Details

analyze124.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample35.0ms (0.1%)

Algorithm

1×

intervals

Results

11.0ms	205×	body	128	valid
6.0ms	27×	body	1024	valid
6.0ms	256×	pre	128	true
2.0ms	12×	body	512	valid
1.0ms	10×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify166.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5371	43

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

22.8b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize12.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

1.1b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

20.0b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite88.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_1107`
47×	`*-un-lft-identity_binary64_1101`
25×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
17×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
14×	`associate-/r/_binary64_1047`
11×	`distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `flip-+_binary64_1075`
10×	`associate-/l*_binary64_1046`
9×	`associate-/l/_binary64_1048`
7×	`div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r*_binary64_1045`
5×	`add-log-exp_binary64_1140`
4×	`frac-times_binary64_1111`
3×	`pow1_binary64_1162` `flip--_binary64_1076` `flip3--_binary64_1105`
2×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

3 → 111

Calls

3 calls:

37.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

21.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

15.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series2.2s (7.6%)

Counts

3 → 69

Calls

3 calls:

1.0s

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

928.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

216.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 7749 to 6024 computations (22.3% saved)

simplify121.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4973	10446
1	4973	10446

prune443.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	175	5	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	5	181

Error

0.1b

Counts

181 → 5

Compiler

Compiled 9056 to 4817 computations (46.8% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
2.1b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
2.4b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))

rewrite156.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

321×	`times-frac_binary64_1107`
290×	`*-un-lft-identity_binary64_1101`
211×	`add-sqr-sqrt_binary64_1123`
140×	`add-cube-cbrt_binary64_1136`
90×	`associate-r_binary64_1041`
44×	`distribute-lft-out_binary64_1052`
31×	`difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053`
26×	`associate-/l*_binary64_1046`
24×	`associate-/r/_binary64_1047`
20×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
15×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
12×	`div-inv_binary64_1098`
7×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r*_binary64_1045`
6×	`add-log-exp_binary64_1140` `pow1_binary64_1162`
4×	`associate-l_binary64_1042`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-/l/_binary64_1048` `unswap-sqr_binary64_1069` `div-sub_binary64_1106`
2×	`frac-times_binary64_1111` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-*l/_binary64_1044`
1×	`-commutative_binary64_1032` `sum-log_binary64_1192` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-r/_binary64_1043` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172`

Counts

4 → 295

Calls

4 calls:

46.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
28.0ms	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
19.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
16.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series2.9s (10.3%)

Counts

4 → 91

Calls

4 calls:

1.1s	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))) 1)
965.0ms	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
690.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
204.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 10732 to 8276 computations (22.9% saved)

simplify183.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

386 → 386

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5437	20318

prune1.2s (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	385	1	386
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	386	5	391

Error

0.1b

Counts

391 → 5

Compiler

Compiled 19706 to 10550 computations (46.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
1.1b	(+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.6b	(log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
20.0b	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

rewrite97.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1101`
10×	`add-exp-log_binary64_1139`
9×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
8×	`associate-/l/_binary64_1048` `log-prod_binary64_1187`
7×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
6×	`add-log-exp_binary64_1140` `pow1_binary64_1162`
4×	`exp-sum_binary64_1147` `frac-times_binary64_1111` `exp-prod_binary64_1153` `log-div_binary64_1188`
3×	`distribute-lft-out_binary64_1052` `flip--_binary64_1076` `flip3--_binary64_1105` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
2×	`exp-diff_binary64_1149` `associate-r/_binary64_1043` `associate-/r/_binary64_1047` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `log-pow_binary64_1190` `associate-l/_binary64_1044`
1×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `rem-exp-log_binary64_1141` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `rem-log-exp_binary64_1142` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `+-commutative_binary64_1031`

Counts

4 → 76

Calls

4 calls:

26.0ms	(log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
23.0ms	(+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
23.0ms	(exp.f64 (log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
15.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

series7.6s (26.6%)

Counts

4 → 81

Calls

4 calls:

4.0s	(log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
2.3s	(exp.f64 (log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
1.1s	(+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
218.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

Compiler

Compiled 15954 to 12586 computations (21.1% saved)

simplify116.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5822	12057

prune511.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	157	5	162

Error

0.1b

Counts

162 → 5

Compiler

Compiled 10088 to 5993 computations (40.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 E.f64 (log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
1.1b	(+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
2.6b	(log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
20.0b	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

rewrite100.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_1101`
11×	`add-exp-log_binary64_1139`
10×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
9×	`add-cbrt-cube_binary64_1137`
8×	`associate-/l/_binary64_1048` `log-prod_binary64_1187`
7×	`pow1_binary64_1162` `flip3-+_binary64_1104` `flip-+_binary64_1075`
6×	`add-log-exp_binary64_1140`
4×	`frac-times_binary64_1111` `unpow-prod-up_binary64_1179` `pow-unpow_binary64_1178` `log-div_binary64_1188`
3×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052` `flip--_binary64_1076` `flip3--_binary64_1105` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
2×	`pow-exp_binary64_1169` `associate-r/_binary64_1043` `associate-/r/_binary64_1047` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `pow-sub_binary64_1177` `log-pow_binary64_1190` `associate-l/_binary64_1044`
1×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-pow_binary64_1173` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `rem-log-exp_binary64_1142` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `+-commutative_binary64_1031` `sqr-pow_binary64_1073` `e-exp-1_binary64_1146` `pow-to-exp_binary64_1170`

Counts

4 → 83

Calls

4 calls:

26.0ms	(log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
25.0ms	(pow.f64 E.f64 (log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
24.0ms	(+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
15.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

series8.4s (29.4%)

Counts

4 → 81

Calls

4 calls:

3.9s	(log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i))))))
3.2s	(pow.f64 E.f64 (log.f64 (+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))))
1.1s	(+.f64 1 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
213.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

Compiler

Compiled 16040 to 12672 computations (21% saved)

simplify128.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5951	12750

prune551.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	164	5	169

Error

0.1b

Counts

169 → 5

Compiler

Compiled 10456 to 6101 computations (41.7% saved)

regimes1.1s (3.7%)

Accuracy

Total 1.4b remaining (95.9%)

Threshold costs 0b (0%)

Compiler

Compiled 15948 to 10723 computations (32.8% saved)

bsearch4.0ms (0%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	271	185
1	271	185

end0.0ms (0%)

sample2.3s (7.9%)

Algorithm

1×

intervals

Results

372.0ms	6533×	body	128	valid
176.0ms	8000×	pre	128	true
151.0ms	662×	body	1024	valid
77.0ms	476×	body	512	valid
32.0ms	272×	body	256	valid
16.0ms	57×	body	2048	valid

Compiler

Compiled 2113 to 1403 computations (33.6% saved)

Details

analyze124.0ms (0.4%)

sample35.0ms (0.1%)

simplify166.0ms (0.6%)

prune3.0ms (0%)

localize12.0ms (0%)

rewrite88.0ms (0.3%)

series2.2s (7.6%)

simplify121.0ms (0.4%)

prune443.0ms (1.6%)

localize12.0ms (0%)

rewrite156.0ms (0.5%)

series2.9s (10.3%)

simplify183.0ms (0.6%)

prune1.2s (4.3%)

localize16.0ms (0.1%)

rewrite97.0ms (0.3%)

series7.6s (26.6%)

simplify116.0ms (0.4%)

prune511.0ms (1.8%)

localize16.0ms (0.1%)

rewrite100.0ms (0.4%)

series8.4s (29.4%)

simplify128.0ms (0.4%)

prune551.0ms (1.9%)

regimes1.1s (3.7%)

bsearch4.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample2.3s (7.9%)

Profiling