Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample23.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms	55×	body	512	valid
6.0ms	145×	body	128	valid
4.0ms	29×	body	1024	valid
2.0ms	27×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify182.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune3.0ms (0.1%)

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: 11.7b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite96.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_1111`
74×	`times-frac_binary64_1117`
72×	`add-sqr-sqrt_binary64_1133`
39×	`add-cube-cbrt_binary64_1146`
26×	`cancel-sign-sub-inv_binary64_1077`
18×	`distribute-lft-out--_binary64_1063`
17×	`distribute-lft-out_binary64_1062`
14×	`associate-+l+_binary64_1044` `difference-of-squares_binary64_1080`
12×	`add-exp-log_binary64_1149`
11×	`associate-/r*_binary64_1055` `add-log-exp_binary64_1150`
10×	`div-inv_binary64_1108`
8×	`add-cbrt-cube_binary64_1147`
6×	`associate-/l*_binary64_1056` `pow1_binary64_1172`
4×	`div-exp_binary64_1162` `difference-of-sqr-1_binary64_1081` `associate-/r/_binary64_1057`
3×	`flip3--_binary64_1115` `frac-add_binary64_1119` `flip--_binary64_1086`
2×	`frac-sub_binary64_1120` `flip-+_binary64_1085` `pow-flip_binary64_1185` `frac-2neg_binary64_1122` `diff-log_binary64_1203` `flip3-+_binary64_1114` `1-exp_binary64_1155` `rec-exp_binary64_1161` `cbrt-undiv_binary64_1145` `sum-log_binary64_1202` `sub-neg_binary64_1104` `clear-num_binary64_1110` `inv-pow_binary64_1196`
1×	`associate-+l-_binary64_1046` `+-commutative_binary64_1041`

Counts

4 → 161

Calls

4 calls:

47.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
21.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series178.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
26.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
19.0ms	(/.f64 1 (+.f64 x 1))
19.0ms	(/.f64 1 (-.f64 x 1))

simplify74.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4911	2799
1	4911	2799

prune504.0ms (15.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	170	4	174

Merged error: 0.3b

Counts

174 → 4

Compiler

Compiled 9383 to 7633 computations (18.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(*.f64 x (+.f64 1 x))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
16.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite72.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`associate-*r/_binary64_1053`
40×	`*-un-lft-identity_binary64_1111`
32×	`frac-add_binary64_1119`
25×	`flip3--_binary64_1115` `flip--_binary64_1086`
21×	`times-frac_binary64_1117`
20×	`add-sqr-sqrt_binary64_1133` `flip-+_binary64_1085` `flip3-+_binary64_1114`
18×	`associate-/l/_binary64_1058` `add-cube-cbrt_binary64_1146`
16×	`frac-times_binary64_1121`
9×	`distribute-lft-out_binary64_1062`
8×	`distribute-rgt-out_binary64_1064` `add-cbrt-cube_binary64_1147` `associate-*l/_binary64_1054` `add-log-exp_binary64_1150` `unpow3_binary64_1177` `add-exp-log_binary64_1149`
7×	`associate-/r*_binary64_1055`
6×	`pow1_binary64_1172`
4×	`distribute-lft-in_binary64_1060` `associate-r_binary64_1051` `associate-+l+_binary64_1044` `neg-mul-1_binary64_1107` `distribute-rgt-in_binary64_1061` `distribute-lft-neg-in_binary64_1068` `distribute-rgt-neg-in_binary64_1069`
3×	`cancel-sign-sub-inv_binary64_1077` `associate-/l_binary64_1056` `associate-l*_binary64_1052` `sub-neg_binary64_1104`
2×	`associate-+r+_binary64_1043` `associate-/r/_binary64_1057`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `frac-2neg_binary64_1122` `diff-log_binary64_1203` `+-commutative_binary64_1041` `div-exp_binary64_1162` `pow-prod-down_binary64_1182` `cbrt-undiv_binary64_1145` `unswap-sqr_binary64_1079` `sum-log_binary64_1202` `clear-num_binary64_1110`

Counts

4 → 131

Calls

4 calls:

24.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
15.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
7.0ms	(*.f64 x (+.f64 1 x))
4.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series159.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(*.f64 x (+.f64 1 x))
61.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
26.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
8.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify96.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4949	5492
1	4949	5492

prune304.0ms (9.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	145	2	147

Merged error: 0.3b

Counts

147 → 2

Compiler

Compiled 6361 to 4423 computations (30.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (pow.f64 x 3) (neg.f64 x))
0.3b	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_1111`
21×	`times-frac_binary64_1117`
14×	`add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
10×	`distribute-rgt-out_binary64_1064` `unpow3_binary64_1177` `distribute-lft-out_binary64_1062`
7×	`associate-/r*_binary64_1055`
6×	`add-log-exp_binary64_1150`
5×	`neg-mul-1_binary64_1107` `distribute-lft-neg-in_binary64_1068` `distribute-rgt-neg-in_binary64_1069`
4×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
3×	`associate-/l*_binary64_1056`
2×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `pow1_binary64_1172` `sum-log_binary64_1202` `associate-/r/_binary64_1057`
1×	`div-inv_binary64_1108` `frac-2neg_binary64_1122` `neg-log_binary64_1204` `+-commutative_binary64_1041` `div-exp_binary64_1162` `neg-sub0_binary64_1106` `cbrt-undiv_binary64_1145` `unsub-neg_binary64_1105` `associate-+r-_binary64_1045` `clear-num_binary64_1110`

Counts

2 → 63

Calls

2 calls:

16.0ms	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))
11.0ms	(+.f64 (pow.f64 x 3) (neg.f64 x))

series129.0ms (3.9%)

Counts

2 → 6

Calls

2 calls:

79.0ms	(+.f64 (pow.f64 x 3) (neg.f64 x))
49.0ms	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

simplify63.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4894	964
1	4894	964

prune156.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Merged error: 0.0b

Counts

71 → 5

Compiler

Compiled 2306 to 1839 computations (20.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.1b	(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary64_1117`
50×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
14×	`difference-of-sqr--1_binary64_1082`
13×	`associate-/l*_binary64_1056`
6×	`add-cbrt-cube_binary64_1147` `div-inv_binary64_1108` `add-exp-log_binary64_1149`
4×	`associate-/r*_binary64_1055`
3×	`div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
2×	`associate-/r/_binary64_1057`
1×	`flip-+_binary64_1085` `frac-2neg_binary64_1122` `associate-/l/_binary64_1058` `flip3-+_binary64_1114` `add-log-exp_binary64_1150` `pow1_binary64_1172` `clear-num_binary64_1110`

Counts

1 → 86

Calls

1 calls:

12.0ms

(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))

series53.0ms (1.6%)

Counts

1 → 3

Calls

1 calls:

53.0ms

(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5378	2264

prune106.0ms (3.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	88	6	94

Merged error: 0b

Counts

94 → 6

Compiler

Compiled 1946 to 1295 computations (33.5% saved)

regimes13.0ms (0.4%)

Compiler: Compiled 72 to 60 computations (16.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	13
1	9	13

end0.0ms (0%)

sample944.0ms (28.5%)

Algorithm

1×

intervals

Results

293.0ms	1480×	body	512	valid
176.0ms	1282×	body	1024	valid
173.0ms	4437×	body	128	valid
58.0ms	801×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 104 to 87 computations (16.3% saved)

Details

analyze6.0ms (0.2%)

sample23.0ms (0.7%)

simplify182.0ms (5.5%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

rewrite96.0ms (2.9%)

series178.0ms (5.4%)

simplify74.0ms (2.2%)

prune504.0ms (15.2%)

localize13.0ms (0.4%)

rewrite72.0ms (2.2%)

series159.0ms (4.8%)

simplify96.0ms (2.9%)

prune304.0ms (9.2%)

localize6.0ms (0.2%)

rewrite32.0ms (1%)

series129.0ms (3.9%)

simplify63.0ms (1.9%)

prune156.0ms (4.7%)

localize5.0ms (0.2%)

rewrite21.0ms (0.6%)

series53.0ms (1.6%)

simplify67.0ms (2%)

prune106.0ms (3.2%)

regimes13.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample944.0ms (28.5%)

Profiling