Details

analyze2.5s (17.3%)

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)

sample58.0ms (0.4%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
6.0ms	92×	body	128	nan
3.0ms	45×	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 (36.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (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

13.8b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
11.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite227.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

7.5b

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:

17.0ms	(.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 (9.4%)

Error

7.0b

Counts

4 → 57

Calls

4 calls:

528.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
443.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
223.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
130.0ms	(/.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

prune205.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	163	10	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	10	174

Error

4.8b

Counts

174 → 10

Compiler

Compiled 4040 to 2186 computations (45.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
7.6b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite280.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

210×	`add-exp-log_binary64_1139`
121×	`prod-exp_binary64_1150`
43×	`div-exp_binary64_1152`
33×	`add-cbrt-cube_binary64_1137`
30×	`pow-exp_binary64_1169`
23×	`add-sqr-sqrt_binary64_1123` `associate-r_binary64_1041`
20×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101` `times-frac_binary64_1107`
19×	`cbrt-unprod_binary64_1134`
11×	`associate-l_binary64_1042`
9×	`cbrt-prod_binary64_1132`
7×	`pow1_binary64_1162` `cbrt-undiv_binary64_1135`
6×	`pow-to-exp_binary64_1170` `unpow-prod-down_binary64_1180`
4×	`add-log-exp_binary64_1140` `unswap-sqr_binary64_1069`
3×	`div-inv_binary64_1098` `sqrt-prod_binary64_1117`
2×	`pow-prod-down_binary64_1172` `*-commutative_binary64_1032` `sqrt-div_binary64_1118` `unpow2_binary64_1166` `sqr-pow_binary64_1073`
1×	`associate-r/_binary64_1043` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r*_binary64_1045` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114` `pow2_binary64_1182`

Counts

4 → 145

Calls

4 calls:

19.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
13.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 5167 to 2359 computations (54.3% saved)

series1.6s (11.2%)

Error

4.1b

Counts

4 → 51

Calls

4 calls:

650.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
562.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
246.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
126.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3582 to 3102 computations (13.4% saved)

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5091	4207

prune231.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	196	10	206

Error

4.8b

Counts

206 → 10

Compiler

Compiled 5113 to 2533 computations (50.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
6.2b	(/.f64 (.f64 M D) (.f64 2 d))
8.8b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite185.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

69×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
26×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
21×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
19×	`add-sqr-sqrt_binary64_1123`
13×	`add-cube-cbrt_binary64_1136` `-un-lft-identity_binary64_1101` `times-frac_binary64_1107` `associate-r*_binary64_1041`
7×	`pow1_binary64_1162`
5×	`associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`sqrt-prod_binary64_1117`
2×	`unswap-sqr_binary64_1069` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `sqrt-div_binary64_1118`
1×	`pow-prod-down_binary64_1172` `frac-times_binary64_1111` `associate-l/_binary64_1044` `associate-r/_binary64_1043` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 109

Calls

4 calls:

12.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
5.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3773 to 1881 computations (50.1% saved)

series861.0ms (5.9%)

Error

4.1b

Counts

4 → 48

Calls

4 calls:

346.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
224.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
132.0ms	(/.f64 (.f64 M D) (.f64 2 d))
116.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3199 to 2472 computations (22.7% saved)

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5394	2658

prune184.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	153	4	157
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	156	11	167

Error

2.8b

Counts

167 → 11

Compiler

Compiled 4321 to 2101 computations (51.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
5.4b	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)
6.0b	(/.f64 (*.f64 M D) d)
6.2b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite138.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

2.8b

Rules

41×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
13×	`prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134`
10×	`add-sqr-sqrt_binary64_1123`
9×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
7×	`times-frac_binary64_1107` `associate-/r*_binary64_1045`
5×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `sqrt-prod_binary64_1117`
2×	`associate-*r/_binary64_1043` `sqrt-div_binary64_1118`
1×	`associate-/l/_binary64_1048` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 85

Calls

4 calls:

9.0ms	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
4.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 2875 to 1456 computations (49.4% saved)

series855.0ms (5.8%)

Error

2.8b

Counts

4 → 48

Calls

4 calls:

355.0ms	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)
224.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
132.0ms	(/.f64 (.f64 M D) (.f64 2 d))
104.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 3199 to 2462 computations (23% saved)

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4965	2184
1	4965	2184

prune141.0ms (1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	133	11	144

Error

2.8b

Counts

144 → 11

Compiler

Compiled 3459 to 1651 computations (52.3% saved)

regimes2.1s (14.5%)

Accuracy

Total 5.9b remaining (62%)

Threshold costs 0b (0%)

Compiler

Compiled 27080 to 24147 computations (10.8% saved)

bsearch4.0ms (0%)

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

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	200	127
1	200	127

Compiler

Compiled 168 to 114 computations (32.1% saved)

end0.0ms (0%)

sample3.2s (21.6%)

Algorithm

1×

intervals

Results

591.0ms	8000×	body	128	valid
222.0ms	3063×	body	128	nan
87.0ms	1248×	body	128	invalid

Compiler

Compiled 1598 to 1413 computations (11.6% saved)

Details

analyze2.5s (17.3%)

sample58.0ms (0.4%)

simplify42.0ms (0.3%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite227.0ms (1.6%)

series1.4s (9.4%)

simplify65.0ms (0.4%)

prune205.0ms (1.4%)

localize17.0ms (0.1%)

rewrite280.0ms (1.9%)

series1.6s (11.2%)

simplify95.0ms (0.6%)

prune231.0ms (1.6%)

localize14.0ms (0.1%)

rewrite185.0ms (1.3%)

series861.0ms (5.9%)

simplify60.0ms (0.4%)

prune184.0ms (1.3%)

localize18.0ms (0.1%)

rewrite138.0ms (0.9%)

series855.0ms (5.8%)

simplify83.0ms (0.6%)

prune141.0ms (1%)

regimes2.1s (14.5%)

bsearch4.0ms (0%)

simplify17.0ms (0.1%)

end0.0ms (0%)

sample3.2s (21.6%)

Profiling