Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	55×	body	512	valid
7.0ms	146×	body	128	valid
4.0ms	45×	body	256	valid
2.0ms	10×	body	1024	valid

Compiler

Compiled 19 to 18 computations (5.3% saved)

simplify167.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	73	13
1	73	13

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.6b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
3.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64_737`
46×	`add-sqr-sqrt_binary64_759`
45×	`times-frac_binary64_743`
22×	`add-cube-cbrt_binary64_772`
13×	`cancel-sign-sub-inv_binary64_703`
10×	`distribute-lft-out--_binary64_689`
9×	`difference-of-squares_binary64_706`
7×	`distribute-lft-out_binary64_688`
6×	`add-exp-log_binary64_775` `div-inv_binary64_734`
4×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776` `associate-/r*_binary64_681`
3×	`associate-/l*_binary64_682` `pow1_binary64_798`
2×	`associate-/r/_binary64_683` `div-exp_binary64_788`
1×	`diff-log_binary64_829` `flip3-+_binary64_740` `frac-2neg_binary64_748` `clear-num_binary64_736` `1-exp_binary64_781` `sub-neg_binary64_730` `inv-pow_binary64_822` `pow-flip_binary64_811` `flip3--_binary64_741` `cbrt-undiv_binary64_771` `flip-+_binary64_711` `flip--_binary64_712` `rec-exp_binary64_787` `frac-sub_binary64_746`

Counts

2 → 81

Calls

4 calls:

35.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
9.0ms	(/.f64 1 (+.f64 x 1))
0.0ms	(/.f64 1 (+.f64 x 1))
0.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series100.0ms (1.6%)

Counts

2 → 20

Calls

2 calls:

53.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
47.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 278 to 242 computations (12.9% saved)

simplify164.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4841	1454
1	4841	1454

prune175.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Error

0.0b

Counts

102 → 3

Compiler

Compiled 1452 to 1147 computations (21% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 -1 (*.f64 x (+.f64 1 x)))
0.0b	(*.f64 x (+.f64 1 x))
0.0b	(*.f64 x (+.f64 1 x))
0.2b	(/.f64 -1 (*.f64 x (+.f64 1 x)))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775`
8×	`add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
6×	`add-cube-cbrt_binary64_772`
4×	`pow1_binary64_798` `associate-r_binary64_677` `associate-*r/_binary64_679`
3×	`associate-/l_binary64_682` `associate-l*_binary64_678` `times-frac_binary64_743`
2×	`associate-/r/_binary64_683` `add-log-exp_binary64_776` `flip3-+_binary64_740` `cbrt-unprod_binary64_770` `prod-exp_binary64_786` `cbrt-undiv_binary64_771` `flip-+_binary64_711` `div-exp_binary64_788`
1×	`unswap-sqr_binary64_705` `distribute-lft-in_binary64_686` `frac-2neg_binary64_748` `clear-num_binary64_736` `associate-/r_binary64_681` `div-inv_binary64_734` `distribute-rgt-in_binary64_687` `distribute-lft-out_binary64_688` `pow-prod-down_binary64_808` `-commutative_binary64_668`

Counts

2 → 46

Calls

4 calls:

15.0ms	(/.f64 -1 (*.f64 x (+.f64 1 x)))
12.0ms	(*.f64 x (+.f64 1 x))
0.0ms	(*.f64 x (+.f64 1 x))
0.0ms	(/.f64 -1 (*.f64 x (+.f64 1 x)))

series132.0ms (2.1%)

Counts

2 → 16

Calls

2 calls:

76.0ms	(*.f64 x (+.f64 1 x))
56.0ms	(/.f64 -1 (*.f64 x (+.f64 1 x)))

Compiler

Compiled 182 to 163 computations (10.4% saved)

simplify131.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4927	677
1	4927	677

prune105.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	58	4	62
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	60	5	65

Error

0.0b

Counts

65 → 5

Compiler

Compiled 710 to 519 computations (26.9% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (/.f64 -1 x) (+.f64 1 x))
0.1b	(/.f64 (/.f64 -1 x) (+.f64 1 x))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary64_743`
78×	`*-un-lft-identity_binary64_737`
50×	`add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759`
14×	`distribute-lft-out_binary64_688`
13×	`associate-/l*_binary64_682`
6×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775` `div-inv_binary64_734`
4×	`associate-/r*_binary64_681`
3×	`cbrt-undiv_binary64_771` `div-exp_binary64_788`
2×	`associate-/r/_binary64_683`
1×	`add-log-exp_binary64_776` `flip3-+_binary64_740` `frac-2neg_binary64_748` `clear-num_binary64_736` `pow1_binary64_798` `flip-+_binary64_711` `associate-/l/_binary64_684`

Counts

1 → 86

Calls

2 calls:

14.0ms	(/.f64 (/.f64 -1 x) (+.f64 1 x))
0.0ms	(/.f64 (/.f64 -1 x) (+.f64 1 x))

series48.0ms (0.8%)

Counts

1 → 10

Calls

1 calls:

48.0ms

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

Compiler

Compiled 127 to 114 computations (10.2% saved)

simplify154.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4907	1978
1	4907	1978

prune163.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	94	7	101

Error

Counts

101 → 7

Compiler

Compiled 1580 to 1131 computations (28.4% saved)

localize28.0ms (0.5%)

Local error

Found 8 expressions with local error:

0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(cbrt.f64 (+.f64 x 1))
0.2b	(/.f64 (cbrt.f64 (/.f64 -1 x)) (cbrt.f64 (+.f64 x 1)))
0.1b	(/.f64 (.f64 (cbrt.f64 (/.f64 -1 x)) (cbrt.f64 (/.f64 -1 x))) (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))
0.5b	(*.f64 (cbrt.f64 (/.f64 -1 x)) (cbrt.f64 (/.f64 -1 x)))
0.6b	(cbrt.f64 (/.f64 -1 x))
0.6b	(cbrt.f64 (/.f64 -1 x))
0.6b	(cbrt.f64 (/.f64 -1 x))

rewrite81.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`cbrt-prod_binary64_768`
81×	`add-sqr-sqrt_binary64_759`
69×	`times-frac_binary64_743`
57×	`add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
16×	`swap-sqr_binary64_704` `associate-l_binary64_678` `associate-r_binary64_677`
11×	`pow1_binary64_798`
9×	`pow1/3_binary64_819` `unswap-sqr_binary64_705`
7×	`cbrt-div_binary64_769` `div-inv_binary64_734`
6×	`add-exp-log_binary64_775`
4×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776`
2×	`pow-prod-up_binary64_807` `pow-sqr_binary64_710` `pow-prod-down_binary64_808`
1×	`frac-times_binary64_747` `cbrt-unprod_binary64_770` `prod-exp_binary64_786` `associate-l/_binary64_680` `pow2_binary64_818` `pow-plus_binary64_800` `-commutative_binary64_668` `associate-*r/_binary64_679`

Counts

4 → 144

Calls

8 calls:

31.0ms	(*.f64 (cbrt.f64 (/.f64 -1 x)) (cbrt.f64 (/.f64 -1 x)))
5.0ms	(cbrt.f64 (/.f64 -1 x))
5.0ms	(cbrt.f64 (/.f64 -1 x))
4.0ms	(cbrt.f64 (/.f64 -1 x))
0.0ms	(/.f64 (.f64 (cbrt.f64 (/.f64 -1 x)) (cbrt.f64 (/.f64 -1 x))) (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))

series696.0ms (11.2%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(*.f64 (cbrt.f64 (/.f64 -1 x)) (cbrt.f64 (/.f64 -1 x)))
175.0ms	(cbrt.f64 (/.f64 -1 x))
169.0ms	(cbrt.f64 (/.f64 -1 x))
157.0ms	(cbrt.f64 (/.f64 -1 x))

Compiler

Compiled 758 to 644 computations (15% saved)

simplify128.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5040	2446

prune551.0ms (8.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	156	7	163

Error

Counts

163 → 7

Compiler

Compiled 5448 to 4285 computations (21.3% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	146	353
1	146	353

regimes67.0ms (1.1%)

Accuracy

Total 0.1b remaining (91.8%)

Threshold costs 0.1b (91.8%)

Compiler

Compiled 239 to 205 computations (14.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample3.1s (50%)

Algorithm

1×

intervals

Results

270.0ms	1948×	body	512	valid
230.0ms	4600×	body	128	valid
96.0ms	1035×	body	256	valid
76.0ms	417×	body	1024	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 735 to 631 computations (14.1% saved)

Pareto

0.5851147235797718

Details

analyze9.0ms (0.1%)

sample30.0ms (0.5%)

simplify167.0ms (2.7%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

rewrite56.0ms (0.9%)

series100.0ms (1.6%)

simplify164.0ms (2.6%)

prune175.0ms (2.8%)

localize9.0ms (0.2%)

rewrite34.0ms (0.5%)

series132.0ms (2.1%)

simplify131.0ms (2.1%)

prune105.0ms (1.7%)

localize9.0ms (0.1%)

rewrite31.0ms (0.5%)

series48.0ms (0.8%)

simplify154.0ms (2.5%)

prune163.0ms (2.6%)

localize28.0ms (0.5%)

rewrite81.0ms (1.3%)

series696.0ms (11.2%)

simplify128.0ms (2.1%)

prune551.0ms (8.9%)

simplify13.0ms (0.2%)

regimes67.0ms (1.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.1s (50%)

Profiling