Details

analyze2.1s (12.9%)

Algorithm

1×

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

Compiler

Compiled 19 to 19 computations (0% saved)

sample50.0ms (0.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
6.0ms	87×	body	128	nan
3.0ms	40×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify132.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

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

16.1b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
7.6b	(/.f64 (.f64 M D) (.f64 2 d))
11.7b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite225.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

9.4b

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 (9.6%)

Error

8.7b

Counts

4 → 57

Calls

4 calls:

735.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
436.0ms	(.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))))
118.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3306 to 2982 computations (9.8% saved)

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5385	3695

prune215.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	161	12	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	12	174

Error

5.2b

Counts

174 → 12

Compiler

Compiled 4086 to 2227 computations (45.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
5.5b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.9b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
7.6b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite229.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

165×	`add-exp-log_binary64_1139`
91×	`prod-exp_binary64_1150`
40×	`div-exp_binary64_1152`
30×	`add-cbrt-cube_binary64_1137`
25×	`pow-exp_binary64_1169`
23×	`associate-r_binary64_1041`
22×	`add-sqr-sqrt_binary64_1123`
15×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
11×	`cbrt-unprod_binary64_1134` `times-frac_binary64_1107`
8×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
7×	`pow1_binary64_1162`
6×	`cbrt-undiv_binary64_1135` `unpow-prod-down_binary64_1180`
5×	`pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140` `associate-l_binary64_1042` `unswap-sqr_binary64_1069`
3×	`div-inv_binary64_1098` `sqrt-prod_binary64_1117`
2×	`*-commutative_binary64_1032` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sqrt-div_binary64_1118`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow-prod-down_binary64_1172` `un-div-inv_binary64_1099` `associate-*r/_binary64_1043` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 130

Calls

4 calls:

12.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))

Compiler

Compiled 3800 to 2447 computations (35.6% saved)

series1.3s (7.7%)

Error

5.2b

Counts

4 → 51

Calls

4 calls:

522.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
336.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
218.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
124.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3217 to 2929 computations (9% saved)

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5011	3445

prune230.0ms (1.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	177	16	193

Error

4.5b

Counts

193 → 16

Compiler

Compiled 4340 to 2807 computations (35.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))))
4.6b	(*.f64 (/.f64 M 2) (/.f64 D d))
5.5b	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
6.9b	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))

rewrite280.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

4.5b

Rules

165×	`add-exp-log_binary64_1139`
91×	`prod-exp_binary64_1150`
45×	`add-sqr-sqrt_binary64_1123`
40×	`div-exp_binary64_1152`
32×	`associate-r_binary64_1041`
31×	`times-frac_binary64_1107`
30×	`add-cbrt-cube_binary64_1137`
28×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
25×	`pow-exp_binary64_1169`
17×	`associate-l_binary64_1042`
11×	`cbrt-unprod_binary64_1134`
9×	`pow1_binary64_1162`
8×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
7×	`unswap-sqr_binary64_1069`
6×	`cbrt-undiv_binary64_1135`
5×	`pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140`
3×	`div-inv_binary64_1098` `*-commutative_binary64_1032` `sqrt-prod_binary64_1117`
2×	`pow-prod-down_binary64_1172` `associate-*r/_binary64_1043` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sqrt-div_binary64_1118`
1×	`un-div-inv_binary64_1099` `unpow-prod-down_binary64_1180` `frac-times_binary64_1111` `associate-*l/_binary64_1044` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 154

Calls

4 calls:

12.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))
11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
7.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))))

Compiler

Compiled 4473 to 2860 computations (36.1% saved)

series1.3s (7.7%)

Error

4.5b

Counts

4 → 51

Calls

4 calls:

542.0ms	(.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))
336.0ms	(.f64 h (pow.f64 (.f64 (/.f64 M 2) (/.f64 D d)) 2))
215.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2)) (/.f64 1 l))))
119.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

Compiler

Compiled 3217 to 2929 computations (9% saved)

simplify84.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5105	3895

prune264.0ms (1.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	206	15	221

Error

4.5b

Counts

221 → 15

Compiler

Compiled 5062 to 3082 computations (39.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (*.f64 (/.f64 M 2) (/.f64 D d))) (/.f64 1 l))))
4.6b	(*.f64 (/.f64 M 2) (/.f64 D d))
4.6b	(*.f64 (/.f64 M 2) (/.f64 D d))
6.9b	(.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (*.f64 (/.f64 M 2) (/.f64 D d))) (/.f64 1 l))

rewrite891.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Error

4.3b

Rules

879×	`add-exp-log_binary64_1139`
528×	`prod-exp_binary64_1150`
469×	`add-cbrt-cube_binary64_1137`
268×	`cbrt-unprod_binary64_1134`
246×	`div-exp_binary64_1152`
127×	`cbrt-undiv_binary64_1135`
65×	`add-sqr-sqrt_binary64_1123`
53×	`times-frac_binary64_1107`
51×	`frac-times_binary64_1111`
49×	`associate-*r/_binary64_1043`
40×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
39×	`associate-l/_binary64_1044` `associate-r*_binary64_1041`
38×	`pow1_binary64_1162`
31×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
27×	`associate-l_binary64_1042`
24×	`pow-prod-down_binary64_1172`
8×	`unswap-sqr_binary64_1069`
5×	`div-inv_binary64_1098`
4×	`add-log-exp_binary64_1140`
3×	`*-commutative_binary64_1032` `sqrt-prod_binary64_1117`
2×	`sqrt-div_binary64_1118`
1×	`un-div-inv_binary64_1099` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 362

Calls

4 calls:

33.0ms	(.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (*.f64 (/.f64 M 2) (/.f64 D d))) (/.f64 1 l))
11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
11.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
8.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (*.f64 (/.f64 M 2) (/.f64 D d))) (/.f64 1 l))))

Compiler

Compiled 14521 to 7710 computations (46.9% saved)

series1.1s (6.6%)

Error

4.5b

Counts

4 → 48

Calls

4 calls:

544.0ms	(.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (*.f64 (/.f64 M 2) (/.f64 D d))) (/.f64 1 l))
221.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (*.f64 (/.f64 M 2) (/.f64 D d))) (/.f64 1 l))))
137.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))
137.0ms	(*.f64 (/.f64 M 2) (/.f64 D d))

Compiler

Compiled 3217 to 2750 computations (14.5% saved)

simplify147.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

410 → 410

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4995	9010
1	4995	9010

prune624.0ms (3.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	407	3	410
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	411	14	425

Error

4.2b

Counts

425 → 14

Compiler

Compiled 10553 to 5750 computations (45.5% saved)

regimes2.5s (15.4%)

Accuracy

Total 5.3b remaining (59.1%)

Threshold costs 0b (0%)

Compiler

Compiled 29708 to 26381 computations (11.2% saved)

bsearch3.0ms (0%)

Compiler: Compiled 7 to 10 computations (-42.9% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	299	131
1	299	131

end0.0ms (0%)

sample3.0s (18.1%)

Algorithm

1×

intervals

Results

606.0ms	8000×	body	128	valid
224.0ms	3144×	body	128	nan
104.0ms	1372×	body	128	invalid

Compiler

Compiled 1770 to 1561 computations (11.8% saved)

Details

analyze2.1s (12.9%)

sample50.0ms (0.3%)

simplify132.0ms (0.8%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite225.0ms (1.4%)

series1.6s (9.6%)

simplify70.0ms (0.4%)

prune215.0ms (1.3%)

localize17.0ms (0.1%)

rewrite229.0ms (1.4%)

series1.3s (7.7%)

simplify81.0ms (0.5%)

prune230.0ms (1.4%)

localize15.0ms (0.1%)

rewrite280.0ms (1.7%)

series1.3s (7.7%)

simplify84.0ms (0.5%)

prune264.0ms (1.6%)

localize14.0ms (0.1%)

rewrite891.0ms (5.5%)

series1.1s (6.6%)

simplify147.0ms (0.9%)

prune624.0ms (3.8%)

regimes2.5s (15.4%)

bsearch3.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample3.0s (18.1%)

Profiling