Details

analyze310.0ms (10.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample31.0ms (1%)

Algorithm

1×

intervals

Results

13.0ms	88×	body	1024	valid
7.0ms	41×	body	512	valid
3.0ms	97×	body	128	valid
2.0ms	9×	body	2048	valid
1.0ms	21×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	11
1	9	11

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: 42.0b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.8b	(-.f64 (exp.f64 x) 1)

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64`
5×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`add-exp-log_binary64` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series92.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

74.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
18.0ms	(-.f64 (exp.f64 x) 1)

simplify64.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5711	1129

prune130.0ms (4.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

Compiler

Compiled 1841 to 1105 computations (40% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.0b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.3b	(*.f64 x 1/6)

rewrite31.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
13×	`pow1_binary64`
9×	`associate-l_binary64` `times-frac_binary64`
7×	`associate-r_binary64`
6×	`associate-*r/_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`associate-/r/_binary64` `unswap-sqr_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 93

Calls

4 calls:

8.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
6.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
4.0ms	(*.f64 x 1/6)

series238.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
76.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
50.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
21.0ms	(*.f64 x 1/6)

simplify68.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4961	1834
1	4961	1834

prune106.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Merged error: 0.0b

Counts

109 → 4

Compiler

Compiled 2163 to 1345 computations (37.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1/2 (/.f64 1 x))
0.0b	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
0.3b	(*.f64 x 1/12)

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`sum-log_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

3 → 44

Calls

3 calls:

10.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
9.0ms	(+.f64 1/2 (/.f64 1 x))
4.0ms	(*.f64 x 1/12)

series56.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

23.0ms	(*.f64 x 1/12)
17.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
15.0ms	(+.f64 1/2 (/.f64 1 x))

simplify64.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4873	576
1	4873	576

prune52.0ms (1.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	52	5	57

Merged error: 0.0b

Counts

57 → 5

Compiler

Compiled 817 to 659 computations (19.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.4b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.4b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))

rewrite66.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

24.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))
12.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
10.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
9.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))

series310.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
79.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))
75.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
75.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))

simplify98.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4825	2822
1	4825	2822

prune224.0ms (7.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	99	5	104

Merged error: 0.0b

Counts

104 → 5

Compiler

Compiled 4081 to 3351 computations (17.9% saved)

regimes21.0ms (0.7%)

Compiler: Compiled 148 to 124 computations (16.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms (0%)

sample970.0ms (32.2%)

Algorithm

1×

intervals

Results

409.0ms	2614×	body	1024	valid
119.0ms	1318×	body	512	valid
80.0ms	3114×	body	128	valid
55.0ms	289×	body	2048	valid
38.0ms	665×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 100 to 83 computations (17% saved)

Details

analyze310.0ms (10.3%)

sample31.0ms (1%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite18.0ms (0.6%)

series92.0ms (3.1%)

simplify64.0ms (2.1%)

prune130.0ms (4.3%)

localize9.0ms (0.3%)

rewrite31.0ms (1%)

series238.0ms (7.9%)

simplify68.0ms (2.3%)

prune106.0ms (3.5%)

localize6.0ms (0.2%)

rewrite25.0ms (0.8%)

series56.0ms (1.9%)

simplify64.0ms (2.1%)

prune52.0ms (1.7%)

localize10.0ms (0.3%)

rewrite66.0ms (2.2%)

series310.0ms (10.3%)

simplify98.0ms (3.2%)

prune224.0ms (7.4%)

regimes21.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample970.0ms (32.2%)

Profiling