Details

analyze3.6s (16.8%)

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)

sample113.0ms (0.5%)

Algorithm

1×

intervals

Results

35.0ms	256×	body	128	valid
19.0ms	86×	body	128	nan
5.0ms	35×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify75.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	6100	27

prune6.0ms (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

12.3b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.7b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.9b	(/.f64 (.f64 M D) (.f64 2 d))
8.1b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite543.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

7.0b

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:

21.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
15.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
11.0ms	(/.f64 (.f64 M D) (.f64 2 d))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

Compiler

Compiled 3226 to 1835 computations (43.1% saved)

series3.5s (16.3%)

Error

5.2b

Counts

4 → 61

Calls

4 calls:

1.4s	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
1.3s	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
537.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
283.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2885 to 2741 computations (5% saved)

simplify124.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5011	3807

prune215.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	166	11	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	11	178

Error

4.7b

Counts

178 → 11

Compiler

Compiled 2626 to 1531 computations (41.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
4.7b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
5.4b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
5.9b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite288.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

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` `sqrt-prod_binary64_1117` `unpow-prod-down_binary64_1180`
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` `sqrt-div_binary64_1118` `difference-of-squares_binary64_1070` `unpow2_binary64_1166` `sqr-pow_binary64_1073`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `rem-sqrt-square_binary64_1114` `*-commutative_binary64_1032`

Counts

4 → 99

Calls

4 calls:

8.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
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 2610 to 1612 computations (38.2% saved)

series1.9s (8.8%)

Error

4.7b

Counts

4 → 51

Calls

4 calls:

835.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
544.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
330.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
174.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2328 to 2277 computations (2.2% saved)

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4987	2858
1	4987	2858

prune332.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	149	12	161

Error

3.6b

Counts

161 → 12

Compiler

Compiled 2030 to 1315 computations (35.2% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.7b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
5.4b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 (.f64 M D) (.f64 2 d))) l)
5.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.9b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite750.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

233×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
107×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
83×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
11×	`add-sqr-sqrt_binary64_1123`
10×	`*-un-lft-identity_binary64_1101`
7×	`add-cube-cbrt_binary64_1136`
6×	`sqrt-prod_binary64_1117`
5×	`pow1_binary64_1162` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
4×	`add-log-exp_binary64_1140`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l_binary64_1046` `associate-r/_binary64_1043` `associate-/l/_binary64_1048`
2×	`sqrt-div_binary64_1118` `difference-of-squares_binary64_1070`
1×	`frac-times_binary64_1111` `associate-*l/_binary64_1044` `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 → 142

Calls

4 calls:

30.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 (.f64 M D) (.f64 2 d))) l)
17.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
10.0ms	(/.f64 (.f64 M D) (.f64 2 d))
10.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 5654 to 2786 computations (50.7% saved)

series1.9s (8.7%)

Error

3.6b

Counts

4 → 48

Calls

4 calls:

934.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 (.f64 M D) (.f64 2 d))) l)
331.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 (.f64 M D) (.f64 2 d))) l)))
303.0ms	(/.f64 (.f64 M D) (.f64 d 2))
302.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2348 to 2143 computations (8.7% saved)

simplify85.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5064	4549

prune239.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	190	12	202

Error

3.5b

Counts

202 → 12

Compiler

Compiled 3023 to 1769 computations (41.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 l (/.f64 (.f64 M D) (*.f64 d 2))))))
5.2b	(/.f64 l (/.f64 (.f64 M D) (.f64 d 2)))
5.9b	(/.f64 (.f64 M D) (.f64 d 2))
5.9b	(/.f64 (.f64 M D) (.f64 d 2))

rewrite294.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

46×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
21×	`times-frac_binary64_1107`
19×	`add-sqr-sqrt_binary64_1123`
18×	`*-un-lft-identity_binary64_1101`
17×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
15×	`add-cube-cbrt_binary64_1136`
12×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
7×	`div-inv_binary64_1098` `associate-/r*_binary64_1045`
6×	`sqrt-prod_binary64_1117`
5×	`pow1_binary64_1162` `associate-/l*_binary64_1046`
4×	`add-log-exp_binary64_1140`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100`
2×	`sqrt-div_binary64_1118` `difference-of-squares_binary64_1070`
1×	`associate-/r/_binary64_1047` `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 → 104

Calls

4 calls:

14.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 l (/.f64 (.f64 M D) (*.f64 d 2))))))
7.0ms	(/.f64 l (/.f64 (.f64 M D) (.f64 d 2)))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 3471 to 1891 computations (45.5% saved)

series1.1s (4.9%)

Error

3.5b

Counts

4 → 45

Calls

4 calls:

338.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (/.f64 (.f64 M D) (.f64 d 2))) (/.f64 l (/.f64 (.f64 M D) (*.f64 d 2))))))
337.0ms	(/.f64 l (/.f64 (.f64 M D) (.f64 d 2)))
190.0ms	(/.f64 (.f64 M D) (.f64 d 2))
180.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 2266 to 1960 computations (13.5% saved)

simplify80.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4958	2615
1	4958	2615

prune192.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	149	12	161

Error

3.5b

Counts

161 → 12

Compiler

Compiled 2435 to 1270 computations (47.8% saved)

regimes3.8s (17.7%)

Accuracy

Total 5.2b remaining (58.4%)

Threshold costs 0b (0%)

Compiler

Compiled 39056 to 37340 computations (4.4% saved)

bsearch6.0ms (0%)

Compiler: Compiled 18 to 18 computations (0% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	189	179
1	189	179

end21.0ms (0.1%)

Compiler: Compiled 354 to 237 computations (33.1% saved)

sample2.2s (10.4%)

Algorithm

1×

intervals

Results

634.0ms	8000×	body	128	valid
237.0ms	3061×	body	128	nan
99.0ms	1333×	body	128	invalid

Compiler

Compiled 377 to 342 computations (9.3% saved)

Details

analyze3.6s (16.8%)

sample113.0ms (0.5%)

simplify75.0ms (0.3%)

prune6.0ms (0%)

localize28.0ms (0.1%)

rewrite543.0ms (2.5%)

series3.5s (16.3%)

simplify124.0ms (0.6%)

prune215.0ms (1%)

localize14.0ms (0.1%)

rewrite288.0ms (1.3%)

series1.9s (8.8%)

simplify58.0ms (0.3%)

prune332.0ms (1.5%)

localize36.0ms (0.2%)

rewrite750.0ms (3.5%)

series1.9s (8.7%)

simplify85.0ms (0.4%)

prune239.0ms (1.1%)

localize14.0ms (0.1%)

rewrite294.0ms (1.4%)

series1.1s (4.9%)

simplify80.0ms (0.4%)

prune192.0ms (0.9%)

regimes3.8s (17.7%)

bsearch6.0ms (0%)

simplify5.0ms (0%)

end21.0ms (0.1%)

sample2.2s (10.4%)

Profiling