Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample19.0ms (1%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify175.0ms (8.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4783	13
1	4783	13

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite10.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_1442`
15×	`times-frac_binary64_1448`
11×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
5×	`associate-/r*_binary64_1386`
4×	`cosh-undef_binary64_1636` `distribute-lft-out_binary64_1393`
3×	`add-cbrt-cube_binary64_1478` `associate-/l*_binary64_1387` `add-exp-log_binary64_1480`
2×	`associate-/r/_binary64_1388`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `add-log-exp_binary64_1481` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503` `div-exp_binary64_1493`

Counts

1 → 37

Calls

2 calls:

7.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

series58.0ms (2.9%)

Counts

1 → 6

Calls

1 calls:

58.0ms

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

Compiler

Compiled 74 to 68 computations (8.1% saved)

simplify56.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4876	778
1	4876	778

prune44.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	3	44

Error

Counts

44 → 3

Compiler

Compiled 626 to 283 computations (54.8% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
0.0b	(/.f64 (sqrt.f64 2) (cosh.f64 x))
0.0b	(/.f64 (sqrt.f64 2) (cosh.f64 x))
0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))

rewrite35.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64_1464`
66×	`times-frac_binary64_1448`
43×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
36×	`sqrt-prod_binary64_1458`
23×	`associate-r_binary64_1382`
22×	`associate-l_binary64_1383`
16×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
9×	`unswap-sqr_binary64_1410`
6×	`associate-/l*_binary64_1387`
5×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
4×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `pow1_binary64_1503`
3×	`associate-/r*_binary64_1386` `div-inv_binary64_1439`
2×	`associate-/r/_binary64_1388` `add-log-exp_binary64_1481` `cosh-def_binary64_1628`
1×	`associate-r/_binary64_1384` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `frac-times_binary64_1452` `associate-*l/_binary64_1385`

Counts

2 → 114

Calls

4 calls:

20.0ms	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
4.0ms	(/.f64 (sqrt.f64 2) (cosh.f64 x))
0.0ms	(/.f64 (sqrt.f64 2) (cosh.f64 x))
0.0ms	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))

series222.0ms (11.2%)

Counts

2 → 12

Calls

2 calls:

137.0ms	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
86.0ms	(/.f64 (sqrt.f64 2) (cosh.f64 x))

Compiler

Compiled 284 to 272 computations (4.2% saved)

simplify68.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4928	1881
1	4928	1881

prune114.0ms (5.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	126	3	129

Error

Counts

129 → 3

Compiler

Compiled 1885 to 1412 computations (25.1% saved)

localize13.0ms (0.6%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 5/24 (pow.f64 x 4))
0.1b	(*.f64 61/720 (pow.f64 x 6))
0.0b	(.f64 1/2 (.f64 x x))
0.0b	(+.f64 (.f64 1/2 (.f64 x x)) (*.f64 61/720 (pow.f64 x 6)))
0.0b	(.f64 1/2 (.f64 x x))
0.1b	(*.f64 61/720 (pow.f64 x 6))
0.1b	(*.f64 5/24 (pow.f64 x 4))
23.1b	(-.f64 (+.f64 1 (.f64 5/24 (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 61/720 (pow.f64 x 6))))

rewrite37.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1464`
19×	`add-exp-log_binary64_1480`
16×	`add-log-exp_binary64_1481`
15×	`associate-r_binary64_1382`
14×	`*-un-lft-identity_binary64_1442`
13×	`add-cbrt-cube_binary64_1478`
12×	`add-cube-cbrt_binary64_1477`
9×	`associate-l_binary64_1383` `prod-exp_binary64_1491` `pow1_binary64_1503`
8×	`unpow-prod-down_binary64_1521`
7×	`unswap-sqr_binary64_1410`
5×	`cbrt-unprod_binary64_1475`
4×	`sum-log_binary64_1533` `frac-sub_binary64_1451` `diff-log_binary64_1534` `sqr-pow_binary64_1414` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`cancel-sign-sub-inv_binary64_1408` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373`
2×	`pow-exp_binary64_1510` `pow-to-exp_binary64_1511`
1×	`associate--l+_binary64_1379` `sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `associate--r+_binary64_1378` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`

Counts

4 → 94

Calls

8 calls:

12.0ms	(-.f64 (+.f64 1 (.f64 5/24 (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 61/720 (pow.f64 x 6))))
6.0ms	(*.f64 61/720 (pow.f64 x 6))
6.0ms	(.f64 1/2 (.f64 x x))
5.0ms	(*.f64 5/24 (pow.f64 x 4))
0.0ms	(+.f64 (.f64 1/2 (.f64 x x)) (*.f64 61/720 (pow.f64 x 6)))

series147.0ms (7.4%)

Counts

4 → 17

Calls

4 calls:

44.0ms	(-.f64 (+.f64 1 (.f64 5/24 (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 x x)) (.f64 61/720 (pow.f64 x 6))))
39.0ms	(*.f64 61/720 (pow.f64 x 6))
37.0ms	(*.f64 5/24 (pow.f64 x 4))
26.0ms	(.f64 1/2 (.f64 x x))

Compiler

Compiled 448 to 392 computations (12.5% saved)

simplify74.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4969	1985
1	4969	1985

prune155.0ms (7.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	111	3	114

Error

Counts

114 → 3

Compiler

Compiled 2729 to 2085 computations (23.6% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	103	144
1	103	144

regimes62.0ms (3.1%)

Compiler: Compiled 395 to 321 computations (18.7% saved)

bsearch0.0ms (0%)

regimes21.0ms (1%)

Compiler: Compiled 12 to 14 computations (-16.7% saved)

bsearch30.0ms (1.5%)

Steps

Iters	Range		Point
7	1.2251308373656755	166.89569812005223	1.4186901835741934
11	-3.1959860145551867e+18	-0.007102553974907408	-1.4015561200794018

Compiler

Compiled 1 to 1 computations (0% saved)

regimes19.0ms (1%)

Accuracy

Total 0.0b remaining (93.5%)

Threshold costs 0.0b (93.5%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch30.0ms (1.5%)

Steps

Iters	Range		Point
7	166.89569812005223	3300.8171630890365	357.8019380154624
11	-3.1959860145551867e+18	-0.007102553974907408	-359.26091895379255

Compiler

Compiled 34 to 31 computations (8.8% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	46
1	58	46

end0.0ms (0%)

sample566.0ms (28.6%)

Algorithm

1×

intervals

Results

236.0ms

8000×

body

128

valid

Compiler

Compiled 135 to 114 computations (15.6% saved)

Pareto

0.8886223613186864

Details

analyze1.0ms (0.1%)

sample19.0ms (1%)

simplify175.0ms (8.9%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

rewrite10.0ms (0.5%)

series58.0ms (2.9%)

simplify56.0ms (2.8%)

prune44.0ms (2.2%)

localize6.0ms (0.3%)

rewrite35.0ms (1.8%)

series222.0ms (11.2%)

simplify68.0ms (3.5%)

prune114.0ms (5.8%)

localize13.0ms (0.6%)

rewrite37.0ms (1.9%)

series147.0ms (7.4%)

simplify74.0ms (3.7%)

prune155.0ms (7.8%)

simplify5.0ms (0.2%)

regimes62.0ms (3.1%)

bsearch0.0ms (0%)

regimes21.0ms (1%)

bsearch30.0ms (1.5%)

regimes19.0ms (1%)

bsearch30.0ms (1.5%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample566.0ms (28.6%)

Profiling