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)

sample24.0ms (0.8%)

Algorithm

1×

intervals

Results

6.0ms	44×	body	1024	valid
5.0ms	145×	body	128	valid
5.0ms	43×	body	512	valid
2.0ms	24×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify179.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune2.0ms (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: 8.9b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize9.0ms (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))
3.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite97.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64_1088`
58×	`add-sqr-sqrt_binary64_1109`
56×	`times-frac_binary64_1094`
25×	`add-cube-cbrt_binary64_1120`
18×	`distribute-lft-out--_binary64_1042`
17×	`distribute-lft-out_binary64_1041`
14×	`difference-of-squares_binary64_1057`
12×	`add-exp-log_binary64_1123`
11×	`associate-/r*_binary64_1034` `add-log-exp_binary64_1124`
8×	`add-cbrt-cube_binary64_1121` `div-inv_binary64_1085`
6×	`pow1_binary64_1146` `associate-/l*_binary64_1035`
4×	`difference-of-sqr-1_binary64_1058` `associate-/r/_binary64_1036` `div-exp_binary64_1136`
3×	`frac-add_binary64_1096` `flip3--_binary64_1092` `flip--_binary64_1063`
2×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `inv-pow_binary64_1170` `sub-neg_binary64_1081` `rec-exp_binary64_1135` `frac-sub_binary64_1097` `sum-log_binary64_1176` `1-exp_binary64_1129` `diff-log_binary64_1177` `flip-+_binary64_1062` `cbrt-undiv_binary64_1119` `pow-flip_binary64_1159` `flip3-+_binary64_1091`
1×	`associate-+l-_binary64_1025` `associate-+l+_binary64_1023` `+-commutative_binary64_1020`

Counts

4 → 135

Calls

4 calls:

48.0ms	(+.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))
7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series173.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
29.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
18.0ms	(/.f64 1 (-.f64 x 1))
18.0ms	(/.f64 1 (+.f64 x 1))

simplify80.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5051	2576

prune198.0ms (6.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	3	148

Merged error: 0.1b

Counts

148 → 3

Compiler

Compiled 3233 to 2596 computations (19.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 x 1))
0.3b	(cbrt.f64 (-.f64 x 1))
0.3b	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
16.8b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (cbrt.f64 (-.f64 x 1)))))

rewrite68.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`cbrt-prod_binary64_1116`
50×	`add-sqr-sqrt_binary64_1109`
40×	`*-un-lft-identity_binary64_1088`
16×	`cbrt-div_binary64_1117`
14×	`swap-sqr_binary64_1055` `add-cube-cbrt_binary64_1120` `difference-of-squares_binary64_1057`
12×	`frac-add_binary64_1096` `flip3--_binary64_1092` `flip--_binary64_1063`
11×	`pow1_binary64_1146`
10×	`associate-r_binary64_1030` `associate-l_binary64_1031`
9×	`add-log-exp_binary64_1124`
8×	`difference-of-sqr-1_binary64_1058` `pow1/3_binary64_1167` `distribute-lft-out--_binary64_1042`
7×	`frac-times_binary64_1098`
6×	`add-exp-log_binary64_1123`
5×	`associate-l/_binary64_1033` `associate-r/_binary64_1032`
4×	`add-cbrt-cube_binary64_1121` `unswap-sqr_binary64_1056` `frac-sub_binary64_1097`
3×	`un-div-inv_binary64_1086`
2×	`sum-log_binary64_1176` `pow-prod-down_binary64_1156` `pow-sqr_binary64_1061` `pow-prod-up_binary64_1155`
1×	`associate-+l-_binary64_1025` `*-commutative_binary64_1021` `pow-plus_binary64_1148` `cbrt-unprod_binary64_1118` `pow2_binary64_1166` `sub-neg_binary64_1081` `associate-+l+_binary64_1023` `+-commutative_binary64_1020` `diff-log_binary64_1177` `flip-+_binary64_1062` `prod-exp_binary64_1134` `flip3-+_binary64_1091`

Counts

4 → 124

Calls

4 calls:

28.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (cbrt.f64 (-.f64 x 1)))))
15.0ms	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
4.0ms	(cbrt.f64 (-.f64 x 1))
4.0ms	(cbrt.f64 (-.f64 x 1))

series285.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (cbrt.f64 (-.f64 x 1)))))
65.0ms	(*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))
55.0ms	(cbrt.f64 (-.f64 x 1))
52.0ms	(cbrt.f64 (-.f64 x 1))

simplify57.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5103	3245

prune287.0ms (9.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	136	3	139

Merged error: 0.1b

Counts

139 → 3

Compiler

Compiled 4807 to 3908 computations (18.7% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

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) x))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
18.0b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite76.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64_1109`
42×	`associate-*r/_binary64_1032`
35×	`*-un-lft-identity_binary64_1088`
32×	`frac-add_binary64_1096` `flip3--_binary64_1092` `flip--_binary64_1063`
27×	`times-frac_binary64_1094`
20×	`frac-times_binary64_1098` `add-cube-cbrt_binary64_1120`
18×	`associate-/l/_binary64_1037` `flip-+_binary64_1062` `flip3-+_binary64_1091` `difference-of-squares_binary64_1057`
10×	`associate-*l/_binary64_1033`
9×	`associate-/r*_binary64_1034`
8×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `add-log-exp_binary64_1124`
7×	`associate-l_binary64_1031`
6×	`pow1_binary64_1146`
5×	`sub-neg_binary64_1081` `distribute-lft-out--_binary64_1042`
4×	`unpow3_binary64_1151` `cube-prod_binary64_1113` `unpow-prod-down_binary64_1164` `sqr-pow_binary64_1060` `distribute-rgt-out--_binary64_1044`
3×	`associate-r_binary64_1030` `distribute-rgt-in_binary64_1040` `associate-/l*_binary64_1035` `distribute-lft-in_binary64_1039`
2×	`associate-+r+_binary64_1022` `associate-+l+_binary64_1023` `associate-/r/_binary64_1036`
1×	`*-commutative_binary64_1021` `clear-num_binary64_1087` `frac-2neg_binary64_1099` `unswap-sqr_binary64_1056` `cbrt-unprod_binary64_1118` `difference-of-sqr-1_binary64_1058` `sum-log_binary64_1176` `div-exp_binary64_1136` `+-commutative_binary64_1020` `diff-log_binary64_1177` `cbrt-undiv_binary64_1119` `pow-prod-down_binary64_1156` `prod-exp_binary64_1134` `div-inv_binary64_1085`

Counts

4 → 145

Calls

4 calls:

25.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
12.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
10.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series116.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
26.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
22.0ms	(.f64 (-.f64 x 1) (-.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)))

simplify108.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5298	6591

prune378.0ms (12.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	159	1	160

Merged error: 0.1b

Counts

160 → 1

Compiler

Compiled 6759 to 4733 computations (30% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1109`
27×	`times-frac_binary64_1094` `*-un-lft-identity_binary64_1088`
16×	`difference-of-squares_binary64_1057`
15×	`add-cube-cbrt_binary64_1120`
9×	`associate-/r*_binary64_1034`
4×	`unpow3_binary64_1151` `cube-prod_binary64_1113` `unpow-prod-down_binary64_1164` `sqr-pow_binary64_1060` `distribute-rgt-out--_binary64_1044` `distribute-lft-out--_binary64_1042`
3×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `associate-/l*_binary64_1035`
2×	`associate-/r/_binary64_1036`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `flip3--_binary64_1092` `flip--_binary64_1063` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119` `add-log-exp_binary64_1124` `pow1_binary64_1146` `div-inv_binary64_1085`

Counts

1 → 53

Calls

1 calls:

10.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

series51.0ms (1.6%)

Counts

1 → 3

Calls

1 calls:

50.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify46.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4948	1071
1	4948	1071

prune56.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Merged error: 0.0b

Counts

57 → 4

Compiler

Compiled 863 to 636 computations (26.3% saved)

regimes10.0ms (0.3%)

Compiler: Compiled 46 to 39 computations (15.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	13
1	18	13

end0.0ms (0%)

sample776.0ms (24.8%)

Algorithm

1×

intervals

Results

183.0ms	1303×	body	1024	valid
169.0ms	4532×	body	128	valid
154.0ms	1434×	body	512	valid
54.0ms	731×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 78 to 66 computations (15.4% saved)

Details

analyze6.0ms (0.2%)

sample24.0ms (0.8%)

simplify179.0ms (5.7%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite97.0ms (3.1%)

series173.0ms (5.5%)

simplify80.0ms (2.6%)

prune198.0ms (6.3%)

localize14.0ms (0.4%)

rewrite68.0ms (2.2%)

series285.0ms (9.1%)

simplify57.0ms (1.8%)

prune287.0ms (9.2%)

localize12.0ms (0.4%)

rewrite76.0ms (2.4%)

series116.0ms (3.7%)

simplify108.0ms (3.4%)

prune378.0ms (12.1%)

localize5.0ms (0.1%)

rewrite17.0ms (0.6%)

series51.0ms (1.6%)

simplify46.0ms (1.5%)

prune56.0ms (1.8%)

regimes10.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample776.0ms (24.8%)

Profiling