Details

analyze8.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 20 computations (31% saved)

sample28.0ms (0%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 57 to 42 computations (26.3% saved)

simplify141.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5047	16

prune8.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Kept	Total
New	4	4
Fresh	4	4
Picked	0	0
Done	0	0
Total	8	8

Error

0.7b

Counts

8 → 5

Compiler

Compiled 12 to 11 computations (8.3% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.4b	(/.f64 1 (*.f64 i i))
0.4b	(/.f64 1 (*.f64 i i))
0.7b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_1123`
35×	`times-frac_binary64_1107`
33×	`*-un-lft-identity_binary64_1101`
17×	`add-cube-cbrt_binary64_1136`
15×	`add-exp-log_binary64_1139`
12×	`difference-of-squares_binary64_1070`
10×	`pow1_binary64_1162`
9×	`add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
8×	`distribute-lft-out--_binary64_1053`
6×	`div-inv_binary64_1098` `associate-/l*_binary64_1046` `pow-flip_binary64_1175`
5×	`div-exp_binary64_1152`
3×	`prod-exp_binary64_1150` `cbrt-undiv_binary64_1135`
2×	`1-exp_binary64_1145` `add-log-exp_binary64_1140` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r/_binary64_1047` `rec-exp_binary64_1151`
1×	`inv-pow_binary64_1186` `pow-plus_binary64_1164` `cbrt-unprod_binary64_1134` `pow-prod-up_binary64_1171` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172` `pow2_binary64_1182`

Counts

2 → 81

Calls

4 calls:

9.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))
0.0ms	(/.f64 1 (*.f64 i i))
0.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

series67.0ms (0%)

Counts

2 → 15

Calls

2 calls:

47.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
19.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 211 to 201 computations (4.7% saved)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5026	1341

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

42.2b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))
13.1b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
0.1b	(.f64 (.f64 i i) (*.f64 i i))
0.1b	(.f64 (.f64 i i) (*.f64 i i))
13.1b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
42.2b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

rewrite126.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

302×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
168×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
114×	`pow1_binary64_1162`
76×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
38×	`times-frac_binary64_1107`
36×	`pow-prod-up_binary64_1171`
23×	`pow-prod-down_binary64_1172`
22×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `pow-sqr_binary64_1074`
18×	`pow-plus_binary64_1164`
16×	`add-cube-cbrt_binary64_1136`
13×	`pow2_binary64_1182`
12×	`difference-of-squares_binary64_1070`
9×	`div-inv_binary64_1098`
7×	`associate-/r*_binary64_1045`
6×	`difference-of-sqr-1_binary64_1071` `associate-/l*_binary64_1046`
3×	`add-log-exp_binary64_1140`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r/_binary64_1047`
1×	`-commutative_binary64_1032` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069`

Counts

3 → 232

Calls

6 calls:

48.0ms	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
29.0ms	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))
10.0ms	(.f64 (.f64 i i) (*.f64 i i))
0.0ms	(.f64 (.f64 i i) (*.f64 i i))
0.0ms	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

series145.0ms (0.1%)

Counts

3 → 18

Calls

3 calls:

81.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

33.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

31.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

Compiler

Compiled 373 to 327 computations (12.3% saved)

simplify126.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4869	3583
1	4869	3583

prune1.3s (1%)

Pruning

96 alts after pruning (94 fresh and 2 done)

	Pruned	Kept	Total
New	254	92	346
Fresh	1	2	3
Picked	0	0	0
Done	0	2	2
Total	255	96	351

Error

Counts

351 → 96

Compiler

Compiled 4550 to 3445 computations (24.3% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1)))
0.0b	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))
0.0b	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))
0.0b	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1)))

rewrite37.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_1123`
31×	`times-frac_binary64_1107`
24×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
16×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
15×	`associate-r_binary64_1041` `associate-l_binary64_1042`
6×	`associate-/r/_binary64_1047`
5×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow1_binary64_1162` `unswap-sqr_binary64_1069`
3×	`div-inv_binary64_1098` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`add-log-exp_binary64_1140` `flip--_binary64_1076` `flip3--_binary64_1105`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `associate-*l/_binary64_1044`

Counts

2 → 83

Calls

4 calls:

20.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1)))
6.0ms	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))
0.0ms	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))
0.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1)))

series251.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

182.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1)))
68.0ms	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))

Compiler

Compiled 768 to 656 computations (14.6% saved)

simplify59.0ms (0%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5215	3109

localize3.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 (.f64 i i) -1/4)
0.0b	(.f64 (.f64 i i) -1/4)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
3×	`add-sqr-sqrt_binary64_1123` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-r_binary64_1041` `pow-prod-down_binary64_1172`
2×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
1×	`-commutative_binary64_1032` `add-log-exp_binary64_1140` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069`

Counts

1 → 19

Calls

2 calls:

6.0ms	(.f64 (.f64 i i) -1/4)
0.0ms	(.f64 (.f64 i i) -1/4)

series28.0ms (0%)

Counts

1 → 3

Calls

1 calls:

28.0ms

(*.f64 (*.f64 i i) -1/4)

Compiler

Compiled 30 to 30 computations (0% saved)

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5391	182

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

0.4b	(/.f64 1/64 (*.f64 i i))
0.3b	(/.f64 1/256 (pow.f64 i 4))
0.0b	(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4)))
0.0b	(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4)))
0.3b	(/.f64 1/256 (pow.f64 i 4))
0.4b	(/.f64 1/64 (*.f64 i i))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_1101`
24×	`times-frac_binary64_1107`
21×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
13×	`add-exp-log_binary64_1139`
12×	`unpow-prod-down_binary64_1180`
10×	`add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045`
6×	`associate-/l*_binary64_1046`
5×	`div-exp_binary64_1152`
4×	`sqr-pow_binary64_1073`
3×	`distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `pow1_binary64_1162` `cbrt-undiv_binary64_1135`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `flip-+_binary64_1075` `frac-add_binary64_1109`
1×	`pow-exp_binary64_1169` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `+-commutative_binary64_1031` `pow-to-exp_binary64_1170` `associate-+l+_binary64_1034`

Counts

3 → 83

Calls

6 calls:

17.0ms	(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4)))
6.0ms	(/.f64 1/64 (*.f64 i i))
5.0ms	(/.f64 1/256 (pow.f64 i 4))
0.0ms	(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4)))
0.0ms	(/.f64 1/256 (pow.f64 i 4))

series120.0ms (0.1%)

Counts

3 → 13

Calls

3 calls:

57.0ms	(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4)))
36.0ms	(/.f64 1/256 (pow.f64 i 4))
27.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 264 to 243 computations (8% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4883	1364
1	4883	1364

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
0.3b	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.3b	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.7b	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
9×	`pow1_binary64_1162`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
4×	`difference-of-squares_binary64_1070` `associate-/r*_binary64_1045`
3×	`associate-/l_binary64_1046` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l*_binary64_1042`
2×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `pow-prod-up_binary64_1171` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `sqr-abs_binary64_1116` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069` `pow2_binary64_1182`

Counts

2 → 59

Calls

4 calls:

6.0ms	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
4.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.0ms	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))

series105.0ms (0.1%)

Counts

2 → 6

Calls

2 calls:

81.0ms	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
24.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))

Compiler

Compiled 120 to 120 computations (0% saved)

simplify63.0ms (0%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4954	933
1	4954	933

localize20.0ms (0%)

Local error

Found 6 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
0.0b	(-.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 4 (pow.f64 i 6)))
0.0b	(.f64 (.f64 i i) -1/4)
0.0b	(.f64 (.f64 i i) -1/4)
0.0b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
0.0b	(-.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 4 (pow.f64 i 6)))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cancel-sign-sub-inv_binary64_1067`
10×	`add-log-exp_binary64_1140`
9×	`add-sqr-sqrt_binary64_1123`
8×	`*-un-lft-identity_binary64_1101` `add-exp-log_binary64_1139` `pow1_binary64_1162` `associate--l+_binary64_1038` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
6×	`unpow-prod-down_binary64_1180`
4×	`diff-log_binary64_1193`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sub-neg_binary64_1094` `associate-r_binary64_1041` `pow-prod-down_binary64_1172`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `sqr-pow_binary64_1073`
1×	`-commutative_binary64_1032` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069` `associate--l-_binary64_1039`

Counts

3 → 59

Calls

6 calls:

12.0ms	(-.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 4 (pow.f64 i 6)))
8.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
7.0ms	(.f64 (.f64 i i) -1/4)
0.0ms	(.f64 (.f64 i i) -1/4)
0.0ms	(-.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 4 (pow.f64 i 6)))

series283.0ms (0.2%)

Counts

3 → 18

Calls

3 calls:

178.0ms	(-.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 4 (pow.f64 i 6)))
75.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
30.0ms	(.f64 (.f64 i i) -1/4)

Compiler

Compiled 522 to 453 computations (13.2% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4877	1114
1	4877	1114

prune7.6s (5.5%)

Pruning

224 alts after pruning (219 fresh and 5 done)

	Pruned	Kept	Total
New	226	141	367
Fresh	11	78	89
Picked	0	0	0
Done	2	5	7
Total	239	224	463

Error

Counts

463 → 224

Compiler

Compiled 11388 to 9028 computations (20.7% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (.f64 i 2) 1))))
0.0b	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))
0.0b	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))
0.0b	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (.f64 i 2) 1))))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64_1139`
25×	`add-cbrt-cube_binary64_1137`
18×	`prod-exp_binary64_1150` `times-frac_binary64_1107`
17×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
15×	`associate-l_binary64_1042`
10×	`cbrt-unprod_binary64_1134` `div-exp_binary64_1152`
7×	`pow1_binary64_1162`
6×	`cbrt-undiv_binary64_1135`
4×	`1-exp_binary64_1145` `associate-/r/_binary64_1047`
3×	`associate-r/_binary64_1043` `associate-/l_binary64_1046` `pow-prod-down_binary64_1172` `associate-/r*_binary64_1045`
2×	`add-log-exp_binary64_1140` `div-inv_binary64_1098`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-r_binary64_1041` `flip-+_binary64_1075` `associate-l/_binary64_1044`

Counts

2 → 74

Calls

4 calls:

17.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (.f64 i 2) 1))))
6.0ms	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))
0.0ms	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))
0.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (.f64 i 2) 1))))

series249.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

185.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (.f64 i 2) 1))))
64.0ms	(/.f64 (fabs.f64 (/.f64 i 2)) (-.f64 (*.f64 i 2) 1))

Compiler

Compiled 792 to 680 computations (14.1% saved)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4979	2546
1	4979	2546

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

13.2b	(.f64 (/.f64 (/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (-.f64 (pow.f64 (.f64 i 2) 3) 1)) (+.f64 (.f64 (.f64 i 2) (.f64 i 2)) (+.f64 (.f64 1 1) (.f64 (.f64 i 2) 1))))
12.7b	(/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1))
5.6b	(/.f64 (/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (-.f64 (pow.f64 (*.f64 i 2) 3) 1))
0.0b	(+.f64 (.f64 (.f64 i 2) (.f64 i 2)) (+.f64 (.f64 1 1) (.f64 (.f64 i 2) 1)))
0.0b	(+.f64 (.f64 (.f64 i 2) (.f64 i 2)) (+.f64 (.f64 1 1) (.f64 (.f64 i 2) 1)))
5.6b	(/.f64 (/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (-.f64 (pow.f64 (*.f64 i 2) 3) 1))
12.7b	(/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1))
13.2b	(.f64 (/.f64 (/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (-.f64 (pow.f64 (.f64 i 2) 3) 1)) (+.f64 (.f64 (.f64 i 2) (.f64 i 2)) (+.f64 (.f64 1 1) (.f64 (.f64 i 2) 1))))

rewrite172.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`times-frac_binary64_1107`
172×	`add-sqr-sqrt_binary64_1123`
145×	`*-un-lft-identity_binary64_1101`
96×	`associate-l_binary64_1042`
80×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
76×	`difference-of-squares_binary64_1070`
69×	`add-cube-cbrt_binary64_1136`
57×	`sqr-pow_binary64_1073`
48×	`associate-/r/_binary64_1047`
39×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
38×	`difference-of-sqr-1_binary64_1071`
25×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
24×	`div-inv_binary64_1098`
19×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out--_binary64_1053`
13×	`associate-/r*_binary64_1045`
10×	`associate-/l*_binary64_1046`
9×	`add-log-exp_binary64_1140`
6×	`pow1_binary64_1162`
4×	`associate-/l/_binary64_1048`
3×	`frac-times_binary64_1111` `sum-log_binary64_1192` `associate-r/_binary64_1043` `associate-r*_binary64_1041` `unswap-sqr_binary64_1069`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-*l/_binary64_1044`
1×	`*-commutative_binary64_1032` `distribute-lft-in_binary64_1050` `associate-+r+_binary64_1033` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `distribute-rgt-in_binary64_1051`

Counts

4 → 311

Calls

8 calls:

55.0ms	(.f64 (/.f64 (/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (-.f64 (pow.f64 (.f64 i 2) 3) 1)) (+.f64 (.f64 (.f64 i 2) (.f64 i 2)) (+.f64 (.f64 1 1) (.f64 (.f64 i 2) 1))))
22.0ms	(/.f64 (/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (-.f64 (pow.f64 (*.f64 i 2) 3) 1))
14.0ms	(+.f64 (.f64 (.f64 i 2) (.f64 i 2)) (+.f64 (.f64 1 1) (.f64 (.f64 i 2) 1)))
12.0ms	(/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1))
0.0ms	(+.f64 (.f64 (.f64 i 2) (.f64 i 2)) (+.f64 (.f64 1 1) (.f64 (.f64 i 2) 1)))

series385.0ms (0.3%)

Counts

4 → 45

Calls

4 calls:

150.0ms	(.f64 (/.f64 (/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (-.f64 (pow.f64 (.f64 i 2) 3) 1)) (+.f64 (.f64 (.f64 i 2) (.f64 i 2)) (+.f64 (.f64 1 1) (.f64 (.f64 i 2) 1))))
110.0ms	(/.f64 (/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (-.f64 (pow.f64 (*.f64 i 2) 3) 1))
81.0ms	(+.f64 (.f64 (.f64 i 2) (.f64 i 2)) (+.f64 (.f64 1 1) (.f64 (.f64 i 2) 1)))
45.0ms	(/.f64 (.f64 (/.f64 i 2) (/.f64 i 2)) (+.f64 (.f64 i 2) 1))

Compiler

Compiled 1377 to 1198 computations (13% saved)

simplify144.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5061	14909

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

23.2b	(.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 1 i) 4))) (+.f64 4 (.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
0.3b	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.3b	(pow.f64 (/.f64 1 i) 4)
0.0b	(/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 1 i) 4)))
0.0b	(/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 1 i) 4)))
0.3b	(pow.f64 (/.f64 1 i) 4)
0.3b	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
23.2b	(.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 1 i) 4))) (+.f64 4 (.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))

rewrite66.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`add-sqr-sqrt_binary64_1123`
78×	`times-frac_binary64_1107`
65×	`*-un-lft-identity_binary64_1101`
44×	`add-cube-cbrt_binary64_1136`
36×	`associate-l_binary64_1042`
35×	`difference-of-squares_binary64_1070`
34×	`unpow-prod-down_binary64_1180`
18×	`add-exp-log_binary64_1139`
15×	`pow1_binary64_1162`
13×	`add-cbrt-cube_binary64_1137`
9×	`associate-/r*_binary64_1045`
8×	`sqr-pow_binary64_1073`
7×	`distribute-lft-out--_binary64_1053`
6×	`associate-r_binary64_1041`
4×	`pow-exp_binary64_1169` `add-log-exp_binary64_1140` `associate-/r/_binary64_1047` `div-exp_binary64_1152`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-pow_binary64_1173` `pow-unpow_binary64_1178` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `swap-sqr_binary64_1068` `unswap-sqr_binary64_1069`
2×	`-commutative_binary64_1032` `frac-times_binary64_1111` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`
1×	`inv-pow_binary64_1186` `pow-plus_binary64_1164` `1-exp_binary64_1145` `pow-prod-up_binary64_1171` `frac-2neg_binary64_1112` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `pow-sqr_binary64_1074` `rec-exp_binary64_1151` `sqr-abs_binary64_1116` `associate-*l/_binary64_1044` `pow2_binary64_1182` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051` `pow-flip_binary64_1175`

Counts

4 → 169

Calls

8 calls:

22.0ms	(.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 1 i) 4))) (+.f64 4 (.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
13.0ms	(/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 1 i) 4)))
6.0ms	(pow.f64 (/.f64 1 i) 4)
4.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.0ms	(/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 1 i) 4)))

series288.0ms (0.2%)

Counts

4 → 18

Calls

4 calls:

174.0ms	(.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 1 i) 4))) (+.f64 4 (.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
54.0ms	(/.f64 1/4 (-.f64 16 (pow.f64 (/.f64 1 i) 4)))
33.0ms	(pow.f64 (/.f64 1 i) 4)
27.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))

Compiler

Compiled 722 to 651 computations (9.8% saved)

simplify107.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4958	3612
1	4958	3612

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))) (/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2)))))
0.0b	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (/.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))) (/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2))))))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 i 2)))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 i 2)))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 i 2)))
0.0b	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (/.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))) (/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2))))))
0.2b	(/.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))) (/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2)))))
0.3b	(/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2))))

rewrite188.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

552×	`times-frac_binary64_1107`
343×	`add-sqr-sqrt_binary64_1123`
287×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
277×	`sqrt-prod_binary64_1117`
137×	`associate-r_binary64_1041`
32×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
28×	`associate-/r*_binary64_1045`
17×	`div-inv_binary64_1098`
15×	`associate-l_binary64_1042`
14×	`unswap-sqr_binary64_1069`
13×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
9×	`associate-/l*_binary64_1046`
7×	`pow1_binary64_1162`
6×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
4×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `frac-times_binary64_1111` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `associate-*l/_binary64_1044` `pow1/2_binary64_1181` `div-sub_binary64_1106`

Counts

4 → 420

Calls

8 calls:

83.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (/.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))) (/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2))))))
13.0ms	(/.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))) (/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2)))))
8.0ms	(/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2))))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 i 2)))
0.0ms	(sqrt.f64 (fabs.f64 (/.f64 i 2)))

series393.0ms (0.3%)

Counts

4 → 33

Calls

4 calls:

186.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (/.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))) (/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2))))))
118.0ms	(/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2))))
66.0ms	(/.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))) (/.f64 (-.f64 (*.f64 i 2) 1) (sqrt.f64 (fabs.f64 (/.f64 i 2)))))
23.0ms	(sqrt.f64 (fabs.f64 (/.f64 i 2)))

Compiler

Compiled 1234 to 1057 computations (14.3% saved)

simplify224.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

453 → 453

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4966	18600
1	4966	18600

prune41.8s (30.2%)

Pruning

644 alts after pruning (635 fresh and 9 done)

	Pruned	Kept	Total
New	645	449	1094
Fresh	28	186	214
Picked	0	0	0
Done	1	9	10
Total	674	644	1318

Error

Counts

1318 → 644

Compiler

Compiled 51553 to 43339 computations (15.9% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (.f64 i 2)))))
0.0b	(/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (*.f64 i 2)))
0.0b	(/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (*.f64 i 2)))
0.0b	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (.f64 i 2)))))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`times-frac_binary64_1107`
37×	`add-exp-log_binary64_1139`
32×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
25×	`add-cbrt-cube_binary64_1137`
18×	`prod-exp_binary64_1150`
15×	`associate-l_binary64_1042`
12×	`distribute-rgt-neg-in_binary64_1059` `distribute-lft-neg-in_binary64_1058`
10×	`cbrt-unprod_binary64_1134` `associate-/l*_binary64_1046` `div-exp_binary64_1152`
7×	`pow1_binary64_1162`
6×	`cbrt-undiv_binary64_1135`
4×	`1-exp_binary64_1145` `neg-mul-1_binary64_1097` `associate-/r/_binary64_1047`
3×	`associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `associate-/r_binary64_1045`
2×	`add-log-exp_binary64_1140` `distribute-frac-neg_binary64_1064` `div-inv_binary64_1098` `distribute-rgt-neg-out_binary64_1061`
1×	`-commutative_binary64_1032` `frac-times_binary64_1111` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `neg-sub0_binary64_1096` `associate-r_binary64_1041` `flip-+_binary64_1075` `associate-l/_binary64_1044` `div-sub_binary64_1106`

Counts

2 → 105

Calls

4 calls:

19.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (.f64 i 2)))))
8.0ms	(/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (*.f64 i 2)))
0.0ms	(/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (*.f64 i 2)))
0.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (.f64 i 2)))))

series281.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

208.0ms	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 1 (/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (.f64 i 2)))))
71.0ms	(/.f64 (neg.f64 (fabs.f64 (/.f64 i 2))) (-.f64 1 (*.f64 i 2)))

Compiler

Compiled 792 to 680 computations (14.1% saved)

simplify106.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4936	3876
1	4936	3876

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 (.f64 i i) 1/4)
0.0b	(.f64 (.f64 i i) 1/4)

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
3×	`add-sqr-sqrt_binary64_1123` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-r_binary64_1041` `pow-prod-down_binary64_1172`
2×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
1×	`-commutative_binary64_1032` `add-log-exp_binary64_1140` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069`

Counts

1 → 19

Calls

2 calls:

7.0ms	(.f64 (.f64 i i) 1/4)
0.0ms	(.f64 (.f64 i i) 1/4)

series25.0ms (0%)

Counts

1 → 3

Calls

1 calls:

25.0ms

(*.f64 (*.f64 i i) 1/4)

Compiler

Compiled 36 to 36 computations (0% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5089	176

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
0.3b	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.3b	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.7b	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))

rewrite14.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
9×	`pow1_binary64_1162`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
4×	`difference-of-squares_binary64_1070` `associate-/r*_binary64_1045`
3×	`associate-/l_binary64_1046` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l*_binary64_1042`
2×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `pow-prod-up_binary64_1171` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `sqr-abs_binary64_1116` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069` `pow2_binary64_1182`

Counts

2 → 59

Calls

4 calls:

5.0ms	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
4.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.0ms	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))

series103.0ms (0.1%)

Counts

2 → 6

Calls

2 calls:

78.0ms	(/.f64 1/4 (-.f64 4 (*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
25.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))

Compiler

Compiled 144 to 144 computations (0% saved)

simplify60.0ms (0%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4954	933
1	4954	933

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

9.4b	(cbrt.f64 (pow.f64 (fabs.f64 (/.f64 1 i)) 12))
0.3b	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
0.2b	(pow.f64 (fabs.f64 (/.f64 1 i)) 12)
0.0b	(/.f64 1/4 (-.f64 16 (cbrt.f64 (pow.f64 (fabs.f64 (/.f64 1 i)) 12))))
0.2b	(pow.f64 (fabs.f64 (/.f64 1 i)) 12)
0.3b	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
9.4b	(cbrt.f64 (pow.f64 (fabs.f64 (/.f64 1 i)) 12))
23.2b	(.f64 (/.f64 1/4 (-.f64 16 (cbrt.f64 (pow.f64 (fabs.f64 (/.f64 1 i)) 12)))) (+.f64 4 (.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64_1123`
33×	`associate-l_binary64_1042`
31×	`*-un-lft-identity_binary64_1101`
25×	`add-cube-cbrt_binary64_1136` `times-frac_binary64_1107`
16×	`cbrt-prod_binary64_1132`
14×	`pow1_binary64_1162`
12×	`difference-of-squares_binary64_1070` `add-exp-log_binary64_1139`
11×	`add-cbrt-cube_binary64_1137`
9×	`unpow-prod-down_binary64_1180`
6×	`associate-r_binary64_1041`
5×	`sqr-pow_binary64_1073`
4×	`add-log-exp_binary64_1140`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out--_binary64_1053` `pow-unpow_binary64_1178` `swap-sqr_binary64_1068` `unswap-sqr_binary64_1069`
2×	`-commutative_binary64_1032` `frac-times_binary64_1111` `flip3-+_binary64_1104` `associate-r/_binary64_1043` `associate-/r/_binary64_1047` `pow-prod-down_binary64_1172` `flip-+_binary64_1075`
1×	`pow-plus_binary64_1164` `pow-exp_binary64_1169` `pow1/3_binary64_1183` `pow-prod-up_binary64_1171` `pow-pow_binary64_1173` `distribute-lft-in_binary64_1050` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `pow-sqr_binary64_1074` `div-exp_binary64_1152` `sqr-abs_binary64_1116` `cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044` `pow2_binary64_1182` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051`

Counts

4 → 113

Calls

8 calls:

21.0ms	(.f64 (/.f64 1/4 (-.f64 16 (cbrt.f64 (pow.f64 (fabs.f64 (/.f64 1 i)) 12)))) (+.f64 4 (.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
4.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))
2.0ms	(pow.f64 (fabs.f64 (/.f64 1 i)) 12)
2.0ms	(cbrt.f64 (pow.f64 (fabs.f64 (/.f64 1 i)) 12))
0.0ms	(/.f64 1/4 (-.f64 16 (cbrt.f64 (pow.f64 (fabs.f64 (/.f64 1 i)) 12))))

series286.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(.f64 (/.f64 1/4 (-.f64 16 (cbrt.f64 (pow.f64 (fabs.f64 (/.f64 1 i)) 12)))) (+.f64 4 (.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))))
79.0ms	(pow.f64 (fabs.f64 (/.f64 1 i)) 12)
36.0ms	(cbrt.f64 (pow.f64 (fabs.f64 (/.f64 1 i)) 12))
27.0ms	(*.f64 (fabs.f64 (/.f64 1 i)) (fabs.f64 (/.f64 1 i)))

Compiler

Compiled 504 to 468 computations (7.1% saved)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5010	2496

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))))
0.0b	(.f64 (/.f64 (fabs.f64 (/.f64 i 2)) (+.f64 (.f64 i 2) 1)) (.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) (-.f64 (.f64 i 2) 1)) (pow.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) 3)))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 i 2)))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 i 2)))
0.1b	(sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))))
0.1b	(/.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) (-.f64 (*.f64 i 2) 1))
0.3b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) (-.f64 (.f64 i 2) 1)) (pow.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) 3))
0.8b	(pow.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) 3)

rewrite86.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

157×	`sqrt-prod_binary64_1117`
147×	`add-sqr-sqrt_binary64_1123`
78×	`times-frac_binary64_1107`
61×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
33×	`associate-l_binary64_1042`
32×	`unswap-sqr_binary64_1069`
30×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180`
24×	`associate-r_binary64_1041`
20×	`add-exp-log_binary64_1139`
12×	`add-cbrt-cube_binary64_1137`
9×	`pow1_binary64_1162` `associate-/l*_binary64_1046`
8×	`sqrt-pow1_binary64_1119`
6×	`prod-exp_binary64_1150` `sqr-pow_binary64_1073`
5×	`pow-pow_binary64_1173`
4×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047` `div-exp_binary64_1152` `pow1/2_binary64_1181`
3×	`pow-exp_binary64_1169` `pow-unpow_binary64_1178` `pow-to-exp_binary64_1170` `associate-/r*_binary64_1045`
2×	`cube-mult_binary64_1131` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `unpow3_binary64_1167` `cbrt-undiv_binary64_1135`
1×	`-commutative_binary64_1032` `rem-cube-cbrt_binary64_1124` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-pow2_binary64_1120` `associate-l/_binary64_1044`

Counts

4 → 218

Calls

8 calls:

35.0ms	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) (-.f64 (.f64 i 2) 1)) (pow.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) 3))
9.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) (-.f64 (*.f64 i 2) 1))
5.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) 3)
2.0ms	(sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))))
0.0ms	(sqrt.f64 (fabs.f64 (/.f64 i 2)))

series406.0ms (0.3%)

Counts

4 → 30

Calls

4 calls:

127.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) (-.f64 (*.f64 i 2) 1))
122.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) 3)
88.0ms	(sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2))))
68.0ms	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) (-.f64 (.f64 i 2) 1)) (pow.f64 (sqrt.f64 (sqrt.f64 (fabs.f64 (/.f64 i 2)))) 3))

Compiler

Compiled 1410 to 1214 computations (13.9% saved)

simplify102.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4997	6687
1	4997	6687

prune37.4s (27.1%)

Pruning

848 alts after pruning (837 fresh and 11 done)

	Pruned	Kept	Total
New	360	229	589
Fresh	22	608	630
Picked	0	0	0
Done	3	11	14
Total	385	848	1233

Error

Counts

1233 → 848

Compiler

Compiled 11803 to 9954 computations (15.7% saved)

simplify958.0ms (0.7%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5874	66293

regimes3.6s (2.6%)

Compiler: Compiled 36110 to 30801 computations (14.7% saved)

bsearch0.0ms (0%)

regimes73.0ms (0.1%)

Compiler: Compiled 568 to 481 computations (15.3% saved)

bsearch0.0ms (0%)

regimes57.0ms (0%)

Compiler: Compiled 377 to 325 computations (13.8% saved)

bsearch0.0ms (0%)

regimes44.0ms (0%)

Compiler: Compiled 247 to 220 computations (10.9% saved)

bsearch0.0ms (0%)

regimes17.0ms (0%)

Compiler: Compiled 60 to 56 computations (6.7% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Compiler: Compiled 51 to 48 computations (5.9% saved)

bsearch19.0ms (0%)

Steps

Iters	Range		Point
8	0.0029702910636194195	109.1603212839411	0.5121179223047105

Compiler

Compiled 1 to 1 computations (0% saved)

regimes263.0ms (0.2%)

Compiler: Compiled 22 to 23 computations (-4.5% saved)

bsearch17.0ms (0%)

Steps

Iters	Range		Point
8	0.0029702910636194195	109.1603212839411	0.5121179223047105

Compiler

Compiled 1 to 1 computations (0% saved)

regimes15.0ms (0%)

Compiler: Compiled 11 to 14 computations (-27.3% saved)

bsearch19.0ms (0%)

Steps

Iters	Range		Point
8	0.0029702910636194195	109.1603212839411	0.5121179223047105

Compiler

Compiled 1 to 1 computations (0% saved)

regimes14.0ms (0%)

Compiler: Compiled 6 to 10 computations (-66.7% saved)

bsearch17.0ms (0%)

Steps

Iters	Range		Point
8	0.0029702910636194195	109.1603212839411	0.5121179223047105

Compiler

Compiled 1 to 1 computations (0% saved)

regimes13.0ms (0%)

Accuracy

Total 0.1b remaining (100%)

Threshold costs 0.1b (100%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch24.0ms (0%)

Steps

Iters	Range		Point
8	0.0029702910636194195	109.1603212839411	0.5121179223047105

Compiler

Compiled 115 to 101 computations (12.2% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	163
1	84	163

end0.0ms (0%)

sample38.5s (27.9%)

Algorithm

1×

intervals

Results

449.0ms	8000×	body	128	valid
110.0ms	8000×	pre	128	true

Compiler

Compiled 36365 to 31020 computations (14.7% saved)

Pareto

0.5177650150892609