Details

analyze4.0ms (0.1%)

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 9 to 8 computations (11.1% saved)

sample77.0ms (1.5%)

Algorithm

1×

intervals

Results

47.0ms	128×	body	1024	valid
12.0ms	63×	body	512	valid
7.0ms	14×	body	2048	valid
3.0ms	28×	body	256	valid
1.0ms	23×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify205.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (198.0ms)

Iter	Nodes	Cost
0	4989	12
1	4989	12

prune6.0ms (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: 58.6b

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 (-.f64 1 eps) (+.f64 1 eps))
7.0b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
30×	`log-prod_binary64`
25×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/l*_binary64`
4×	`associate-/r*_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `add-log-exp_binary64` `rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip--_binary64`

Counts

2 → 92

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
8.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

series81.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

56.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
25.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5224	1892

prune113.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	2	99

Merged error: 0.0b

Counts

99 → 2

Compiler

Compiled 1533 to 1180 computations (23% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (pow.f64 eps 5) -2/5) (.f64 (pow.f64 eps 3) -2/3))
0.1b	(*.f64 (pow.f64 eps 5) -2/5)
0.1b	(*.f64 (pow.f64 eps 3) -2/3)

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`associate-l_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`unpow-prod-down_binary64`
7×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
6×	`associate-r_binary64` `prod-exp_binary64`
5×	`add-log-exp_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`pow1_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

3 → 67

Calls

3 calls:

6.0ms	(*.f64 (pow.f64 eps 3) -2/3)
6.0ms	(+.f64 (.f64 (pow.f64 eps 5) -2/5) (.f64 (pow.f64 eps 3) -2/3))
5.0ms	(*.f64 (pow.f64 eps 5) -2/5)

series288.0ms (5.6%)

Counts

3 → 9

Calls

3 calls:

180.0ms	(+.f64 (.f64 (pow.f64 eps 5) -2/5) (.f64 (pow.f64 eps 3) -2/3))
62.0ms	(*.f64 (pow.f64 eps 5) -2/5)
46.0ms	(*.f64 (pow.f64 eps 3) -2/3)

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4941	890
1	4941	890

prune86.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	76	2	78

Merged error: 0.0b

Counts

78 → 2

Compiler

Compiled 1517 to 1212 computations (20.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (log.f64 (sqrt.f64 (-.f64 1 eps))) (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
7.0b	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
7.1b	(log.f64 (sqrt.f64 (-.f64 1 eps)))

rewrite74.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

169×	`*-un-lft-identity_binary64`
109×	`add-sqr-sqrt_binary64`
108×	`times-frac_binary64`
102×	`log-prod_binary64`
90×	`sqrt-prod_binary64`
64×	`add-cube-cbrt_binary64`
42×	`associate-+r+_binary64`
32×	`distribute-lft-out_binary64`
30×	`difference-of-squares_binary64`
15×	`distribute-lft-out--_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64`
9×	`associate-+l+_binary64` `associate-/l*_binary64`
8×	`log-pow_binary64`
6×	`add-cbrt-cube_binary64` `associate-/r/_binary64` `log-div_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `associate-/r*_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`flip3--_binary64` `rem-log-exp_binary64` `div-inv_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `associate-+l-_binary64` `div-exp_binary64`
1×	`associate-+r-_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 209

Calls

4 calls:

21.0ms	(+.f64 (log.f64 (sqrt.f64 (-.f64 1 eps))) (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))))
10.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
10.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
5.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))

series321.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(+.f64 (log.f64 (sqrt.f64 (-.f64 1 eps))) (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))))
73.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
56.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
42.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))

simplify208.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4957	5050
1	4957	5050

prune339.0ms (6.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	221	2	223

Merged error: 0b

Counts

223 → 2

Compiler

Compiled 5170 to 4111 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
0.2b	(exp.f64 (log.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))))
7.0b	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
7.1b	(log.f64 (sqrt.f64 (-.f64 1 eps)))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
72×	`times-frac_binary64`
60×	`sqrt-prod_binary64`
55×	`log-prod_binary64`
46×	`add-cube-cbrt_binary64`
20×	`difference-of-squares_binary64`
19×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
9×	`pow1_binary64` `associate-/l*_binary64`
6×	`log-pow_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `exp-sum_binary64` `sqrt-div_binary64` `exp-prod_binary64`
3×	`rem-log-exp_binary64` `log-div_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 156

Calls

4 calls:

12.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
10.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
5.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))
3.0ms	(exp.f64 (log.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))))

series316.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(exp.f64 (log.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))))
64.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
45.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
41.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	6446	3819

prune272.0ms (5.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	168	2	170

Merged error: 0b

Counts

170 → 2

Compiler

Compiled 4276 to 3453 computations (19.2% saved)

regimes8.0ms (0.2%)

Compiler: Compiled 34 to 30 computations (11.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	22
1	19	22

end0.0ms (0%)

sample2.4s (46.1%)

Algorithm

1×

intervals

Results

1.4s	3897×	body	1024	valid
383.0ms	2043×	body	512	valid
226.0ms	427×	body	2048	valid
107.0ms	1022×	body	256	valid
31.0ms	611×	body	128	valid

Compiler

Compiled 71 to 63 computations (11.3% saved)

Details

analyze4.0ms (0.1%)

sample77.0ms (1.5%)

simplify205.0ms (4%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite26.0ms (0.5%)

series81.0ms (1.6%)

simplify71.0ms (1.4%)

prune113.0ms (2.2%)

localize9.0ms (0.2%)

rewrite23.0ms (0.4%)

series288.0ms (5.6%)

simplify62.0ms (1.2%)

prune86.0ms (1.7%)

localize9.0ms (0.2%)

rewrite74.0ms (1.5%)

series321.0ms (6.3%)

simplify208.0ms (4.1%)

prune339.0ms (6.7%)

localize10.0ms (0.2%)

rewrite48.0ms (0.9%)

series316.0ms (6.2%)

simplify87.0ms (1.7%)

prune272.0ms (5.3%)

regimes8.0ms (0.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (46.1%)

Profiling