Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample18.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	pre	80	true
6.0ms	256×	body	80	valid

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify77.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	499	10
1	499	10

prune6.0ms (0.2%)

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: 8.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.2b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
6×	`associate-/r*_binary64`
5×	`distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `insert-posit16` `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 → 57

Calls

2 calls:

16.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
7.0ms	(/.f64 x0 (-.f64 1 x1))

series121.0ms (4.1%)

Counts

2 → 6

Calls

2 calls:

62.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
60.0ms	(/.f64 x0 (-.f64 1 x1))

simplify94.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4959	952
1	4959	952

prune51.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	2	64

Merged error: 6.5b

Counts

64 → 2

Compiler

Compiled 890 to 538 computations (39.6% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
5.7b	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

rewrite58.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64` `times-frac_binary64`
18×	`difference-of-squares_binary64`
11×	`pow1_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `swap-sqr_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
6×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
4×	`insert-posit16` `frac-times_binary64`
3×	`sub-neg_binary64` `associate-/l*_binary64`
2×	`associate-r/_binary64` `associate-/r/_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `pow-prod-up_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 117

Calls

4 calls:

20.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
13.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
13.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
7.0ms	(/.f64 x0 (-.f64 1 x1))

series259.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
58.0ms	(/.f64 x0 (-.f64 1 x1))
54.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
17.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))

simplify134.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	5408	1807

prune150.0ms (5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	129	2	131

Merged error: 5.1b

Counts

131 → 2

Compiler

Compiled 3452 to 2154 computations (37.6% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 x1 (+.f64 x1 -2))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
5.7b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite42.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64` `pow1_binary64`
5×	`distribute-lft-out--_binary64`
4×	`associate-r_binary64` `insert-posit16`
3×	`associate-l_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

12.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
12.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
8.0ms	(*.f64 x1 (+.f64 x1 -2))
7.0ms	(/.f64 x0 (-.f64 1 x1))

series297.0ms (10%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
55.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
50.0ms	(*.f64 x1 (+.f64 x1 -2))
49.0ms	(/.f64 x0 (-.f64 1 x1))

simplify84.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4934	1580
1	4934	1580

prune125.0ms (4.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	106	2	108

Merged error: 4.1b

Counts

108 → 2

Compiler

Compiled 2944 to 1846 computations (37.3% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
4.6b	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
5.7b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite47.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64`
7×	`log-pow_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `exp-prod_binary64`
5×	`pow1_binary64`
4×	`log-prod_binary64` `insert-posit16`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `exp-sum_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 91

Calls

4 calls:

13.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
12.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
12.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
7.0ms	(/.f64 x0 (-.f64 1 x1))

series379.0ms (12.7%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
135.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
56.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
48.0ms	(/.f64 x0 (-.f64 1 x1))

simplify117.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5051	1819

prune135.0ms (4.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	2	105

Merged error: 3.0b

Counts

105 → 2

Compiler

Compiled 3053 to 1975 computations (35.3% saved)

regimes22.0ms (0.7%)

Compiler: Compiled 136 to 108 computations (20.6% saved)

bsearch15.0ms (0.5%)

Steps

Iters	Range		Point
7	0.000209	0.0186	0.00021208908081054686

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	108
1	59	108

end0.0ms (0%)

sample672.0ms (22.5%)

Algorithm

1×

intervals

Results

229.0ms	8000×	pre	80	true
178.0ms	8000×	body	80	valid

Compiler

Compiled 165 to 126 computations (23.6% saved)

Details

analyze3.0ms (0.1%)

sample18.0ms (0.6%)

simplify77.0ms (2.6%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite25.0ms (0.8%)

series121.0ms (4.1%)

simplify94.0ms (3.1%)

prune51.0ms (1.7%)

localize11.0ms (0.4%)

rewrite58.0ms (1.9%)

series259.0ms (8.7%)

simplify134.0ms (4.5%)

prune150.0ms (5%)

localize12.0ms (0.4%)

rewrite42.0ms (1.4%)

series297.0ms (10%)

simplify84.0ms (2.8%)

prune125.0ms (4.2%)

localize16.0ms (0.5%)

rewrite47.0ms (1.6%)

series379.0ms (12.7%)

simplify117.0ms (3.9%)

prune135.0ms (4.5%)

regimes22.0ms (0.7%)

bsearch15.0ms (0.5%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample672.0ms (22.5%)

Profiling