Details

analyze2.5s (16.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5015	432
0	6	6
1	6	6

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Symmetry

(sort M D)

Compiler

Compiled 19 to 19 computations (0% saved)

sample61.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	103×	body	128	nan
3.0ms	43×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify42.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	6100	27

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

9.8b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
2.1b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))
10.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite219.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

4.6b

Rules

67×	`add-exp-log_binary64_1139`
38×	`add-sqr-sqrt_binary64_1123`
27×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
19×	`div-exp_binary64_1152` `associate-r_binary64_1041`
17×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
15×	`times-frac_binary64_1107`
13×	`associate-l_binary64_1042`
10×	`pow-exp_binary64_1169` `unswap-sqr_binary64_1069`
7×	`pow1_binary64_1162` `cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`unpow2_binary64_1166` `sqr-pow_binary64_1073` `associate-*r/_binary64_1043` `div-inv_binary64_1098`
2×	`pow-to-exp_binary64_1170` `*-commutative_binary64_1032` `flip3--_binary64_1105` `flip--_binary64_1076`
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` `rem-sqrt-square_binary64_1114` `pow-prod-down_binary64_1172`

Counts

4 → 116

Calls

4 calls:

12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

Compiler

Compiled 3444 to 1962 computations (43% saved)

series1.4s (9.1%)

Error

4.5b

Counts

4 → 57

Calls

4 calls:

523.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
440.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
220.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
131.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3306 to 2982 computations (9.8% saved)

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5385	3695

prune200.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	165	8	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	8	174

Error

2.5b

Counts

174 → 8

Compiler

Compiled 3974 to 2133 computations (46.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.1b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
3.9b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
4.0b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
4.3b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite166.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

67×	`add-exp-log_binary64_1139`
26×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
20×	`div-exp_binary64_1152` `add-sqr-sqrt_binary64_1123`
13×	`*-un-lft-identity_binary64_1101`
10×	`add-cube-cbrt_binary64_1136` `pow-exp_binary64_1169` `associate-r_binary64_1041`
6×	`cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `sqrt-prod_binary64_1117`
5×	`pow1_binary64_1162` `times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045` `unswap-sqr_binary64_1069`
3×	`div-inv_binary64_1098` `associate-l_binary64_1042`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046` `pow-to-exp_binary64_1170` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sqrt-div_binary64_1118` `difference-of-squares_binary64_1070`
1×	`*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114`

Counts

4 → 99

Calls

4 calls:

8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
7.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
6.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2731 to 1689 computations (38.2% saved)

series1.3s (8.7%)

Error

2.3b

Counts

4 → 51

Calls

4 calls:

551.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
366.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
229.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
121.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3091 to 2803 computations (9.3% saved)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4987	2858
1	4987	2858

prune172.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	148	10	158

Error

2.2b

Counts

158 → 10

Compiler

Compiled 3375 to 2070 computations (38.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.1b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
3.9b	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
4.0b	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
4.9b	(*.f64 (/.f64 M 2) (/.f64 D d))

rewrite212.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

67×	`add-exp-log_binary64_1139`
43×	`add-sqr-sqrt_binary64_1123`
26×	`prod-exp_binary64_1150` `*-un-lft-identity_binary64_1101`
25×	`times-frac_binary64_1107`
23×	`add-cbrt-cube_binary64_1137` `add-cube-cbrt_binary64_1136`
20×	`div-exp_binary64_1152`
19×	`associate-r_binary64_1041`
16×	`associate-l_binary64_1042`
10×	`pow-exp_binary64_1169`
7×	`pow1_binary64_1162` `unswap-sqr_binary64_1069`
6×	`cbrt-unprod_binary64_1134` `cbrt-undiv_binary64_1135` `sqrt-prod_binary64_1117`
4×	`add-log-exp_binary64_1140`
3×	`div-inv_binary64_1098` `associate-/r*_binary64_1045`
2×	`*-commutative_binary64_1032` `pow-to-exp_binary64_1170` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sqrt-div_binary64_1118` `difference-of-squares_binary64_1070`
1×	`pow-prod-down_binary64_1172` `frac-times_binary64_1111` `associate-l/_binary64_1044` `associate-r/_binary64_1043` `unpow-prod-down_binary64_1180` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114`

Counts

4 → 123

Calls

4 calls:

11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
6.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
6.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
6.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))

Compiler

Compiled 3356 to 2054 computations (38.8% saved)

series1.3s (8.5%)

Error

2.2b

Counts

4 → 51

Calls

4 calls:

533.0ms	(/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)
346.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
213.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2)) l)))
133.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

Compiler

Compiled 3091 to 2803 computations (9.3% saved)

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5686	3308

prune200.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	174	10	184

Error

1.9b

Counts

184 → 10

Compiler

Compiled 4069 to 2319 computations (43% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.5b	(.f64 h (.f64 (/.f64 M 2) (/.f64 D d)))
3.9b	(/.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (.f64 (/.f64 M 2) (/.f64 D d))) l)
4.9b	(*.f64 (/.f64 M 2) (/.f64 D d))
4.9b	(*.f64 (/.f64 M 2) (/.f64 D d))

rewrite422.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

251×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
116×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
87×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
59×	`add-sqr-sqrt_binary64_1123`
47×	`times-frac_binary64_1107`
35×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
29×	`associate-r/_binary64_1043` `associate-l*_binary64_1042`
27×	`associate-r_binary64_1041`
20×	`frac-times_binary64_1111`
15×	`associate-/l/_binary64_1048`
14×	`associate-*l/_binary64_1044`
13×	`pow1_binary64_1162`
8×	`unswap-sqr_binary64_1069`
5×	`pow-prod-down_binary64_1172` `div-inv_binary64_1098`
4×	`add-log-exp_binary64_1140`
3×	`-commutative_binary64_1032` `associate-/r_binary64_1045`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046`

Counts

4 → 221

Calls

4 calls:

25.0ms	(/.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (.f64 (/.f64 M 2) (/.f64 D d))) l)
11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
9.0ms	(.f64 h (.f64 (/.f64 M 2) (/.f64 D d)))

Compiler

Compiled 7954 to 3964 computations (50.2% saved)

series1.0s (6.9%)

Error

1.9b

Counts

4 → 45

Calls

4 calls:

529.0ms	(/.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (.f64 (/.f64 M 2) (/.f64 D d))) l)
218.0ms	(.f64 h (.f64 (/.f64 M 2) (/.f64 D d)))
126.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
126.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

Compiler

Compiled 3150 to 2520 computations (20% saved)

simplify117.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4995	4598
1	4995	4598

prune357.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	264	2	266
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	266	10	276

Error

1.7b

Counts

276 → 10

Compiler

Compiled 7034 to 3834 computations (45.5% saved)

regimes2.1s (14.3%)

Accuracy

Total 4.4b remaining (53%)

Threshold costs 0b (0%)

Compiler

Compiled 26507 to 24472 computations (7.7% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	36
1	84	36

Remove

(sort M D)

Compiler

Compiled 48 to 40 computations (16.7% saved)

end0.0ms (0%)

sample2.9s (19.4%)

Algorithm

1×

intervals

Results

603.0ms	8000×	body	128	valid
232.0ms	3115×	body	128	nan
101.0ms	1381×	body	128	invalid

Compiler

Compiled 1561 to 1435 computations (8.1% saved)

Details

analyze2.5s (16.9%)

sample61.0ms (0.4%)

simplify42.0ms (0.3%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite219.0ms (1.5%)

series1.4s (9.1%)

simplify65.0ms (0.4%)

prune200.0ms (1.3%)

localize13.0ms (0.1%)

rewrite166.0ms (1.1%)

series1.3s (8.7%)

simplify54.0ms (0.4%)

prune172.0ms (1.1%)

localize16.0ms (0.1%)

rewrite212.0ms (1.4%)

series1.3s (8.5%)

simplify63.0ms (0.4%)

prune200.0ms (1.3%)

localize13.0ms (0.1%)

rewrite422.0ms (2.8%)

series1.0s (6.9%)

simplify117.0ms (0.8%)

prune357.0ms (2.4%)

regimes2.1s (14.3%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample2.9s (19.4%)

Profiling