Details

analyze2.6s (13.7%)

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)

sample65.0ms (0.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	91×	body	128	nan
3.0ms	43×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify42.0ms (0.2%)

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

14.4b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.3b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
10.6b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite224.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

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)

series1.7s (9%)

Error

7.0b

Counts

4 → 67

Calls

4 calls:

631.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
542.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
349.0ms	(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 4544 to 3949 computations (13.1% saved)

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5009	4517

prune242.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	170	13	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	13	184

Error

3.9b

Counts

184 → 13

Compiler

Compiled 4676 to 2508 computations (46.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.5b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
4.3b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
5.3b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite238.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

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` `unswap-sqr_binary64_1069` `associate-l_binary64_1042`
3×	`div-inv_binary64_1098` `sqrt-prod_binary64_1117`
2×	`unpow2_binary64_1166` `sqr-pow_binary64_1073` `*-commutative_binary64_1032` `sqrt-div_binary64_1118`
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` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114` `pow-prod-down_binary64_1172` `un-div-inv_binary64_1099` `associate-*r/_binary64_1043`

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)

series1.4s (7.4%)

Error

3.9b

Counts

4 → 56

Calls

4 calls:

540.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
352.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
344.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
130.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3825 to 3412 computations (10.8% saved)

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5321	3823

prune237.0ms (1.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	184	15	199

Error

3.2b

Counts

199 → 15

Compiler

Compiled 4575 to 2927 computations (36% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.3b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
9.4b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite188.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

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:

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

Compiler

Compiled 3773 to 1881 computations (50.1% saved)

series996.0ms (5.2%)

Error

3.2b

Counts

4 → 53

Calls

4 calls:

349.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
345.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
127.0ms	(/.f64 (.f64 M D) (.f64 2 d))
120.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3807 to 2955 computations (22.4% saved)

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5118	3069

prune196.0ms (1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	162	15	177

Error

2.9b

Counts

177 → 15

Compiler

Compiled 4666 to 2273 computations (51.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
4.3b	(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))))
5.1b	(/.f64 M (/.f64 2 (/.f64 D d)))
10.6b	(*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))

rewrite1.0s (5.4%)

Algorithm

1×	rewrite-expression-head

Error

2.9b

Rules

754×	`times-frac_binary64_1107`
399×	`add-sqr-sqrt_binary64_1123`
351×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
145×	`unpow-prod-down_binary64_1180` `associate-l_binary64_1042`
55×	`add-exp-log_binary64_1139`
44×	`associate-/r*_binary64_1045`
31×	`div-inv_binary64_1098`
24×	`div-exp_binary64_1152`
20×	`add-cbrt-cube_binary64_1137`
19×	`associate-r_binary64_1041`
16×	`unswap-sqr_binary64_1069`
13×	`prod-exp_binary64_1150`
9×	`associate-/r/_binary64_1047`
8×	`pow-exp_binary64_1169`
7×	`pow1_binary64_1162` `cbrt-undiv_binary64_1135` `sqrt-prod_binary64_1117`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`cbrt-unprod_binary64_1134` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `associate-r/_binary64_1043` `associate-/l_binary64_1046`
2×	`pow-to-exp_binary64_1170` `*-commutative_binary64_1032` `flip3--_binary64_1105` `flip--_binary64_1076`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `pow-prod-down_binary64_1172`

Counts

4 → 427

Calls

4 calls:

65.0ms	(*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))
18.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))))

Compiler

Compiled 14020 to 7634 computations (45.5% saved)

series1.7s (9%)

Error

2.9b

Counts

4 → 67

Calls

4 calls:

650.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
541.0ms	(*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))
345.0ms	(sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l))))
128.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

Compiler

Compiled 4544 to 3949 computations (13.1% saved)

simplify149.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

494 → 494

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5019	12511

prune839.0ms (4.4%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	493	1	494
Fresh	2	10	12
Picked	0	1	1
Done	0	2	2
Total	495	14	509

Error

2.7b

Counts

509 → 14

Compiler

Compiled 14578 to 7660 computations (47.5% saved)

regimes3.1s (15.9%)

Accuracy

Total 5.0b remaining (64.8%)

Threshold costs 0b (0%)

Compiler

Compiled 30080 to 26917 computations (10.5% saved)

bsearch4.0ms (0%)

Compiler: Compiled 15 to 16 computations (-6.7% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	299	182
1	299	182

Compiler

Compiled 242 to 154 computations (36.4% saved)

end0.0ms (0%)

sample3.9s (20.2%)

Algorithm

1×

intervals

Results

640.0ms	8000×	body	128	valid
252.0ms	3278×	body	128	nan
109.0ms	1330×	body	128	invalid

Compiler

Compiled 1863 to 1643 computations (11.8% saved)

Details

analyze2.6s (13.7%)

sample65.0ms (0.3%)

simplify42.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

rewrite224.0ms (1.2%)

series1.7s (9%)

simplify86.0ms (0.4%)

prune242.0ms (1.3%)

localize15.0ms (0.1%)

rewrite238.0ms (1.2%)

series1.4s (7.4%)

simplify66.0ms (0.3%)

prune237.0ms (1.2%)

localize16.0ms (0.1%)

rewrite188.0ms (1%)

series996.0ms (5.2%)

simplify76.0ms (0.4%)

prune196.0ms (1%)

localize14.0ms (0.1%)

rewrite1.0s (5.4%)

series1.7s (9%)

simplify149.0ms (0.8%)

prune839.0ms (4.4%)

regimes3.1s (15.9%)

bsearch4.0ms (0%)

simplify20.0ms (0.1%)

end0.0ms (0%)

sample3.9s (20.2%)

Profiling