Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 13 computations (0% saved)

sample36.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms	66×	body	2048	valid
6.0ms	133×	body	128	valid
5.0ms	27×	body	1024	valid
3.0ms	21×	body	512	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify353.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.4b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 1 x)
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1109` `*-un-lft-identity_binary64_1088`
13×	`add-cube-cbrt_binary64_1120`
9×	`times-frac_binary64_1094`
8×	`sqrt-prod_binary64_1103`
6×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `add-log-exp_binary64_1124`
5×	`pow1_binary64_1146`
4×	`difference-of-squares_binary64_1057`
3×	`associate-/r_binary64_1034` `distribute-lft-out--_binary64_1042` `associate-/l_binary64_1035`
2×	`sqrt-div_binary64_1104` `distribute-lft-out_binary64_1041`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `rem-sqrt-square_binary64_1101` `flip3--_binary64_1092` `sub-neg_binary64_1081` `flip--_binary64_1063` `div-exp_binary64_1136` `diff-log_binary64_1177` `flip-+_binary64_1062` `cbrt-undiv_binary64_1119` `flip3-+_binary64_1091` `sqrt-pow1_binary64_1105` `div-inv_binary64_1085` `pow1/2_binary64_1165`

Counts

4 → 68

Calls

4 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
4.0ms	(/.f64 1/2 (hypot.f64 1 x))
1.0ms	(hypot.f64 1 x)

series258.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
96.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
39.0ms	(/.f64 1/2 (hypot.f64 1 x))
4.0ms	(hypot.f64 1 x)

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4839	1209
1	4839	1209

prune93.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	5	81

Merged error: 14.9b

Counts

81 → 5

Compiler

Compiled 1340 to 1219 computations (9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite54.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1088`
76×	`add-sqr-sqrt_binary64_1109`
44×	`times-frac_binary64_1094`
33×	`distribute-lft-out_binary64_1041`
20×	`sqrt-prod_binary64_1103`
19×	`add-cube-cbrt_binary64_1120`
16×	`difference-of-squares_binary64_1057`
8×	`add-log-exp_binary64_1124` `distribute-lft-out--_binary64_1042`
6×	`add-cbrt-cube_binary64_1121` `associate-/r_binary64_1034` `add-exp-log_binary64_1123` `associate-/l_binary64_1035`
5×	`pow1_binary64_1146`
3×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
2×	`flip3--_binary64_1092` `associate-/l/_binary64_1037` `flip--_binary64_1063` `associate-/r/_binary64_1036` `sqrt-div_binary64_1104`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `rem-sqrt-square_binary64_1101` `sub-neg_binary64_1081` `sum-log_binary64_1176` `div-exp_binary64_1136` `div-sub_binary64_1093` `+-commutative_binary64_1020` `diff-log_binary64_1177` `cbrt-undiv_binary64_1119` `sqrt-pow1_binary64_1105` `div-inv_binary64_1085` `pow1/2_binary64_1165`

Counts

4 → 109

Calls

4 calls:

19.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
7.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series589.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

326.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
103.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
97.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
64.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4974	3605
1	4974	3605

prune235.0ms (3.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Merged error: 14.9b

Counts

126 → 5

Compiler

Compiled 3462 to 3116 computations (10% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 (exp.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.1b	(exp.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite67.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`*-un-lft-identity_binary64_1088`
97×	`add-sqr-sqrt_binary64_1109`
63×	`times-frac_binary64_1094`
48×	`exp-sum_binary64_1131` `log-prod_binary64_1171`
44×	`distribute-lft-out_binary64_1041`
30×	`add-cube-cbrt_binary64_1120`
22×	`sqrt-prod_binary64_1103`
18×	`difference-of-squares_binary64_1057`
9×	`distribute-lft-out--_binary64_1042` `associate-/l*_binary64_1035`
8×	`add-log-exp_binary64_1124`
6×	`add-cbrt-cube_binary64_1121` `associate-/r*_binary64_1034`
5×	`add-exp-log_binary64_1123` `pow1_binary64_1146`
4×	`exp-prod_binary64_1137` `log-div_binary64_1172` `exp-diff_binary64_1133`
3×	`flip3--_binary64_1092` `flip--_binary64_1063`
2×	`associate-/l/_binary64_1037` `associate-/r/_binary64_1036` `flip-+_binary64_1062` `flip3-+_binary64_1091`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `log-pow_binary64_1174` `sub-neg_binary64_1081` `rem-exp-log_binary64_1125` `sum-log_binary64_1176` `div-exp_binary64_1136` `+-commutative_binary64_1020` `diff-log_binary64_1177` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`

Counts

4 → 133

Calls

4 calls:

22.0ms	(/.f64 (exp.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
8.0ms	(exp.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series979.0ms (15.9%)

Counts

4 → 12

Calls

4 calls:

523.0ms	(/.f64 (exp.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
272.0ms	(exp.f64 (log.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
118.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
65.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify104.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4849	4493
1	4849	4493

prune272.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	144	6	150

Merged error: 14.9b

Counts

150 → 6

Compiler

Compiled 4283 to 3868 computations (9.7% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.1b	(exp.f64 (log.f64 (-.f64 (.f64 1/2 1/2) (.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x))))))
0.1b	(*.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x)))
1.2b	(-.f64 (.f64 1/2 1/2) (.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x))))

rewrite61.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64_1109`
43×	`*-un-lft-identity_binary64_1088`
40×	`times-frac_binary64_1094`
36×	`add-cube-cbrt_binary64_1120`
19×	`associate-r_binary64_1030`
18×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123`
17×	`associate-l_binary64_1031`
14×	`pow1_binary64_1146`
13×	`swap-sqr_binary64_1055`
6×	`flip-+_binary64_1062` `add-log-exp_binary64_1124` `flip3-+_binary64_1091`
5×	`unswap-sqr_binary64_1056` `cbrt-unprod_binary64_1118` `frac-times_binary64_1098` `prod-exp_binary64_1134` `distribute-lft-out_binary64_1041`
4×	`exp-sum_binary64_1131` `log-prod_binary64_1171` `exp-prod_binary64_1137` `div-exp_binary64_1136` `cbrt-undiv_binary64_1119` `div-inv_binary64_1085`
3×	`associate-l/_binary64_1033` `associate-r/_binary64_1032`
2×	`*-commutative_binary64_1021` `flip3--_binary64_1092` `sqrt-prod_binary64_1103` `flip--_binary64_1063` `log-div_binary64_1172` `pow-prod-down_binary64_1156` `exp-diff_binary64_1133` `difference-of-squares_binary64_1057`
1×	`pow-plus_binary64_1148` `log-pow_binary64_1174` `distribute-rgt-in_binary64_1040` `pow2_binary64_1166` `sub-neg_binary64_1081` `rem-exp-log_binary64_1125` `diff-log_binary64_1177` `pow-sqr_binary64_1061` `pow-prod-up_binary64_1155` `distribute-lft-in_binary64_1039`

Counts

4 → 129

Calls

4 calls:

20.0ms	(*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
12.0ms	(*.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x)))
6.0ms	(exp.f64 (log.f64 (-.f64 (.f64 1/2 1/2) (.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x))))))
5.0ms	(-.f64 (.f64 1/2 1/2) (.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x))))

series860.0ms (14%)

Counts

4 → 12

Calls

4 calls:

411.0ms	(exp.f64 (log.f64 (-.f64 (.f64 1/2 1/2) (.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x))))))
224.0ms	(*.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
134.0ms	(-.f64 (.f64 1/2 1/2) (.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x))))
91.0ms	(*.f64 (/.f64 1/2 (hypot.f64 1 x)) (/.f64 1/2 (hypot.f64 1 x)))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4949	2871
1	4949	2871

prune384.0ms (6.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	5	141
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	140	7	147

Merged error: 14.6b

Counts

147 → 7

Compiler

Compiled 5743 to 5149 computations (10.3% saved)

regimes50.0ms (0.8%)

Compiler: Compiled 560 to 518 computations (7.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	31
1	32	31

end0.0ms (0%)

sample1.4s (23.3%)

Algorithm

1×

intervals

Results

536.0ms	2114×	body	2048	valid
181.0ms	978×	body	1024	valid
180.0ms	4158×	body	128	valid
67.0ms	489×	body	512	valid
22.0ms	261×	body	256	valid

Compiler

Compiled 309 to 288 computations (6.8% saved)

Details

analyze2.0ms (0%)

sample36.0ms (0.6%)

simplify353.0ms (5.7%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite27.0ms (0.4%)

series258.0ms (4.2%)

simplify74.0ms (1.2%)

prune93.0ms (1.5%)

localize11.0ms (0.2%)

rewrite54.0ms (0.9%)

series589.0ms (9.6%)

simplify76.0ms (1.2%)

prune235.0ms (3.8%)

localize13.0ms (0.2%)

rewrite67.0ms (1.1%)

series979.0ms (15.9%)

simplify104.0ms (1.7%)

prune272.0ms (4.4%)

localize19.0ms (0.3%)

rewrite61.0ms (1%)

series860.0ms (14%)

simplify91.0ms (1.5%)

prune384.0ms (6.2%)

regimes50.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (23.3%)

Profiling