Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample17.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify293.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

prune8.0ms (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: 15.9b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

15.9b

(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cube-cbrt_binary64_783` `times-frac_binary64_757` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
3×	`associate-/r_binary64_697` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786` `associate-/l_binary64_698`
2×	`associate-/r/_binary64_699`
1×	`flip3-+_binary64_754` `pow1_binary64_809` `add-log-exp_binary64_787` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `flip-+_binary64_725` `div-exp_binary64_799`

Counts

1 → 29

Calls

1 calls:

12.0ms

(/.f64 x (+.f64 (*.f64 x x) 1))

series95.0ms (2.1%)

Counts

1 → 3

Calls

1 calls:

95.0ms

(/.f64 x (+.f64 (*.f64 x x) 1))

simplify100.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5078	550

prune69.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0b

Counts

33 → 3

Compiler

Compiled 502 to 281 computations (44% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
15.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
15.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite125.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_772`
76×	`times-frac_binary64_757`
53×	`*-un-lft-identity_binary64_751`
47×	`add-cube-cbrt_binary64_783` `sqrt-prod_binary64_766`
28×	`add-exp-log_binary64_786`
24×	`associate-l_binary64_694` `associate-r_binary64_693`
18×	`add-cbrt-cube_binary64_784`
15×	`unswap-sqr_binary64_719`
10×	`sqrt-div_binary64_767`
9×	`div-exp_binary64_799`
8×	`prod-exp_binary64_797` `pow1_binary64_809`
6×	`associate-/r*_binary64_697` `associate-/r/_binary64_699`
5×	`flip3-+_binary64_754` `cbrt-undiv_binary64_782` `flip-+_binary64_725`
4×	`add-log-exp_binary64_787` `cbrt-unprod_binary64_781`
3×	`div-inv_binary64_748` `associate-/l*_binary64_698`
2×	`1-exp_binary64_792` `rec-exp_binary64_798` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `sqrt-pow1_binary64_768`
1×	`frac-times_binary64_761` `pow-prod-down_binary64_819` `-commutative_binary64_684` `associate-r/_binary64_695` `frac-2neg_binary64_762` `clear-num_binary64_750` `associate-*l/_binary64_696`

Counts

4 → 158

Calls

4 calls:

53.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
9.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
9.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series365.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
106.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
70.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
63.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify206.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4881	3380
1	4881	3380

prune329.0ms (7.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	170	3	173

Merged error: 0b

Counts

173 → 3

Compiler

Compiled 3865 to 2346 computations (39.3% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5)))
0.2b	(/.f64 1 (pow.f64 x 5))
0.2b	(pow.f64 (/.f64 1 x) 3)
19.0b	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))

rewrite169.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64_751`
54×	`add-sqr-sqrt_binary64_772`
49×	`times-frac_binary64_757`
37×	`add-cube-cbrt_binary64_783`
28×	`unpow-prod-down_binary64_827`
18×	`add-exp-log_binary64_786`
16×	`cube-prod_binary64_776`
11×	`distribute-lft-out_binary64_704` `add-log-exp_binary64_787` `div-inv_binary64_748`
9×	`add-cbrt-cube_binary64_784`
8×	`difference-of-squares_binary64_720` `div-exp_binary64_799`
7×	`pow-exp_binary64_816` `associate-/r*_binary64_697`
6×	`sqr-pow_binary64_723` `pow1_binary64_809`
5×	`distribute-lft-out--_binary64_705`
4×	`1-exp_binary64_792` `pow-to-exp_binary64_817` `cube-div_binary64_777` `rec-exp_binary64_798`
3×	`frac-sub_binary64_760` `pow-pow_binary64_820` `associate-/l*_binary64_698` `pow-unpow_binary64_825`
2×	`flip3-+_binary64_754` `inv-pow_binary64_833` `rem-cube-cbrt_binary64_773` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `sum-log_binary64_839` `frac-add_binary64_759` `flip-+_binary64_725` `pow-flip_binary64_822`
1×	`cube-mult_binary64_778` `+-commutative_binary64_683` `associate--l+_binary64_690` `flip--_binary64_726` `frac-2neg_binary64_762` `unpow3_binary64_814` `clear-num_binary64_750` `sub-neg_binary64_744` `flip3--_binary64_755`

Counts

4 → 151

Calls

4 calls:

85.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))
39.0ms	(+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5)))
10.0ms	(pow.f64 (/.f64 1 x) 3)
9.0ms	(/.f64 1 (pow.f64 x 5))

series448.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5)))
107.0ms	(/.f64 1 (pow.f64 x 5))
76.0ms	(pow.f64 (/.f64 1 x) 3)
67.0ms	(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))

simplify152.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4974	2632
1	4974	2632

prune384.0ms (8.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	163	3	166

Merged error: 0b

Counts

166 → 3

Compiler

Compiled 3362 to 2673 computations (20.5% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b	(pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3)
15.9b	(/.f64 x (+.f64 (*.f64 x x) 1))
41.5b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3))

rewrite72.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`times-frac_binary64_757`
41×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
36×	`cbrt-prod_binary64_779`
30×	`unpow-prod-down_binary64_827` `cube-prod_binary64_776`
10×	`associate-/r/_binary64_699`
8×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
5×	`flip3-+_binary64_754` `div-inv_binary64_748` `flip-+_binary64_725`
4×	`pow1_binary64_809`
3×	`associate-/r_binary64_697` `add-log-exp_binary64_787` `associate-/l_binary64_698` `pow-unpow_binary64_825`
2×	`cube-mult_binary64_778` `pow-exp_binary64_816` `cube-div_binary64_777` `sqr-pow_binary64_723` `rem-cube-cbrt_binary64_773` `cbrt-undiv_binary64_782` `unpow3_binary64_814` `div-exp_binary64_799`
1×	`rem-cbrt-cube_binary64_774` `pow1/3_binary64_830` `pow-to-exp_binary64_817` `pow-pow_binary64_820` `frac-2neg_binary64_762` `cbrt-div_binary64_780` `clear-num_binary64_750`

Counts

3 → 125

Calls

3 calls:

18.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3))
17.0ms	(pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3)
13.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))

series342.0ms (7.7%)

Counts

3 → 9

Calls

3 calls:

136.0ms	(pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3)
111.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3))
96.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))

simplify104.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4970	2554
1	4970	2554

prune215.0ms (4.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	134	3	137

Merged error: 0b

Counts

137 → 3

Compiler

Compiled 2187 to 1333 computations (39% saved)

regimes82.0ms (1.8%)

Compiler: Compiled 100 to 78 computations (22% saved)

bsearch44.0ms (1%)

Steps

Iters	Range		Point
8	1.3787683654321679	38690.63582523804	399.4443248046047
7	-6525643.746599448	-121719.5481580111	-1137686.7161830382

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	62
1	40	62

end0.0ms (0%)

sample750.0ms (16.9%)

Algorithm

1×

intervals

Results

333.0ms

8000×

body

128

valid

Compiler

Compiled 98 to 77 computations (21.4% saved)

Details

analyze2.0ms (0.1%)

sample17.0ms (0.4%)

simplify293.0ms (6.6%)

prune8.0ms (0.2%)

localize8.0ms (0.2%)

rewrite16.0ms (0.4%)

series95.0ms (2.1%)

simplify100.0ms (2.3%)

prune69.0ms (1.6%)

localize15.0ms (0.3%)

rewrite125.0ms (2.8%)

series365.0ms (8.2%)

simplify206.0ms (4.6%)

prune329.0ms (7.4%)

localize18.0ms (0.4%)

rewrite169.0ms (3.8%)

series448.0ms (10.1%)

simplify152.0ms (3.4%)

prune384.0ms (8.6%)

localize15.0ms (0.3%)

rewrite72.0ms (1.6%)

series342.0ms (7.7%)

simplify104.0ms (2.3%)

prune215.0ms (4.8%)

regimes82.0ms (1.8%)

bsearch44.0ms (1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample750.0ms (16.9%)

Profiling