Details

analyze278.0ms (6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample54.0ms (1.2%)

Algorithm

1×

intervals

Results

20.0ms	128×	body	2048	nan
11.0ms	256×	body	128	valid
8.0ms	59×	body	1024	nan
3.0ms	30×	body	512	nan
1.0ms	21×	body	256	nan
1.0ms	21×	body	128	nan
0.0ms	1×	body	4096	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify295.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	5150	14

prune2.0ms (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

Merged error: 31.9b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
29.7b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1088`
7×	`add-sqr-sqrt_binary64_1109`
6×	`sqrt-prod_binary64_1103`
5×	`add-log-exp_binary64_1124` `pow1_binary64_1146` `add-cube-cbrt_binary64_1120`
4×	`log-prod_binary64_1171` `add-exp-log_binary64_1123`
3×	`add-cbrt-cube_binary64_1121`
2×	`sqrt-div_binary64_1104` `log-div_binary64_1172` `flip-+_binary64_1062` `flip3-+_binary64_1091` `distribute-lft-out_binary64_1041` `difference-of-squares_binary64_1057`
1×	`log-pow_binary64_1174` `rem-sqrt-square_binary64_1101` `rem-log-exp_binary64_1126` `difference-of-sqr-1_binary64_1058` `flip3--_binary64_1092` `sum-log_binary64_1176` `flip--_binary64_1063` `+-commutative_binary64_1020` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`

Counts

3 → 45

Calls

3 calls:

8.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
8.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
6.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series209.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

99.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
61.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
48.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify41.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5056	920

prune52.0ms (1.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Merged error: 0.0b

Counts

55 → 2

Compiler

Compiled 835 to 555 computations (33.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.2b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1109`
15×	`sqrt-prod_binary64_1103`
13×	`*-un-lft-identity_binary64_1088`
12×	`sqrt-div_binary64_1104`
10×	`associate-r_binary64_1030`
8×	`pow1_binary64_1146` `add-cube-cbrt_binary64_1120`
7×	`associate-l_binary64_1031`
6×	`add-exp-log_binary64_1123`
5×	`add-cbrt-cube_binary64_1121` `flip-+_binary64_1062` `add-log-exp_binary64_1124` `flip3-+_binary64_1091`
4×	`unswap-sqr_binary64_1056` `frac-times_binary64_1098`
3×	`log-prod_binary64_1171` `flip3--_binary64_1092` `flip--_binary64_1063` `pow-prod-down_binary64_1156`
2×	`associate-l/_binary64_1033` `log-div_binary64_1172` `sqrt-pow1_binary64_1105` `associate-r/_binary64_1032` `difference-of-squares_binary64_1057` `pow1/2_binary64_1165`
1×	`*-commutative_binary64_1021` `log-pow_binary64_1174` `cbrt-unprod_binary64_1118` `rem-log-exp_binary64_1126` `difference-of-sqr-1_binary64_1058` `sum-log_binary64_1176` `+-commutative_binary64_1020` `sqrt-unprod_binary64_1107` `prod-exp_binary64_1134` `distribute-lft-out_binary64_1041` `distribute-lft-out--_binary64_1042`

Counts

3 → 68

Calls

3 calls:

14.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
3.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

series210.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

81.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
67.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
61.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify83.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4898	1681
1	4898	1681

prune86.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	2	79

Merged error: 0.0b

Counts

79 → 2

Compiler

Compiled 1524 to 1157 computations (24.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
0.2b	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
0.4b	(/.f64 3/32 (pow.f64 x 4))
0.6b	(/.f64 1/4 (*.f64 x x))

rewrite62.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_1088`
30×	`add-sqr-sqrt_binary64_1109`
25×	`times-frac_binary64_1094`
24×	`add-cube-cbrt_binary64_1120`
14×	`add-exp-log_binary64_1123` `distribute-lft-out--_binary64_1042`
12×	`unpow-prod-down_binary64_1164`
11×	`add-cbrt-cube_binary64_1121` `pow1_binary64_1146`
10×	`add-log-exp_binary64_1124`
8×	`associate-/r*_binary64_1034`
7×	`log-pow_binary64_1174`
6×	`log-prod_binary64_1171` `distribute-lft-out_binary64_1041` `associate-/l*_binary64_1035`
5×	`div-exp_binary64_1136` `diff-log_binary64_1177`
4×	`associate--r+_binary64_1026` `sqr-pow_binary64_1060`
3×	`associate--l+_binary64_1027` `cbrt-undiv_binary64_1119` `difference-of-squares_binary64_1057`
2×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `flip3--_binary64_1092` `sub-neg_binary64_1081` `sum-log_binary64_1176` `flip--_binary64_1063` `div-inv_binary64_1085`
1×	`cbrt-unprod_binary64_1118` `associate-+r-_binary64_1024` `associate--r-_binary64_1029` `pow-exp_binary64_1153` `pow-to-exp_binary64_1154` `prod-exp_binary64_1134`

Counts

4 → 111

Calls

4 calls:

31.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
9.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
5.0ms	(/.f64 1/4 (*.f64 x x))
5.0ms	(/.f64 3/32 (pow.f64 x 4))

series354.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
87.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
46.0ms	(/.f64 3/32 (pow.f64 x 4))
32.0ms	(/.f64 1/4 (*.f64 x x))

simplify66.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4925	2166
1	4925	2166

prune155.0ms (3.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	123	2	125

Merged error: 0b

Counts

125 → 2

Compiler

Compiled 2782 to 1886 computations (32.2% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 3/32 (pow.f64 x 4))
0.5b	(cbrt.f64 (pow.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))) 3))
0.6b	(/.f64 1/4 (*.f64 x x))
0.7b	(pow.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))) 3)

rewrite89.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`*-un-lft-identity_binary64_1088`
48×	`distribute-lft-out--_binary64_1042`
36×	`unpow-prod-down_binary64_1164` `add-sqr-sqrt_binary64_1109`
30×	`cbrt-prod_binary64_1116`
29×	`pow1_binary64_1146`
28×	`add-cube-cbrt_binary64_1120`
24×	`cube-prod_binary64_1113` `log-pow_binary64_1174` `times-frac_binary64_1094` `distribute-lft-out_binary64_1041`
15×	`add-exp-log_binary64_1123`
12×	`add-cbrt-cube_binary64_1121`
8×	`associate-/r*_binary64_1034`
6×	`sqr-pow_binary64_1060` `associate-/l*_binary64_1035`
5×	`div-exp_binary64_1136`
4×	`cube-div_binary64_1114` `add-log-exp_binary64_1124` `difference-of-squares_binary64_1057`
3×	`cbrt-undiv_binary64_1119` `pow-unpow_binary64_1162`
2×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `unpow3_binary64_1151` `cube-mult_binary64_1115` `cbrt-div_binary64_1117` `flip3--_binary64_1092` `flip--_binary64_1063` `pow-exp_binary64_1153` `pow-to-exp_binary64_1154` `div-inv_binary64_1085`
1×	`rem-cube-cbrt_binary64_1110` `cbrt-unprod_binary64_1118` `rem-cbrt-cube_binary64_1111` `pow-pow_binary64_1157` `pow1/3_binary64_1167` `prod-exp_binary64_1134`

Counts

4 → 150

Calls

4 calls:

31.0ms	(pow.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))) 3)
29.0ms	(cbrt.f64 (pow.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))) 3))
5.0ms	(/.f64 1/4 (*.f64 x x))
5.0ms	(/.f64 3/32 (pow.f64 x 4))

series365.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(pow.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))) 3)
85.0ms	(cbrt.f64 (pow.f64 (-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x)))) 3))
46.0ms	(/.f64 3/32 (pow.f64 x 4))
31.0ms	(/.f64 1/4 (*.f64 x x))

simplify99.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4976	4742
1	4976	4742

prune281.0ms (6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	162	2	164

Merged error: 0b

Counts

164 → 2

Compiler

Compiled 4670 to 3370 computations (27.8% saved)

regimes23.0ms (0.5%)

Compiler: Compiled 34 to 29 computations (14.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample1.7s (37.3%)

Algorithm

1×

intervals

Results

642.0ms	3983×	body	2048	nan
358.0ms	8000×	body	128	valid
255.0ms	2002×	body	1024	nan
90.0ms	971×	body	512	nan
35.0ms	519×	body	256	nan
17.0ms	496×	body	128	nan
3.0ms	13×	body	4096	nan

Compiler

Compiled 54 to 46 computations (14.8% saved)

Details

analyze278.0ms (6%)

sample54.0ms (1.2%)

simplify295.0ms (6.4%)

prune2.0ms (0%)

localize7.0ms (0.2%)

rewrite25.0ms (0.5%)

series209.0ms (4.5%)

simplify41.0ms (0.9%)

prune52.0ms (1.1%)

localize9.0ms (0.2%)

rewrite29.0ms (0.6%)

series210.0ms (4.5%)

simplify83.0ms (1.8%)

prune86.0ms (1.9%)

localize14.0ms (0.3%)

rewrite62.0ms (1.3%)

series354.0ms (7.6%)

simplify66.0ms (1.4%)

prune155.0ms (3.3%)

localize17.0ms (0.4%)

rewrite89.0ms (1.9%)

series365.0ms (7.9%)

simplify99.0ms (2.1%)

prune281.0ms (6%)

regimes23.0ms (0.5%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.7s (37.3%)

Profiling