Details

analyze128.0ms (0.8%)

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)

sample37.0ms (0.2%)

Algorithm

1×

intervals

Results

11.0ms	201×	body	128	valid
6.0ms	256×	pre	128	true
5.0ms	21×	body	1024	valid
3.0ms	18×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify217.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5063	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

Merged error: 26.8b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b

(/.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))

3.4b

(+.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)

20.7b

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

rewrite98.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_1094`
47×	`*-un-lft-identity_binary64_1088`
25×	`add-sqr-sqrt_binary64_1109` `add-cube-cbrt_binary64_1120`
17×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
14×	`associate-/r/_binary64_1036`
11×	`flip-+_binary64_1062` `flip3-+_binary64_1091` `distribute-lft-out_binary64_1041`
10×	`associate-/l*_binary64_1035`
9×	`associate-/l/_binary64_1037`
7×	`associate-/r*_binary64_1034` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`
5×	`add-log-exp_binary64_1124`
4×	`frac-times_binary64_1098`
3×	`flip3--_binary64_1092` `flip--_binary64_1063` `pow1_binary64_1146`
2×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `associate-l/_binary64_1033` `cbrt-unprod_binary64_1118` `prod-exp_binary64_1134` `associate-r/_binary64_1032`
1×	`sum-log_binary64_1176` `+-commutative_binary64_1020`

Counts

3 → 111

Calls

3 calls:

42.0ms

(+.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)

25.0ms

(/.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))

16.0ms

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

series1.4s (8.8%)

Counts

3 → 9

Calls

3 calls:

687.0ms

(+.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)

586.0ms

(/.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))

126.0ms

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

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4937	5261
1	4937	5261

prune253.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 5.8b

Counts

121 → 10

Compiler

Compiled 5408 to 2838 computations (47.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.3b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
3.6b	(.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)))))
5.1b	(+.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)

rewrite171.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

321×	`times-frac_binary64_1094`
290×	`*-un-lft-identity_binary64_1088`
211×	`add-sqr-sqrt_binary64_1109`
140×	`add-cube-cbrt_binary64_1120`
90×	`associate-r_binary64_1030`
44×	`distribute-lft-out_binary64_1041`
31×	`distribute-lft-out--_binary64_1042` `difference-of-squares_binary64_1057`
26×	`associate-/l*_binary64_1035`
24×	`associate-/r/_binary64_1036`
20×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
15×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
12×	`div-inv_binary64_1085`
7×	`associate-/r*_binary64_1034` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119`
6×	`add-log-exp_binary64_1124` `pow1_binary64_1146`
4×	`associate-l_binary64_1031`
3×	`unswap-sqr_binary64_1056` `cbrt-unprod_binary64_1118` `associate-/l/_binary64_1037` `div-sub_binary64_1093` `prod-exp_binary64_1134`
2×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `associate-*l/_binary64_1033` `frac-times_binary64_1098`
1×	`-commutative_binary64_1021` `flip3--_binary64_1092` `sum-log_binary64_1176` `flip--_binary64_1063` `+-commutative_binary64_1020` `pow-prod-down_binary64_1156` `associate-r/_binary64_1032`

Counts

4 → 295

Calls

4 calls:

51.0ms	(.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)))))
30.0ms	(+.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)
21.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series1.7s (10.6%)

Counts

4 → 12

Calls

4 calls:

674.0ms	(+.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)
595.0ms	(.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)))))
311.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
114.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify155.0ms (1%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4971	13438
1	4971	13438

prune788.0ms (4.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	302	5	307
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	307	10	317

Merged error: 5.8b

Counts

317 → 10

Compiler

Compiled 14724 to 7770 computations (47.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
3.6b	(.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)))))
5.1b	(+.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)
5.1b	(log.f64 (exp.f64 (+.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)))

rewrite161.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_1094`
151×	`*-un-lft-identity_binary64_1088`
116×	`add-sqr-sqrt_binary64_1109`
90×	`associate-r_binary64_1030`
75×	`add-cube-cbrt_binary64_1120`
22×	`distribute-lft-out_binary64_1041`
16×	`distribute-lft-out--_binary64_1042` `difference-of-squares_binary64_1057`
15×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
12×	`associate-/r/_binary64_1036`
9×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
7×	`pow1_binary64_1146`
6×	`add-log-exp_binary64_1124` `div-inv_binary64_1085`
5×	`associate-/l*_binary64_1035`
4×	`log-pow_binary64_1174` `log-prod_binary64_1171` `div-exp_binary64_1136` `associate-l_binary64_1031` `cbrt-undiv_binary64_1119`
3×	`unswap-sqr_binary64_1056` `cbrt-unprod_binary64_1118` `associate-/r*_binary64_1034` `exp-prod_binary64_1137` `prod-exp_binary64_1134`
2×	`associate-*l/_binary64_1033` `frac-times_binary64_1098` `associate-/l/_binary64_1037`
1×	`-commutative_binary64_1021` `clear-num_binary64_1087` `frac-2neg_binary64_1099` `exp-sum_binary64_1131` `rem-log-exp_binary64_1126` `flip3--_binary64_1092` `sum-log_binary64_1176` `flip--_binary64_1063` `div-sub_binary64_1093` `+-commutative_binary64_1020` `pow-prod-down_binary64_1156` `associate-r/_binary64_1032`

Counts

4 → 184

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)))))
34.0ms	(+.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)
31.0ms	(log.f64 (exp.f64 (+.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)))
12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series2.5s (15.6%)

Counts

4 → 12

Calls

4 calls:

1.1s	(log.f64 (exp.f64 (+.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)))
653.0ms	(+.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)
576.0ms	(.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)))))
110.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4948	7173
1	4948	7173

prune458.0ms (2.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	195	11	206

Merged error: 5.7b

Counts

206 → 11

Compiler

Compiled 9626 to 5275 computations (45.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.6b	(.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)))))
3.6b	(.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)))))
5.1b	(+.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)
5.1b	(+.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)

rewrite234.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

294×	`times-frac_binary64_1094`
258×	`*-un-lft-identity_binary64_1088`
188×	`add-sqr-sqrt_binary64_1109`
180×	`associate-r_binary64_1030`
122×	`add-cube-cbrt_binary64_1120`
44×	`distribute-lft-out_binary64_1041`
24×	`distribute-lft-out--_binary64_1042` `difference-of-squares_binary64_1057`
22×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
20×	`associate-/r/_binary64_1036`
16×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
10×	`div-inv_binary64_1085`
8×	`associate-l_binary64_1031` `add-log-exp_binary64_1124` `pow1_binary64_1146`
6×	`unswap-sqr_binary64_1056` `cbrt-unprod_binary64_1118` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119` `prod-exp_binary64_1134`
4×	`associate-*l/_binary64_1033` `frac-times_binary64_1098`
2×	`-commutative_binary64_1021` `sum-log_binary64_1176` `+-commutative_binary64_1020` `pow-prod-down_binary64_1156` `associate-r/_binary64_1032`

Counts

4 → 256

Calls

4 calls:

51.0ms	(.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)))))
47.0ms	(.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)))))
33.0ms	(+.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)
32.0ms	(+.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)

series2.5s (15.5%)

Counts

4 → 12

Calls

4 calls:

675.0ms	(+.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)
660.0ms	(+.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)
570.0ms	(.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)))))
558.0ms	(.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)))))

simplify128.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5152	10534

prune1.5s (9.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	268	11	279

Merged error: 5.7b

Counts

279 → 11

Compiler

Compiled 21816 to 12009 computations (45% saved)

regimes957.0ms (6%)

Compiler: Compiled 15166 to 9750 computations (35.7% saved)

bsearch6.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	164
1	71	164

end0.0ms (0%)

sample2.4s (14.7%)

Algorithm

1×

intervals

Results

369.0ms	6458×	body	128	valid
191.0ms	8000×	pre	128	true
148.0ms	665×	body	1024	valid
86.0ms	521×	body	512	valid
37.0ms	320×	body	256	valid
10.0ms	36×	body	2048	valid

Compiler

Compiled 2251 to 1443 computations (35.9% saved)

Details

analyze128.0ms (0.8%)

sample37.0ms (0.2%)

simplify217.0ms (1.4%)

prune3.0ms (0%)

localize12.0ms (0.1%)

rewrite98.0ms (0.6%)

series1.4s (8.8%)

simplify103.0ms (0.6%)

prune253.0ms (1.6%)

localize13.0ms (0.1%)

rewrite171.0ms (1.1%)

series1.7s (10.6%)

simplify155.0ms (1%)

prune788.0ms (4.9%)

localize16.0ms (0.1%)

rewrite161.0ms (1%)

series2.5s (15.6%)

simplify107.0ms (0.7%)

prune458.0ms (2.9%)

localize20.0ms (0.1%)

rewrite234.0ms (1.5%)

series2.5s (15.5%)

simplify128.0ms (0.8%)

prune1.5s (9.3%)

regimes957.0ms (6%)

bsearch6.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.4s (14.7%)

Profiling