f64 (/.f64 d h))
13.4b	(sqrt.f64 (/.f64 d l))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-exp-log_binary64_1139`
41×	`prod-exp_binary64_1150`
32×	`add-sqr-sqrt_binary64_1123`
29×	`times-frac_binary64_1107`
26×	`*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
21×	`add-cbrt-cube_binary64_1137`
16×	`associate-r_binary64_1041` `div-exp_binary64_1152`
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×	`rem-sqrt-square_binary64_1114` `add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172`
3×	`div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `distribute-lft-in_binary64_1050` `cbrt-undiv_binary64_1135` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051` `pow1/2_binary64_1181`

Counts

4 → 127

Calls

4 calls:

18.0ms	(.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))

series517.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

332.0ms	(.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))))
100.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
43.0ms	(sqrt.f64 (/.f64 d h))
42.0ms	(sqrt.f64 (/.f64 d l))

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5007	3595

prune271.0ms (1.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	117	22	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	22	140

Error

12.8b

Counts

140 → 22

Compiler

Compiled 5488 to 2751 computations (49.9% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.2b	(/.f64 (.f64 M D) (.f64 d 2))
6.9b	(.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	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.4b	(sqrt.f64 (/.f64 d l))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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×	`times-frac_binary64_1107` `div-exp_binary64_1152`
19×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
16×	`cbrt-unprod_binary64_1134` `pow1_binary64_1162` `associate-r_binary64_1041`
13×	`sqrt-prod_binary64_1117` `sqrt-div_binary64_1118`
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` `flip--_binary64_1076` `flip3--_binary64_1105`
3×	`div-inv_binary64_1098`
2×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051`
1×	`frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 126

Calls

4 calls:

20.0ms	(.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))

series1.3s (7.9%)

Counts

4 → 12

Calls

4 calls:

1.2s	(.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))))
95.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
51.0ms	(sqrt.f64 (/.f64 d l))
24.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5089	4485

prune256.0ms (1.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	6	15	21
Picked	1	0	1
Done	0	0	0
Total	137	23	160

Error

11.5b

Counts

160 → 23

Compiler

Compiled 6875 to 2774 computations (59.7% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 d)
5.2b	(/.f64 (.f64 M D) (.f64 d 2))
6.9b	(.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))))
11.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite67.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
46×	`add-cbrt-cube_binary64_1137`
24×	`pow1_binary64_1162`
23×	`cbrt-unprod_binary64_1134`
20×	`div-exp_binary64_1152`
18×	`associate-*r/_binary64_1043`
16×	`associate-r_binary64_1041`
14×	`pow-prod-down_binary64_1172`
13×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
12×	`sqrt-div_binary64_1118`
10×	`pow-exp_binary64_1169` `times-frac_binary64_1107`
9×	`frac-times_binary64_1111`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105`
3×	`cbrt-prod_binary64_1132`
2×	`-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `div-inv_binary64_1098` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051`
1×	`pow1/3_binary64_1183` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

Counts

4 → 118

Calls

4 calls:

29.0ms	(.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))))
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))
1.0ms	(cbrt.f64 d)

series1.5s (8.9%)

Counts

4 → 12

Calls

4 calls:

1.3s	(.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 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
95.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
82.0ms	(cbrt.f64 d)
24.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5055	5275

prune273.0ms (1.6%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	2	20	22
Picked	1	0	1
Done	0	0	0
Total	129	24	153

Error

9.2b

Counts

153 → 24

Compiler

Compiled 7826 to 2720 computations (65.2% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.2b	(/.f64 (.f64 M D) (.f64 d 2))
5.5b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
6.0b	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
6.9b	(.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)))

rewrite81.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
48×	`add-cbrt-cube_binary64_1137`
24×	`pow1_binary64_1162`
23×	`cbrt-unprod_binary64_1134`
21×	`div-exp_binary64_1152`
17×	`associate-*r/_binary64_1043`
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` `sqrt-div_binary64_1118`
10×	`pow-exp_binary64_1169` `times-frac_binary64_1107`
9×	`frac-times_binary64_1111` `associate-r_binary64_1041`
8×	`distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
7×	`cbrt-undiv_binary64_1135`
6×	`associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `associate-/r*_binary64_1045`
2×	`-commutative_binary64_1032` `difference-of-squares_binary64_1070` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-l_binary64_1042` `pow-to-exp_binary64_1170`
1×	`distribute-lft-out--_binary64_1053`

Counts

4 → 130

Calls

4 calls:

34.0ms	(.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)))
10.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
8.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))

series1.5s (9.1%)

Counts

4 → 12

Calls

4 calls:

1.3s	(.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 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)))
101.0ms	(/.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h) l)
76.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) h)
24.0ms	(/.f64 (.f64 M D) (.f64 d 2))

simplify114.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5078	6969

prune236.0ms (1.4%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	1	22	23
Picked	1	0	1
Done	0	0	0
Total	140	26	166

Error

8.5b

Counts

166 → 26

Compiler

Compiled 7682 to 2258 computations (70.6% saved)

regimes1.9s (11.4%)

Accuracy

Total 4.3b remaining (32.4%)

Threshold costs 0b (0%)

Compiler

Compiled 26806 to 18766 computations (30% saved)

bsearch208.0ms (1.2%)

Steps

Iters	Range		Point
10	-2.253358018080734e+71	-3.548157263684111e+56	-8.614834714844364e+65

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	103	197
1	103	197

end0.0ms (0%)

sample6.2s (36.5%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.1s	8491×	body	128	nan
675.0ms	4755×	body	128	invalid

Compiler

Compiled 3958 to 2731 computations (31% saved)

Details

analyze1.7s (9.8%)

sample122.0ms (0.7%)

simplify133.0ms (0.8%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite51.0ms (0.3%)

series517.0ms (3.1%)

simplify87.0ms (0.5%)

prune271.0ms (1.6%)

localize26.0ms (0.2%)

rewrite58.0ms (0.3%)

series1.3s (7.9%)

simplify96.0ms (0.6%)

prune256.0ms (1.5%)

localize29.0ms (0.2%)

rewrite67.0ms (0.4%)

series1.5s (8.9%)

simplify88.0ms (0.5%)

prune273.0ms (1.6%)

localize28.0ms (0.2%)

rewrite81.0ms (0.5%)

series1.5s (9.1%)

simplify114.0ms (0.7%)

prune236.0ms (1.4%)

regimes1.9s (11.4%)

bsearch208.0ms (1.2%)

simplify5.0ms (0%)

end0.0ms (0%)

sample6.2s (36.5%)

Profiling