Details

analyze1.6s (5.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample125.0ms (0.4%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
33.0ms	280×	body	128	nan
20.0ms	148×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify122.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5205	41

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

27.0b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.4b	(sqrt.f64 (/.f64 d h))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
14.5b	(sqrt.f64 (/.f64 d l))

rewrite306.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

14.6b

Rules

77×	`add-exp-log_binary64_1139`
41×	`prod-exp_binary64_1150`
32×	`add-sqr-sqrt_binary64_1123`
29×	`times-frac_binary64_1107`
26×	`add-cube-cbrt_binary64_1136` `sqrt-prod_binary64_1117` `*-un-lft-identity_binary64_1101`
21×	`add-cbrt-cube_binary64_1137`
16×	`div-exp_binary64_1152` `associate-r_binary64_1041`
14×	`sqrt-div_binary64_1118`
13×	`pow1_binary64_1162`
10×	`pow-exp_binary64_1169`
9×	`cbrt-unprod_binary64_1134` `frac-times_binary64_1111`
6×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `rem-sqrt-square_binary64_1114` `pow-prod-down_binary64_1172` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098`
2×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `pow-to-exp_binary64_1170` `cbrt-undiv_binary64_1135` `associate-l_binary64_1042` `*-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`

Counts

4 → 127

Calls

4 calls:

19.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
3.0ms	(sqrt.f64 (/.f64 d l))
3.0ms	(sqrt.f64 (/.f64 d h))

Compiler

Compiled 4932 to 2296 computations (53.4% saved)

series1.5s (5.3%)

Error

18.9b

Counts

4 → 50

Calls

4 calls:

859.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
550.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
42.0ms	(sqrt.f64 (/.f64 d h))
41.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3752 to 2913 computations (22.4% saved)

simplify93.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4979	4371
1	4979	4371

prune288.0ms (1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	155	22	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	22	178

Error

11.3b

Counts

178 → 22

Compiler

Compiled 6280 to 2981 computations (52.5% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.1b	(/.f64 (.f64 M D) (.f64 d 2))
6.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
14.5b	(sqrt.f64 (/.f64 d l))

rewrite295.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

10.6b

Rules

93×	`add-exp-log_binary64_1139`
48×	`prod-exp_binary64_1150`
37×	`add-cbrt-cube_binary64_1137`
22×	`add-sqr-sqrt_binary64_1123`
20×	`times-frac_binary64_1107` `div-exp_binary64_1152`
19×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
16×	`pow1_binary64_1162` `cbrt-unprod_binary64_1134` `associate-r_binary64_1041`
13×	`sqrt-div_binary64_1118` `sqrt-prod_binary64_1117`
12×	`associate-*r/_binary64_1043`
10×	`pow-exp_binary64_1169`
9×	`frac-times_binary64_1111`
7×	`pow-prod-down_binary64_1172`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`div-inv_binary64_1098`
2×	`rem-sqrt-square_binary64_1114` `pow-to-exp_binary64_1170` `associate-l_binary64_1042` `*-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045`

Counts

4 → 126

Calls

4 calls:

21.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6223 to 2306 computations (62.9% saved)

series3.1s (10.5%)

Error

11.0b

Counts

4 → 55

Calls

4 calls:

2.2s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
567.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
145.0ms	(/.f64 (.f64 M D) (.f64 d 2))
44.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 6576 to 4835 computations (26.5% saved)

simplify134.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4947	6103
1	4947	6103

prune334.0ms (1.1%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	170	11	181
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	174	29	203

Error

10.6b

Counts

203 → 29

Compiler

Compiled 8695 to 3537 computations (59.3% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 h)
4.1b	(/.f64 (.f64 M D) (.f64 d 2))
6.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
13.9b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite296.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

8.9b

Rules

102×	`add-exp-log_binary64_1139`
55×	`prod-exp_binary64_1150`
46×	`add-cbrt-cube_binary64_1137`
24×	`pow1_binary64_1162`
23×	`cbrt-unprod_binary64_1134`
20×	`div-exp_binary64_1152`
18×	`associate-*r/_binary64_1043`
16×	`associate-r_binary64_1041`
14×	`pow-prod-down_binary64_1172`
13×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
12×	`sqrt-div_binary64_1118`
10×	`pow-exp_binary64_1169` `times-frac_binary64_1107`
9×	`frac-times_binary64_1111`
6×	`cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`cbrt-prod_binary64_1132`
2×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042` `div-inv_binary64_1098` `*-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `pow1/3_binary64_1183`

Counts

4 → 118

Calls

4 calls:

29.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.0ms	(cbrt.f64 h)

Compiler

Compiled 7220 to 2249 computations (68.9% saved)

series2.9s (9.9%)

Error

9.7b

Counts

4 → 51

Calls

4 calls:

2.1s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
546.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
136.0ms	(/.f64 (.f64 M D) (.f64 d 2))
77.0ms	(cbrt.f64 h)

Compiler

Compiled 7346 to 4952 computations (32.6% saved)

simplify112.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4966	7097
1	4966	7097

prune335.0ms (1.1%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	161	8	169
Fresh	3	25	28
Picked	1	0	1
Done	0	0	0
Total	165	33	198

Error

8.6b

Counts

198 → 33

Compiler

Compiled 9868 to 3423 computations (65.3% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
4.1b	(/.f64 (.f64 M D) (.f64 2 d))
6.1b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
8.6b	(.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))

rewrite520.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

8.0b

Rules

291×	`add-exp-log_binary64_1139`
141×	`prod-exp_binary64_1150`
93×	`div-exp_binary64_1152`
70×	`add-cbrt-cube_binary64_1137`
39×	`cbrt-unprod_binary64_1134`
30×	`pow-exp_binary64_1169`
27×	`add-sqr-sqrt_binary64_1123`
25×	`associate-r_binary64_1041`
24×	`pow1_binary64_1162`
23×	`times-frac_binary64_1107`
21×	`cbrt-undiv_binary64_1135`
19×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
18×	`associate-*r/_binary64_1043`
14×	`pow-prod-down_binary64_1172`
12×	`sqrt-div_binary64_1118`
10×	`frac-times_binary64_1111` `cbrt-prod_binary64_1132`
7×	`associate-*l/_binary64_1044`
6×	`pow-to-exp_binary64_1170` `associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `flip3--_binary64_1105` `flip--_binary64_1076`
3×	`unswap-sqr_binary64_1069`
2×	`-commutative_binary64_1032` `sub-neg_binary64_1094` `distribute-rgt-in_binary64_1051` `cancel-sign-sub-inv_binary64_1067` `distribute-lft-in_binary64_1050` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r*_binary64_1045`

Counts

4 → 182

Calls

4 calls:

31.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
24.0ms	(.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))
11.0ms	(/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 12580 to 3558 computations (71.7% saved)

series3.7s (12.6%)

Error

8.6b

Counts

4 → 60

Calls

4 calls:

2.1s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))))
770.0ms	(/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))
594.0ms	(.f64 (/.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 h (cbrt.f64 l)))
139.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 9154 to 5954 computations (35% saved)

simplify112.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5560	9916

prune651.0ms (2.2%)

Pruning

34 alts after pruning (34 fresh and 0 done)

	Pruned	Kept	Total
New	239	3	242
Fresh	1	31	32
Picked	1	0	1
Done	0	0	0
Total	241	34	275

Error

8.5b

Counts

275 → 34

Compiler

Compiled 13150 to 3670 computations (72.1% saved)

regimes3.5s (11.8%)

Accuracy

Total 4.7b remaining (37.5%)

Threshold costs 0b (0%)

Compiler

Compiled 56289 to 39149 computations (30.4% saved)

bsearch16.0ms (0.1%)

Compiler: Compiled 35 to 31 computations (11.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	148	209
1	148	209

end0.0ms (0%)

sample9.1s (31.1%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
1.0s	8389×	body	128	nan
673.0ms	4787×	body	128	invalid

Compiler

Compiled 8195 to 5679 computations (30.7% saved)

Details

analyze1.6s (5.6%)

sample125.0ms (0.4%)

simplify122.0ms (0.4%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite306.0ms (1%)

series1.5s (5.3%)

simplify93.0ms (0.3%)

prune288.0ms (1%)

localize27.0ms (0.1%)

rewrite295.0ms (1%)

series3.1s (10.5%)

simplify134.0ms (0.5%)

prune334.0ms (1.1%)

localize34.0ms (0.1%)

rewrite296.0ms (1%)

series2.9s (9.9%)

simplify112.0ms (0.4%)

prune335.0ms (1.1%)

localize33.0ms (0.1%)

rewrite520.0ms (1.8%)

series3.7s (12.6%)

simplify112.0ms (0.4%)

prune651.0ms (2.2%)

regimes3.5s (11.8%)

bsearch16.0ms (0.1%)

simplify5.0ms (0%)

end0.0ms (0%)

sample9.1s (31.1%)

Profiling