Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify171.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

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: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_1088`
23×	`add-sqr-sqrt_binary64_1109`
18×	`times-frac_binary64_1094`
17×	`distribute-lft-out_binary64_1041`
14×	`add-cube-cbrt_binary64_1120`
12×	`sqrt-prod_binary64_1103`
6×	`associate-/r*_binary64_1034`
4×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
3×	`pow1_binary64_1146` `associate-/l*_binary64_1035`
2×	`associate-/r/_binary64_1036` `sqrt-div_binary64_1104` `flip-+_binary64_1062` `add-log-exp_binary64_1124` `flip3-+_binary64_1091`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `rem-sqrt-square_binary64_1101` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119` `sqrt-pow1_binary64_1105` `div-inv_binary64_1085` `pow1/2_binary64_1165`

Counts

2 → 57

Calls

2 calls:

9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms	(sqrt.f64 (+.f64 x 1))

series158.0ms (6.1%)

Counts

2 → 6

Calls

2 calls:

131.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify65.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4997	1265
1	4997	1265

prune71.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	3	64

Merged error: 0b

Counts

64 → 3

Compiler

Compiled 1092 to 813 computations (25.5% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))
0.2b	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
2.6b	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0b	(/.f64 x (+.f64 1 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))

rewrite75.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`sqrt-div_binary64_1104`
52×	`*-un-lft-identity_binary64_1088`
38×	`add-sqr-sqrt_binary64_1109`
34×	`sqrt-prod_binary64_1103`
32×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
28×	`associate-*r/_binary64_1032`
26×	`add-cube-cbrt_binary64_1120`
21×	`pow1_binary64_1146`
16×	`frac-sub_binary64_1097`
12×	`frac-times_binary64_1098` `times-frac_binary64_1094` `distribute-lft-out_binary64_1041`
11×	`swap-sqr_binary64_1055`
9×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`
8×	`associate-*l/_binary64_1033`
7×	`cube-prod_binary64_1113` `unpow-prod-down_binary64_1164` `associate-r_binary64_1030` `associate-l_binary64_1031`
6×	`add-log-exp_binary64_1124`
5×	`pow-prod-up_binary64_1155`
4×	`sub-div_binary64_1095` `unswap-sqr_binary64_1056` `associate-/r*_binary64_1034`
3×	`pow-pow_binary64_1157` `pow-prod-down_binary64_1156` `pow-sqr_binary64_1061` `pow-unpow_binary64_1162` `associate-/l*_binary64_1035`
2×	`cube-div_binary64_1114` `associate-/r/_binary64_1036`
1×	`*-commutative_binary64_1021` `clear-num_binary64_1087` `frac-2neg_binary64_1099` `unpow3_binary64_1151` `pow-plus_binary64_1148` `rem-cube-cbrt_binary64_1110` `sqr-pow_binary64_1060` `cbrt-unprod_binary64_1118` `cube-mult_binary64_1115` `distribute-rgt-out--_binary64_1044` `pow2_binary64_1166` `flip3--_binary64_1092` `sub-neg_binary64_1081` `flip--_binary64_1063` `div-exp_binary64_1136` `pow-exp_binary64_1153` `diff-log_binary64_1177` `cbrt-undiv_binary64_1119` `rem-square-sqrt_binary64_1100` `sqrt-unprod_binary64_1107` `pow-to-exp_binary64_1154` `prod-exp_binary64_1134` `div-inv_binary64_1085` `sqrt-pow2_binary64_1106`

Counts

4 → 163

Calls

4 calls:

14.0ms	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
12.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))
12.0ms	(/.f64 x (+.f64 1 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
6.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)

series199.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(/.f64 x (+.f64 1 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
49.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
32.0ms	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
24.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))

simplify92.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4939	3308
1	4939	3308

prune414.0ms (16%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	175	3	178

Merged error: 0b

Counts

178 → 3

Compiler

Compiled 6424 to 5210 computations (18.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite56.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`*-un-lft-identity_binary64_1088`
89×	`add-sqr-sqrt_binary64_1109`
77×	`sqrt-prod_binary64_1103`
76×	`times-frac_binary64_1094`
53×	`distribute-lft-out_binary64_1041`
46×	`add-cube-cbrt_binary64_1120`
42×	`associate-r_binary64_1030`
10×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
6×	`unswap-sqr_binary64_1056` `associate-/r_binary64_1034` `associate-l_binary64_1031` `pow1_binary64_1146` `associate-/l_binary64_1035`
4×	`associate-/r/_binary64_1036`
3×	`flip-+_binary64_1062` `add-log-exp_binary64_1124` `flip3-+_binary64_1091`
2×	`cbrt-unprod_binary64_1118` `div-exp_binary64_1136` `sqrt-div_binary64_1104` `cbrt-undiv_binary64_1119` `prod-exp_binary64_1134` `div-inv_binary64_1085`
1×	`-commutative_binary64_1021` `clear-num_binary64_1087` `frac-2neg_binary64_1099` `rem-sqrt-square_binary64_1101` `pow-prod-down_binary64_1156` `sqrt-pow1_binary64_1105` `associate-r/_binary64_1032` `pow1/2_binary64_1165`

Counts

3 → 146

Calls

3 calls:

26.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
10.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
3.0ms	(sqrt.f64 (+.f64 x 1))

series332.0ms (12.9%)

Counts

3 → 9

Calls

3 calls:

190.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
114.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
28.0ms	(sqrt.f64 (+.f64 x 1))

simplify91.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4950	3539
1	4950	3539

prune163.0ms (6.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	155	3	158

Merged error: 0b

Counts

158 → 3

Compiler

Compiled 3324 to 2104 computations (36.7% saved)

regimes25.0ms (0.9%)

Compiler: Compiled 120 to 102 computations (15% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample609.0ms (23.6%)

Algorithm

1×

intervals

Results

231.0ms	7997×	body	128	valid
0.0ms	3×	body	2048	valid

Compiler

Compiled 68 to 59 computations (13.2% saved)

Details

analyze3.0ms (0.1%)

sample12.0ms (0.5%)

simplify171.0ms (6.6%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite17.0ms (0.7%)

series158.0ms (6.1%)

simplify65.0ms (2.5%)

prune71.0ms (2.7%)

localize14.0ms (0.5%)

rewrite75.0ms (2.9%)

series199.0ms (7.7%)

simplify92.0ms (3.5%)

prune414.0ms (16%)

localize7.0ms (0.3%)

rewrite56.0ms (2.2%)

series332.0ms (12.9%)

simplify91.0ms (3.5%)

prune163.0ms (6.3%)

regimes25.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample609.0ms (23.6%)

Profiling