Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample107.0ms (2%)

Algorithm

1×

intervals

Results

80.0ms	133×	body	2048	valid
15.0ms	62×	body	1024	valid
4.0ms	32×	body	512	valid
1.0ms	15×	body	256	valid
1.0ms	14×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5087	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

Merged error: 29.5b

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) 2)
5.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
4×	`frac-add_binary64` `add-sqr-sqrt_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `pow1_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `neg-sub0_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-diff_binary64` `distribute-lft-out--_binary64` `exp-neg_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

2 → 33

Calls

2 calls:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

series72.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
14.0ms	(-.f64 (exp.f64 x) 2)

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4859	627
1	4859	627

prune52.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	3	40

Merged error: 0.0b

Counts

40 → 3

Compiler

Compiled 598 to 324 computations (45.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64` `add-exp-log_binary64`
11×	`add-log-exp_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
6×	`associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`associate-+r+_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
6.0ms	(*.f64 1/12 (pow.f64 x 4))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
5.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))

series349.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
64.0ms	(*.f64 1/360 (pow.f64 x 6))
58.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
49.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4895	1259
1	4895	1259

prune103.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 0.0b

Counts

89 → 4

Compiler

Compiled 1822 to 1284 computations (29.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6)))
0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64` `add-exp-log_binary64`
11×	`add-log-exp_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
6×	`associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`associate-+l+_binary64`

Counts

4 → 74

Calls

4 calls:

8.0ms	(*.f64 1/360 (pow.f64 x 6))
8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
6.0ms	(*.f64 1/12 (pow.f64 x 4))
4.0ms	(+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6)))

series360.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6)))
67.0ms	(*.f64 1/360 (pow.f64 x 6))
57.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 1/360 (pow.f64 x 6))) (*.f64 1/12 (pow.f64 x 4)))
46.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4832	1211
1	4832	1211

prune95.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

Compiler

Compiled 1795 to 1260 computations (29.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/12 (pow.f64 x 4))
0.1b	(*.f64 1/12 (pow.f64 x 4))
28.9b	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
28.9b	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64` `add-exp-log_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
6×	`pow1_binary64` `associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `sqrt-div_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
6.0ms	(*.f64 1/12 (pow.f64 x 4))
6.0ms	(*.f64 1/12 (pow.f64 x 4))

series269.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
87.0ms	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
46.0ms	(*.f64 1/12 (pow.f64 x 4))
46.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5033	1658

prune192.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	92	4	96

Merged error: 0.0b

Counts

96 → 4

Compiler

Compiled 3624 to 2583 computations (28.7% saved)

regimes13.0ms (0.2%)

Compiler: Compiled 98 to 72 computations (26.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample3.4s (61.5%)

Algorithm

1×

intervals

Results

2.4s	4216×	body	2048	valid
496.0ms	1974×	body	1024	valid
127.0ms	961×	body	512	valid
40.0ms	496×	body	256	valid
15.0ms	353×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 128 to 99 computations (22.7% saved)

Details

analyze4.0ms (0.1%)

sample107.0ms (2%)

simplify77.0ms (1.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite15.0ms (0.3%)

series72.0ms (1.3%)

simplify88.0ms (1.6%)

prune52.0ms (0.9%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series349.0ms (6.4%)

simplify72.0ms (1.3%)

prune103.0ms (1.9%)

localize9.0ms (0.2%)

rewrite33.0ms (0.6%)

series360.0ms (6.6%)

simplify49.0ms (0.9%)

prune95.0ms (1.7%)

localize12.0ms (0.2%)

rewrite36.0ms (0.7%)

series269.0ms (4.9%)

simplify52.0ms (1%)

prune192.0ms (3.5%)

regimes13.0ms (0.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.4s (61.5%)

Profiling