Details

analyze181.0ms (3.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4783	13
1	4783	13
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Symmetry

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample21.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify97.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4783	13
1	4783	13

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

rewrite57.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

22×	`*-un-lft-identity_binary64_1101`
15×	`times-frac_binary64_1107`
12×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123`
5×	`cosh-undef_binary64_1295` `distribute-lft-out_binary64_1052` `associate-/r*_binary64_1045`
4×	`add-exp-log_binary64_1139` `add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`associate-/l*_binary64_1046`
2×	`pow1_binary64_1162` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `flip-+_binary64_1075`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

2 → 50

Calls

2 calls:

7.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
4.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 807 to 304 computations (62.3% saved)

series85.0ms (1.6%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

57.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
19.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 266 to 229 computations (13.9% saved)

simplify90.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5031	1026

prune49.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	3	63

Error

Counts

63 → 3

Compiler

Compiled 867 to 388 computations (55.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0b	(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
0.0b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
0.0b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))

rewrite945.0ms (17.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

496×	`sqrt-prod_binary64_1117`
424×	`times-frac_binary64_1107`
378×	`add-sqr-sqrt_binary64_1123`
342×	`*-un-lft-identity_binary64_1101`
208×	`add-cube-cbrt_binary64_1136`
102×	`swap-sqr_binary64_1068`
59×	`distribute-lft-out_binary64_1052`
54×	`associate-l_binary64_1042` `associate-r_binary64_1041`
43×	`cosh-undef_binary64_1295`
25×	`unswap-sqr_binary64_1069`
20×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
16×	`associate-/r*_binary64_1045`
12×	`sqrt-div_binary64_1118` `associate-/r/_binary64_1047` `associate-/l*_binary64_1046`
11×	`pow1_binary64_1162`
7×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
6×	`div-exp_binary64_1152` `add-log-exp_binary64_1140` `cbrt-undiv_binary64_1135` `sqrt-undiv_binary64_1122` `div-inv_binary64_1098`
4×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`pow2_binary64_1182` `pow-prod-down_binary64_1172` `pow-prod-up_binary64_1171` `pow-plus_binary64_1164` `sqrt-unprod_binary64_1121` `rem-square-sqrt_binary64_1113` `frac-times_binary64_1111` `pow-sqr_binary64_1074` `associate-l/_binary64_1044` `associate-r/_binary64_1043` `*-commutative_binary64_1032` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 428

Calls

4 calls:

68.0ms	(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
9.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
9.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
5.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 15899 to 6567 computations (58.7% saved)

series381.0ms (7.1%)

Error

Counts

4 → 24

Calls

4 calls:

114.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
112.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
94.0ms	(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
23.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 1616 to 1315 computations (18.6% saved)

simplify194.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4924	15316
1	4924	15316

prune597.0ms (11.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	451	1	452
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	453	2	455

Error

Counts

455 → 2

Compiler

Compiled 13132 to 4883 computations (62.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.0b	(/.f64 1 (sqrt.f64 (cosh.f64 x)))
0.0b	(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
0.0b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))

rewrite440.0ms (8.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

173×	`add-sqr-sqrt_binary64_1123`
172×	`times-frac_binary64_1107`
167×	`sqrt-prod_binary64_1117`
131×	`*-un-lft-identity_binary64_1101`
93×	`add-cube-cbrt_binary64_1136`
54×	`associate-l_binary64_1042`
32×	`add-exp-log_binary64_1139`
25×	`unswap-sqr_binary64_1069`
23×	`associate-r_binary64_1041`
20×	`add-cbrt-cube_binary64_1137`
14×	`cosh-undef_binary64_1295` `distribute-lft-out_binary64_1052` `associate-/r*_binary64_1045`
11×	`div-exp_binary64_1152`
9×	`associate-/l*_binary64_1046`
8×	`pow1_binary64_1162` `prod-exp_binary64_1150`
6×	`add-log-exp_binary64_1140` `cbrt-undiv_binary64_1135` `sqrt-div_binary64_1118` `associate-/r/_binary64_1047`
4×	`div-inv_binary64_1098` `cbrt-unprod_binary64_1134`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `1-exp_binary64_1145` `rec-exp_binary64_1151` `pow-flip_binary64_1175`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `cosh-def_binary64_1287`
1×	`sqrt-undiv_binary64_1122` `pow-prod-down_binary64_1172` `frac-times_binary64_1111` `un-div-inv_binary64_1099` `associate-l/_binary64_1044` `associate-r/_binary64_1043` `*-commutative_binary64_1032` `inv-pow_binary64_1186` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 263

Calls

4 calls:

35.0ms	(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
9.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
8.0ms	(/.f64 1 (sqrt.f64 (cosh.f64 x)))
5.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 7299 to 3158 computations (56.7% saved)

series467.0ms (8.7%)

Error

Counts

4 → 24

Calls

4 calls:

194.0ms	(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 1 (sqrt.f64 (cosh.f64 x))))
128.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
86.0ms	(/.f64 1 (sqrt.f64 (cosh.f64 x)))
27.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 1376 to 1163 computations (15.5% saved)

simplify139.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

287 → 287

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4888	7610
1	4888	7610

prune317.0ms (5.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	287	2	289

Error

Counts

289 → 2

Compiler

Compiled 7039 to 3038 computations (56.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (.f64 1/2 (.f64 x x)))
0.1b	(*.f64 5/24 (pow.f64 x 4))
0.2b	(.f64 1/2 (.f64 x x))
14.0b	(+.f64 (-.f64 1 (.f64 1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))

rewrite105.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-exp-log_binary64_1139` `add-sqr-sqrt_binary64_1123`
11×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
9×	`pow1_binary64_1162`
8×	`add-cube-cbrt_binary64_1136` `-un-lft-identity_binary64_1101` `associate-r*_binary64_1041`
6×	`prod-exp_binary64_1150` `associate-l_binary64_1042`
4×	`cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069` `unpow-prod-down_binary64_1180`
3×	`pow-prod-down_binary64_1172`
2×	`diff-log_binary64_1193` `sum-log_binary64_1192` `sub-neg_binary64_1094` `associate-+l+_binary64_1034` `cancel-sign-sub-inv_binary64_1067` `*-commutative_binary64_1032` `sqr-pow_binary64_1073`
1×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-+l-_binary64_1036` `+-commutative_binary64_1031` `pow-to-exp_binary64_1170` `pow-exp_binary64_1169` `flip3--_binary64_1105` `flip--_binary64_1076`

Counts

4 → 71

Calls

4 calls:

6.0ms	(+.f64 (-.f64 1 (.f64 1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))
5.0ms	(.f64 1/2 (.f64 x x))
5.0ms	(*.f64 5/24 (pow.f64 x 4))
3.0ms	(-.f64 1 (.f64 1/2 (.f64 x x)))

Compiler

Compiled 1448 to 1047 computations (27.7% saved)

series161.0ms (3%)

Error

Counts

4 → 17

Calls

4 calls:

50.0ms	(-.f64 1 (.f64 1/2 (.f64 x x)))
40.0ms	(+.f64 (-.f64 1 (.f64 1/2 (.f64 x x))) (*.f64 5/24 (pow.f64 x 4)))
32.0ms	(*.f64 5/24 (pow.f64 x 4))
28.0ms	(.f64 1/2 (.f64 x x))

Compiler

Compiled 506 to 445 computations (12.1% saved)

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5174	1081

prune83.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	88	2	90

Error

Counts

90 → 2

Compiler

Compiled 1451 to 1049 computations (27.7% saved)

regimes93.0ms (1.7%)

Accuracy

Total 0.0b remaining (97.6%)

Threshold costs 0.0b (97.6%)

Compiler

Compiled 698 to 622 computations (10.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	19
1	27	19

Removed

()

end0.0ms (0%)

sample744.0ms (13.9%)

Algorithm

1×

intervals

Results

241.0ms

8000×

body

128

valid

Compiler

Compiled 231 to 207 computations (10.4% saved)

Details

analyze181.0ms (3.4%)

sample21.0ms (0.4%)

simplify97.0ms (1.8%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite57.0ms (1.1%)

series85.0ms (1.6%)

simplify90.0ms (1.7%)

prune49.0ms (0.9%)

localize13.0ms (0.2%)

rewrite945.0ms (17.6%)

series381.0ms (7.1%)

simplify194.0ms (3.6%)

prune597.0ms (11.1%)

localize12.0ms (0.2%)

rewrite440.0ms (8.2%)

series467.0ms (8.7%)

simplify139.0ms (2.6%)

prune317.0ms (5.9%)

localize9.0ms (0.2%)

rewrite105.0ms (2%)

series161.0ms (3%)

simplify68.0ms (1.3%)

prune83.0ms (1.5%)

regimes93.0ms (1.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample744.0ms (13.9%)

Profiling