Details

analyze207.0ms (8.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample23.0ms (1%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify183.0ms (7.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	165	17
1	165	17

prune5.0ms (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: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize17.0ms (0.7%)

Local error

Found 3 expressions with local error:

0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite34.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

12.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series105.0ms (4.4%)

Counts

3 → 9

Calls

3 calls:

47.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
35.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
23.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify71.0ms (3%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5072	2078

prune222.0ms (9.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	2	110

Merged error: 0b

Counts

110 → 2

Compiler

Compiled 3300 to 2739 computations (17% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b	(exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b	(log.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

rewrite74.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`*-un-lft-identity_binary64`
106×	`add-sqr-sqrt_binary64`
97×	`times-frac_binary64`
90×	`sqrt-prod_binary64`
66×	`exp-prod_binary64`
52×	`add-cube-cbrt_binary64`
34×	`log-pow_binary64` `difference-of-squares_binary64`
25×	`distribute-lft-out_binary64`
17×	`distribute-lft-out--_binary64`
8×	`associate-/r/_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64`
4×	`flip3-+_binary64` `associate-/r*_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`log-prod_binary64`
2×	`associate-/l/_binary64` `rem-sqrt-square_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

4 → 179

Calls

4 calls:

15.0ms	(log.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
13.0ms	(exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
10.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series198.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(log.f64 (exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
64.0ms	(exp.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
40.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
22.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify86.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5407	3298

prune268.0ms (11.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	191	2	193

Merged error: 0b

Counts

193 → 2

Compiler

Compiled 3971 to 3258 computations (18% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(atan.f64 (+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2)))
0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2))
0.0b	(.f64 (.f64 x x) 1/2)

rewrite23.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`associate-+l+_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64`
2×	`sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-l_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 43

Calls

3 calls:

9.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2))
7.0ms	(.f64 (.f64 x x) 1/2)
4.0ms	(atan.f64 (+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2)))

series72.0ms (3%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(.f64 (.f64 x x) 1/2)
22.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2))
16.0ms	(atan.f64 (+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2)))

simplify60.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5051	683

prune45.0ms (1.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	52	2	54

Merged error: 0b

Counts

54 → 2

Compiler

Compiled 815 to 579 computations (29% saved)

regimes29.0ms (1.2%)

Compiler: Compiled 107 to 94 computations (12.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	21
1	24	21

end0.0ms (0%)

sample640.0ms (26.9%)

Algorithm

1×

intervals

Results

430.0ms

8000×

body

128

valid

Compiler

Compiled 50 to 46 computations (8% saved)

Details

analyze207.0ms (8.7%)

sample23.0ms (1%)

simplify183.0ms (7.7%)

prune5.0ms (0.2%)

localize17.0ms (0.7%)

rewrite34.0ms (1.4%)

series105.0ms (4.4%)

simplify71.0ms (3%)

prune222.0ms (9.3%)

localize12.0ms (0.5%)

rewrite74.0ms (3.1%)

series198.0ms (8.3%)

simplify86.0ms (3.6%)

prune268.0ms (11.2%)

localize8.0ms (0.3%)

rewrite23.0ms (1%)

series72.0ms (3%)

simplify60.0ms (2.5%)

prune45.0ms (1.9%)

regimes29.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample640.0ms (26.9%)

Profiling