Details

analyze100.0ms (1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	12
1	72	12
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample223.0ms (2.2%)

Algorithm

1×

intervals

Results

180.0ms	134×	body	2048	valid
18.0ms	60×	body	1024	valid
8.0ms	32×	body	512	valid
5.0ms	256×	pre	128	true
3.0ms	6×	body	4096	valid
2.0ms	19×	body	256	valid
0.0ms	5×	body	128	valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	12
1	72	12

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: 60.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
2.3b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1123`
36×	`times-frac_binary64_1107`
35×	`*-un-lft-identity_binary64_1101`
19×	`add-cube-cbrt_binary64_1136`
14×	`cancel-sign-sub-inv_binary64_1067`
9×	`difference-of-squares_binary64_1070`
7×	`distribute-lft-out--_binary64_1053`
6×	`add-exp-log_binary64_1139` `div-inv_binary64_1098`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`pow1_binary64_1162` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`associate-/r/_binary64_1047` `div-exp_binary64_1152` `tan-quot_binary64_1260`
1×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `1-exp_binary64_1145` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `rec-exp_binary64_1151` `frac-sub_binary64_1110` `cbrt-undiv_binary64_1135` `pow-flip_binary64_1175`

Counts

2 → 74

Calls

2 calls:

17.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms	(/.f64 1 (tan.f64 x))

series122.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

75.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
46.0ms	(/.f64 1 (tan.f64 x))

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5505	1072

prune67.0ms (0.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	1	81

Merged error: 0.3b

Counts

81 → 1

Compiler

Compiled 1030 to 641 computations (37.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5)))
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(*.f64 x 1/3)

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_1123`
22×	`associate-r_binary64_1041`
16×	`add-exp-log_binary64_1139`
13×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
10×	`add-cbrt-cube_binary64_1137`
9×	`associate-l_binary64_1042`
8×	`unpow-prod-down_binary64_1180` `unswap-sqr_binary64_1069`
7×	`prod-exp_binary64_1150`
6×	`add-log-exp_binary64_1140` `pow1_binary64_1162`
4×	`cube-prod_binary64_1129` `sqr-pow_binary64_1073`
3×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134`
2×	`pow-exp_binary64_1169` `pow-to-exp_binary64_1170`
1×	`cube-mult_binary64_1131` `sum-log_binary64_1192` `flip3-+_binary64_1104` `unpow3_binary64_1167` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `flip-+_binary64_1075`

Counts

4 → 85

Calls

4 calls:

7.0ms	(*.f64 2/945 (pow.f64 x 5))
7.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5)))
4.0ms	(*.f64 x 1/3)

series144.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5)))
30.0ms	(*.f64 2/945 (pow.f64 x 5))
22.0ms	(*.f64 1/45 (pow.f64 x 3))
11.0ms	(*.f64 x 1/3)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5017	1016

prune122.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	6	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	7	98

Merged error: 0.2b

Counts

98 → 7

Compiler

Compiled 2001 to 1597 computations (20.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1132`
23×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
11×	`pow1_binary64_1162`
9×	`pow1/3_binary64_1183`
6×	`add-exp-log_binary64_1139` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137` `unswap-sqr_binary64_1069`
2×	`pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow2_binary64_1182`

Counts

4 → 73

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series331.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
85.0ms	(cbrt.f64 x)
75.0ms	(cbrt.f64 x)
75.0ms	(cbrt.f64 x)

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4892	563
1	4892	563

prune118.0ms (1.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	80	12	92

Merged error: 0.2b

Counts

92 → 12

Compiler

Compiled 2332 to 1522 computations (34.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
0.7b	(cbrt.f64 (*.f64 x 1/3))
0.7b	(cbrt.f64 (*.f64 x 1/3))
0.7b	(cbrt.f64 (*.f64 x 1/3))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_1162`
10×	`add-sqr-sqrt_binary64_1123`
9×	`pow1/3_binary64_1183`
8×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
7×	`cbrt-prod_binary64_1132`
6×	`add-exp-log_binary64_1139`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l_binary64_1042`
2×	`pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `unswap-sqr_binary64_1069` `pow2_binary64_1182`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
2.0ms	(cbrt.f64 (*.f64 x 1/3))
2.0ms	(cbrt.f64 (*.f64 x 1/3))
2.0ms	(cbrt.f64 (*.f64 x 1/3))

series412.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
100.0ms	(cbrt.f64 (*.f64 x 1/3))
96.0ms	(cbrt.f64 (*.f64 x 1/3))
96.0ms	(cbrt.f64 (*.f64 x 1/3))

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5115	556

prune107.0ms (1.1%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	3	6	9
Picked	0	1	1
Done	0	2	2
Total	67	15	82

Merged error: 0.1b

Counts

82 → 15

Compiler

Compiled 1917 to 1556 computations (18.8% saved)

regimes145.0ms (1.5%)

Compiler: Compiled 1646 to 1313 computations (20.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	22
1	19	22

end0.0ms (0%)

sample7.6s (76.6%)

Algorithm

1×

intervals

Results

5.4s	3965×	body	2048	valid
692.0ms	2005×	body	1024	valid
151.0ms	8000×	pre	128	true
138.0ms	1027×	body	512	valid
120.0ms	227×	body	4096	valid
48.0ms	541×	body	256	valid
11.0ms	235×	body	128	valid

Compiler

Compiled 846 to 674 computations (20.3% saved)

Details

analyze100.0ms (1%)

sample223.0ms (2.2%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite27.0ms (0.3%)

series122.0ms (1.2%)

simplify99.0ms (1%)

prune67.0ms (0.7%)

localize10.0ms (0.1%)

rewrite29.0ms (0.3%)

series144.0ms (1.4%)

simplify67.0ms (0.7%)

prune122.0ms (1.2%)

localize14.0ms (0.1%)

rewrite16.0ms (0.2%)

series331.0ms (3.3%)

simplify63.0ms (0.6%)

prune118.0ms (1.2%)

localize14.0ms (0.1%)

rewrite18.0ms (0.2%)

series412.0ms (4.1%)

simplify65.0ms (0.7%)

prune107.0ms (1.1%)

regimes145.0ms (1.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.6s (76.6%)

Profiling