Details

analyze2.6s (14.2%)

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 (0.3%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
6.0ms	91×	body	128	nan
3.0ms	39×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify48.0ms (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

13.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.1b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
12.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite228.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

6.4b

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)

series1.6s (8.7%)

Error

6.1b

Counts

4 → 71

Calls

4 calls:

547.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
535.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
296.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
127.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4216 to 3713 computations (11.9% saved)

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4982	4087
1	4982	4087

prune233.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	174	13	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	13	188

Error

3.9b

Counts

188 → 13

Compiler

Compiled 4423 to 2344 computations (47% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(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))))
4.6b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
6.1b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))

rewrite281.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

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` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sqrt-div_binary64_1118`
1×	`associate-r/_binary64_1043` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r*_binary64_1045` `pow2_binary64_1182` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 145

Calls

4 calls:

20.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
12.0ms	(.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))
5.0ms	(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)

series1.8s (9.9%)

Error

3.9b

Counts

4 → 58

Calls

4 calls:

674.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
596.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
322.0ms	(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))))
128.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4030 to 3473 computations (13.8% saved)

simplify95.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4993	4433
1	4993	4433

prune248.0ms (1.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	202	14	216

Error

3.7b

Counts

216 → 14

Compiler

Compiled 5400 to 2669 computations (50.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
3.1b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
6.1b	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))

rewrite245.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

82×	`add-exp-log_binary64_1139`
45×	`add-sqr-sqrt_binary64_1123`
39×	`prod-exp_binary64_1150`
28×	`associate-r_binary64_1041`
25×	`times-frac_binary64_1107`
22×	`add-cbrt-cube_binary64_1137` `add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
20×	`div-exp_binary64_1152`
12×	`pow-exp_binary64_1169` `cbrt-prod_binary64_1132`
11×	`unswap-sqr_binary64_1069`
9×	`associate-l_binary64_1042`
7×	`pow1_binary64_1162` `cbrt-unprod_binary64_1134` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sqrt-div_binary64_1118`
3×	`associate-*r/_binary64_1043`
2×	`pow-to-exp_binary64_1170` `div-inv_binary64_1098` `*-commutative_binary64_1032` `flip3--_binary64_1105` `flip--_binary64_1076`
1×	`unpow-prod-down_binary64_1180` `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 → 124

Calls

4 calls:

13.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
7.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4389 to 2234 computations (49.1% saved)

series1.6s (8.9%)

Error

3.4b

Counts

4 → 71

Calls

4 calls:

573.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
539.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
310.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
123.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4379 to 3813 computations (12.9% saved)

simplify92.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4999	5157
1	4999	5157

prune237.0ms (1.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	195	14	209

Error

3.2b

Counts

209 → 14

Compiler

Compiled 5354 to 2619 computations (51.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
3.1b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
5.0b	(*.f64 (/.f64 M 2) (/.f64 D d))
6.1b	(.f64 (pow.f64 (.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))

rewrite304.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

82×	`add-exp-log_binary64_1139`
71×	`add-sqr-sqrt_binary64_1123`
46×	`times-frac_binary64_1107`
41×	`associate-r_binary64_1041`
39×	`prod-exp_binary64_1150`
36×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
22×	`add-cbrt-cube_binary64_1137` `associate-l_binary64_1042`
20×	`div-exp_binary64_1152`
15×	`unswap-sqr_binary64_1069`
12×	`pow-exp_binary64_1169` `cbrt-prod_binary64_1132`
9×	`pow1_binary64_1162`
7×	`cbrt-unprod_binary64_1134` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `associate-*r/_binary64_1043` `sqrt-div_binary64_1118`
3×	`div-inv_binary64_1098` `*-commutative_binary64_1032`
2×	`pow-to-exp_binary64_1170` `pow-prod-down_binary64_1172` `flip3--_binary64_1105` `flip--_binary64_1076`
1×	`unpow-prod-down_binary64_1180` `frac-times_binary64_1111` `associate-*l/_binary64_1044` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`

Counts

4 → 153

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
12.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
9.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 5277 to 2692 computations (49% saved)

series1.7s (9.1%)

Error

3.0b

Counts

4 → 71

Calls

4 calls:

573.0ms	(.f64 (pow.f64 (.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
566.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (.f64 (/.f64 M 2) (/.f64 D d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
314.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
129.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

Compiler

Compiled 4379 to 3813 computations (12.9% saved)

simplify125.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4967	5595
1	4967	5595

prune276.0ms (1.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	223	15	238

Error

3.2b

Counts

238 → 15

Compiler

Compiled 5923 to 2797 computations (52.8% saved)

regimes2.5s (13.8%)

Accuracy

Total 3.9b remaining (48.5%)

Threshold costs 0b (0%)

Compiler

Compiled 31239 to 26291 computations (15.8% saved)

bsearch4.0ms (0%)

Compiler: Compiled 13 to 14 computations (-7.7% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	112	102
1	112	102

Compiler

Compiled 136 to 92 computations (32.4% saved)

end0.0ms (0%)

sample3.8s (20.8%)

Algorithm

1×

intervals

Results

602.0ms	8000×	body	128	valid
217.0ms	3042×	body	128	nan
102.0ms	1392×	body	128	invalid

Compiler

Compiled 1964 to 1644 computations (16.3% saved)

Details

analyze2.6s (14.2%)

sample58.0ms (0.3%)

simplify48.0ms (0.3%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite228.0ms (1.3%)

series1.6s (8.7%)

simplify83.0ms (0.5%)

prune233.0ms (1.3%)

localize17.0ms (0.1%)

rewrite281.0ms (1.6%)

series1.8s (9.9%)

simplify95.0ms (0.5%)

prune248.0ms (1.4%)

localize16.0ms (0.1%)

rewrite245.0ms (1.4%)

series1.6s (8.9%)

simplify92.0ms (0.5%)

prune237.0ms (1.3%)

localize16.0ms (0.1%)

rewrite304.0ms (1.7%)

series1.7s (9.1%)

simplify125.0ms (0.7%)

prune276.0ms (1.5%)

regimes2.5s (13.8%)

bsearch4.0ms (0%)

simplify15.0ms (0.1%)

end0.0ms (0%)

sample3.8s (20.8%)

Profiling