Details

analyze268.0ms (5.8%)

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)

sample58.0ms (1.3%)

Algorithm

1×

intervals

Results

24.0ms	137×	body	2048	nan
11.0ms	256×	body	128	valid
7.0ms	61×	body	1024	nan
4.0ms	41×	body	512	nan
1.0ms	21×	body	256	nan
1.0ms	19×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify258.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5604	14

prune2.0ms (0.1%)

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: 33.4b

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))))
31.1b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1101`
7×	`add-sqr-sqrt_binary64_1123`
6×	`sqrt-prod_binary64_1117`
5×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
4×	`add-exp-log_binary64_1139` `log-prod_binary64_1187`
3×	`add-cbrt-cube_binary64_1137`
2×	`difference-of-squares_binary64_1070` `distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `sqrt-div_binary64_1118` `flip-+_binary64_1075` `log-div_binary64_1188`
1×	`rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `rem-log-exp_binary64_1142` `sqrt-pow1_binary64_1119` `difference-of-sqr-1_binary64_1071` `flip--_binary64_1076` `flip3--_binary64_1105` `+-commutative_binary64_1031` `log-pow_binary64_1190` `pow1/2_binary64_1181`

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))

series197.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

94.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
61.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
42.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4891	923
1	4891	923

prune50.0ms (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 837 to 557 computations (33.5% saved)

localize10.0ms (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)))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1123`
15×	`sqrt-prod_binary64_1117`
13×	`*-un-lft-identity_binary64_1101`
12×	`sqrt-div_binary64_1118`
10×	`associate-r_binary64_1041`
8×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
7×	`associate-l_binary64_1042`
6×	`add-exp-log_binary64_1139`
5×	`add-log-exp_binary64_1140` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `flip-+_binary64_1075`
4×	`frac-times_binary64_1111` `unswap-sqr_binary64_1069`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `log-prod_binary64_1187` `pow-prod-down_binary64_1172`
2×	`difference-of-squares_binary64_1070` `sqrt-pow1_binary64_1119` `associate-r/_binary64_1043` `log-div_binary64_1188` `associate-l/_binary64_1044` `pow1/2_binary64_1181`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `rem-log-exp_binary64_1142` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `+-commutative_binary64_1031` `log-pow_binary64_1190` `sqrt-unprod_binary64_1121`

Counts

3 → 68

Calls

3 calls:

15.0ms	(*.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)))))

series220.0ms (4.8%)

Counts

3 → 9

Calls

3 calls:

91.0ms	(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)))
62.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify103.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4900	1681
1	4900	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))))
0.3b	(/.f64 3/32 (pow.f64 x 4))
0.6b	(/.f64 1/4 (*.f64 x x))

rewrite63.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_1101`
32×	`add-sqr-sqrt_binary64_1123`
26×	`add-cube-cbrt_binary64_1136`
25×	`times-frac_binary64_1107`
16×	`distribute-lft-out--_binary64_1053`
14×	`add-exp-log_binary64_1139`
13×	`pow1_binary64_1162`
12×	`unpow-prod-down_binary64_1180`
11×	`add-cbrt-cube_binary64_1137`
10×	`add-log-exp_binary64_1140` `cancel-sign-sub-inv_binary64_1067`
9×	`distribute-lft-out_binary64_1052` `log-pow_binary64_1190`
8×	`associate-/r*_binary64_1045`
6×	`associate-/l*_binary64_1046` `log-prod_binary64_1187`
5×	`diff-log_binary64_1193` `div-exp_binary64_1152`
4×	`associate--r+_binary64_1037` `sqr-pow_binary64_1073`
3×	`difference-of-squares_binary64_1070` `associate--l+_binary64_1038` `cbrt-undiv_binary64_1135`
2×	`frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098`
1×	`pow-exp_binary64_1169` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-+r-_binary64_1035` `associate--r-_binary64_1040` `pow-to-exp_binary64_1170`

Counts

4 → 121

Calls

4 calls:

28.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
10.0ms	(-.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))

series342.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
81.0ms	(-.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))
31.0ms	(/.f64 1/4 (*.f64 x x))

simplify86.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4931	2312
1	4931	2312

prune149.0ms (3.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	133	2	135

Merged error: 0b

Counts

135 → 2

Compiler

Compiled 2956 to 1996 computations (32.5% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 3/32 (pow.f64 x 4))
0.6b	(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)

rewrite92.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`*-un-lft-identity_binary64_1101`
48×	`distribute-lft-out--_binary64_1053`
36×	`add-sqr-sqrt_binary64_1123` `unpow-prod-down_binary64_1180`
30×	`cbrt-prod_binary64_1132`
29×	`pow1_binary64_1162`
28×	`add-cube-cbrt_binary64_1136`
24×	`cube-prod_binary64_1129` `distribute-lft-out_binary64_1052` `times-frac_binary64_1107` `log-pow_binary64_1190`
15×	`add-exp-log_binary64_1139`
12×	`add-cbrt-cube_binary64_1137`
8×	`associate-/r*_binary64_1045`
6×	`associate-/l*_binary64_1046` `sqr-pow_binary64_1073`
5×	`div-exp_binary64_1152`
4×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140` `cube-div_binary64_1130`
3×	`pow-unpow_binary64_1178` `cbrt-undiv_binary64_1135`
2×	`pow-exp_binary64_1169` `cube-mult_binary64_1131` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `unpow3_binary64_1167` `pow-to-exp_binary64_1170` `cbrt-div_binary64_1133`
1×	`rem-cube-cbrt_binary64_1124` `cbrt-unprod_binary64_1134` `pow1/3_binary64_1183` `prod-exp_binary64_1150` `pow-pow_binary64_1173` `rem-cbrt-cube_binary64_1125`

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)
30.0ms	(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 3/32 (pow.f64 x 4))
5.0ms	(/.f64 1/4 (*.f64 x x))

series360.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(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)
80.0ms	(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))
32.0ms	(/.f64 1/4 (*.f64 x x))

simplify91.0ms (2%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4985	4742
1	4985	4742

prune254.0ms (5.5%)

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)

regimes38.0ms (0.8%)

Compiler: Compiled 210 to 172 computations (18.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample1.7s (37.6%)

Algorithm

1×

intervals

Results

631.0ms	3990×	body	2048	nan
353.0ms	8000×	body	128	valid
249.0ms	1995×	body	1024	nan
91.0ms	998×	body	512	nan
31.0ms	498×	body	256	nan
15.0ms	457×	body	128	nan
2.0ms	8×	body	4096	nan

Compiler

Compiled 80 to 67 computations (16.3% saved)

Details

analyze268.0ms (5.8%)

sample58.0ms (1.3%)

simplify258.0ms (5.6%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite24.0ms (0.5%)

series197.0ms (4.3%)

simplify55.0ms (1.2%)

prune50.0ms (1.1%)

localize10.0ms (0.2%)

rewrite28.0ms (0.6%)

series220.0ms (4.8%)

simplify103.0ms (2.2%)

prune86.0ms (1.9%)

localize14.0ms (0.3%)

rewrite63.0ms (1.4%)

series342.0ms (7.4%)

simplify86.0ms (1.9%)

prune149.0ms (3.2%)

localize18.0ms (0.4%)

rewrite92.0ms (2%)

series360.0ms (7.8%)

simplify91.0ms (2%)

prune254.0ms (5.5%)

regimes38.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (37.6%)

Profiling