Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 11 to 12 computations (-9.1% saved)

sample35.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	56×	body	1280	valid
7.0ms	39×	body	640	valid
4.0ms	129×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

Compiler

Compiled 21 to 25 computations (-19% saved)

simplify94.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4703	15
1	4703	15

prune7.0ms (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: 30.2b

Counts

2 → 1

Compiler

Compiled 20 to 22 computations (-10% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
4.0b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`
5×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `difference-of-sqr-1_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 63

Calls

3 calls:

11.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
4.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

series18.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

10.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
7.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
2.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

simplify110.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4852	1370
1	4852	1370

prune81.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 0.0b

Counts

73 → 3

Compiler

Compiled 1277 to 1159 computations (9.2% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
0.0b	(.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))
0.0b	(/.f64 (+.f64 (/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (.f64 -2 x))))) -1) (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x))))))
4.0b	(+.f64 (/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))) -1)

rewrite66.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
42×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
23×	`distribute-lft-out_binary64`
12×	`difference-of-sqr--1_binary64`
11×	`pow1_binary64`
10×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
9×	`associate-/l*_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64`
4×	`associate-r_binary64` `associate-/r/_binary64` `associate-l_binary64` `frac-times_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 137

Calls

4 calls:

26.0ms	(/.f64 (+.f64 (/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (.f64 -2 x))))) -1) (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x))))))
18.0ms	(+.f64 (/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))) -1)
11.0ms	(.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))
6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

series61.0ms (2%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(/.f64 (+.f64 (/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (.f64 -2 x))))) -1) (+.f64 1 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x))))))
15.0ms	(+.f64 (/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))) -1)
6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
4.0ms	(.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))

simplify129.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4909	4448
1	4909	4448

prune267.0ms (8.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	149	3	152

Merged error: 0.0b

Counts

152 → 3

Compiler

Compiled 5221 to 4714 computations (9.7% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
0.2b	(.f64 (+.f64 1 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))))) (+.f64 -1 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))))))
4.4b	(+.f64 -1 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))))

rewrite51.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64` `times-frac_binary64`
12×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-/l*_binary64`
5×	`associate-l_binary64`
4×	`associate-r_binary64` `associate-/r/_binary64` `frac-times_binary64`
2×	`cbrt-undiv_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 109

Calls

4 calls:

24.0ms	(.f64 (+.f64 1 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))))) (+.f64 -1 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))))))
11.0ms	(+.f64 -1 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))))
6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

series61.0ms (2%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(.f64 (+.f64 1 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))))) (+.f64 -1 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))))))
13.0ms	(+.f64 -1 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))))
7.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

simplify106.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4912	3183
1	4912	3183

prune186.0ms (6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	121	3	124

Merged error: 0.0b

Counts

124 → 3

Compiler

Compiled 3866 to 3538 computations (8.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 2/15 (pow.f64 x 5)))
0.1b	(*.f64 2/15 (pow.f64 x 5))
0.1b	(*.f64 1/3 (pow.f64 x 3))
19.5b	(-.f64 (+.f64 x (.f64 2/15 (pow.f64 x 5))) (.f64 1/3 (pow.f64 x 3)))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`associate-l_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `cube-prod_binary64`
2×	`pow-to-exp_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `unpow3_binary64` `associate--l+_binary64` `cube-mult_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(-.f64 (+.f64 x (.f64 2/15 (pow.f64 x 5))) (.f64 1/3 (pow.f64 x 3)))
7.0ms	(*.f64 1/3 (pow.f64 x 3))
6.0ms	(*.f64 2/15 (pow.f64 x 5))
4.0ms	(+.f64 x (*.f64 2/15 (pow.f64 x 5)))

series29.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(+.f64 x (*.f64 2/15 (pow.f64 x 5)))
7.0ms	(-.f64 (+.f64 x (.f64 2/15 (pow.f64 x 5))) (.f64 1/3 (pow.f64 x 3)))
5.0ms	(*.f64 2/15 (pow.f64 x 5))
4.0ms	(*.f64 1/3 (pow.f64 x 3))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5741	1198

prune74.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	92	3	95

Merged error: 0b

Counts

95 → 3

Compiler

Compiled 1642 to 1269 computations (22.7% saved)

regimes263.0ms (8.4%)

Compiler: Compiled 609 to 612 computations (-0.5% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	73	116
1	73	116

end0.0ms (0%)

sample1.3s (42.4%)

Algorithm

1×

intervals

Results

430.0ms	1724×	body	1280	valid
213.0ms	1250×	body	640	valid
134.0ms	4079×	body	80	valid
75.0ms	639×	body	320	valid
23.0ms	308×	body	160	valid

Compiler

Compiled 151 to 144 computations (4.6% saved)

Details

analyze2.0ms (0.1%)

sample35.0ms (1.1%)

simplify94.0ms (3%)

prune7.0ms (0.2%)

localize7.0ms (0.2%)

rewrite23.0ms (0.8%)

series18.0ms (0.6%)

simplify110.0ms (3.5%)

prune81.0ms (2.6%)

localize12.0ms (0.4%)

rewrite66.0ms (2.1%)

series61.0ms (2%)

simplify129.0ms (4.1%)

prune267.0ms (8.5%)

localize12.0ms (0.4%)

rewrite51.0ms (1.6%)

series61.0ms (2%)

simplify106.0ms (3.4%)

prune186.0ms (6%)

localize10.0ms (0.3%)

rewrite26.0ms (0.8%)

series29.0ms (0.9%)

simplify61.0ms (1.9%)

prune74.0ms (2.4%)

regimes263.0ms (8.4%)

bsearch1.0ms (0%)

simplify5.0ms (0.2%)

end0.0ms (0%)

sample1.3s (42.4%)

Profiling