Details

analyze223.0ms (4.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample66.0ms (1.2%)

Algorithm

1×

intervals

Results

32.0ms	68×	body	1024	valid
12.0ms	143×	body	128	valid
5.0ms	22×	body	512	valid
3.0ms	4×	body	2048	valid
3.0ms	19×	body	256	valid
1.0ms	2×	body	1024	invalid
1.0ms	7×	body	128	invalid
0.0ms	5×	body	128	overflowed

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify223.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4933	41
1	4933	41

prune10.0ms (0.2%)

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

Merged error: 27.5b

Counts

2 → 1

Compiler

Compiled 112 to 96 computations (14.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(*.f64 (+.f64 1 eps) x)
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite70.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_776`
74×	`exp-neg_binary64_814`
72×	`frac-times_binary64_777`
56×	`exp-diff_binary64_815` `neg-sub0_binary64_762`
38×	`associate-*l/_binary64_710`
36×	`associate-*r/_binary64_709`
28×	`flip-+_binary64_741` `flip3-+_binary64_770` `flip--_binary64_742` `flip3--_binary64_771`
18×	`un-div-inv_binary64_765`
12×	`exp-prod_binary64_819`
10×	`add-log-exp_binary64_806` `add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767`
8×	`add-cube-cbrt_binary64_802`
6×	`add-exp-log_binary64_805` `pow1_binary64_828` `add-cbrt-cube_binary64_803`
4×	`associate-l_binary64_708` `rem-exp-log_binary64_807`
3×	`associate-r_binary64_707`
2×	`neg-mul-1_binary64_763` `neg-log_binary64_860` `distribute-lft-neg-in_binary64_724` `distribute-rgt-neg-in_binary64_725`
1×	`unswap-sqr_binary64_735` `distribute-lft-out_binary64_718` `cbrt-unprod_binary64_800` `sub-neg_binary64_760` `prod-exp_binary64_816` `*-commutative_binary64_698` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `pow-prod-down_binary64_838`

Counts

4 → 148

Calls

4 calls:

23.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
7.0ms	(*.f64 (+.f64 1 eps) x)
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

series367.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
40.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
33.0ms	(*.f64 (+.f64 1 eps) x)
31.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

simplify120.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4990	8219
1	4990	8219

prune844.0ms (15.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	158	3	161

Merged error: 0.3b

Counts

161 → 3

Compiler

Compiled 15500 to 12323 computations (20.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)
0.1b	(*.f64 (pow.f64 x 3) 2/3)
7.4b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_789`
12×	`associate-l_binary64_708`
10×	`add-log-exp_binary64_806`
8×	`add-exp-log_binary64_805`
7×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
5×	`add-cbrt-cube_binary64_803`
4×	`unswap-sqr_binary64_735` `cube-prod_binary64_795` `unpow-prod-down_binary64_846`
3×	`associate-r_binary64_707` `prod-exp_binary64_816` `pow1_binary64_828`
2×	`sqr-pow_binary64_739` `diff-log_binary64_859` `sum-log_binary64_858`
1×	`pow-to-exp_binary64_836` `cbrt-unprod_binary64_800` `pow-exp_binary64_835` `sub-neg_binary64_760` `*-commutative_binary64_698` `flip-+_binary64_741` `cancel-sign-sub-inv_binary64_733` `cube-mult_binary64_797` `+-commutative_binary64_697` `flip3-+_binary64_770` `flip--_binary64_742` `unpow3_binary64_833` `flip3--_binary64_771` `difference-of-squares_binary64_736` `associate--l+_binary64_704`

Counts

3 → 57

Calls

3 calls:

9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
7.0ms	(*.f64 (pow.f64 x 3) 2/3)
6.0ms	(+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)

series188.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

103.0ms	(+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)
47.0ms	(*.f64 (pow.f64 x 3) 2/3)
37.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5212	871

prune95.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	65	4	69

Merged error: 0.3b

Counts

69 → 4

Compiler

Compiled 1724 to 1333 computations (22.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
7.4b	(+.f64 (.f64 (pow.f64 x 3) 2/3) (-.f64 2 (.f64 x x)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_789`
12×	`associate-l_binary64_708`
7×	`add-exp-log_binary64_805` `add-log-exp_binary64_806`
6×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
4×	`unswap-sqr_binary64_735` `cube-prod_binary64_795` `unpow-prod-down_binary64_846` `add-cbrt-cube_binary64_803`
3×	`associate-r_binary64_707` `prod-exp_binary64_816`
2×	`sqr-pow_binary64_739` `pow1_binary64_828` `sum-log_binary64_858` `associate-+r+_binary64_699`
1×	`pow-to-exp_binary64_836` `cbrt-unprod_binary64_800` `pow-exp_binary64_835` `sub-neg_binary64_760` `associate-+r-_binary64_701` `*-commutative_binary64_698` `flip-+_binary64_741` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `cube-mult_binary64_797` `+-commutative_binary64_697` `flip3-+_binary64_770` `unpow3_binary64_833`

Counts

2 → 46

Calls

2 calls:

8.0ms	(+.f64 (.f64 (pow.f64 x 3) 2/3) (-.f64 2 (.f64 x x)))
7.0ms	(*.f64 (pow.f64 x 3) 2/3)

series83.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(*.f64 (pow.f64 x 3) 2/3)
37.0ms	(+.f64 (.f64 (pow.f64 x 3) 2/3) (-.f64 2 (.f64 x x)))

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5183	659

prune53.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	52	4	56

Merged error: 0.3b

Counts

56 → 4

Compiler

Compiled 985 to 717 computations (27.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)))
0.1b	(.f64 (.f64 (pow.f64 x 3) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3))
1.0b	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))
7.4b	(-.f64 (+.f64 (.f64 (.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) 2) (.f64 x x))

rewrite62.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64_805`
29×	`add-sqr-sqrt_binary64_789`
26×	`prod-exp_binary64_816`
19×	`associate-l_binary64_708` `cbrt-prod_binary64_798`
17×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
13×	`associate-r_binary64_707` `pow1_binary64_828`
11×	`add-cbrt-cube_binary64_803`
10×	`cbrt-unprod_binary64_800`
9×	`add-log-exp_binary64_806`
8×	`unswap-sqr_binary64_735`
6×	`pow1/3_binary64_849` `swap-sqr_binary64_734`
4×	`pow-to-exp_binary64_836` `cube-prod_binary64_795` `pow-exp_binary64_835` `unpow-prod-down_binary64_846`
3×	`*-commutative_binary64_698` `pow-prod-down_binary64_838`
2×	`sqr-pow_binary64_739` `pow-prod-up_binary64_837` `diff-log_binary64_859` `pow-sqr_binary64_740`
1×	`pow2_binary64_848` `pow-plus_binary64_830` `sub-neg_binary64_760` `cancel-sign-sub-inv_binary64_733` `cube-mult_binary64_797` `sum-log_binary64_858` `flip--_binary64_742` `unpow3_binary64_833` `flip3--_binary64_771` `difference-of-squares_binary64_736` `associate--l+_binary64_704`

Counts

4 → 114

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (.f64 (.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) 2) (.f64 x x))
14.0ms	(.f64 (.f64 (pow.f64 x 3) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3))
11.0ms	(.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)))
7.0ms	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))

series264.0ms (4.9%)

Counts

4 → 10

Calls

4 calls:

110.0ms	(.f64 (.f64 (pow.f64 x 3) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3))
97.0ms	(.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)))
57.0ms	(-.f64 (+.f64 (.f64 (.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) 2) (.f64 x x))
0.0ms	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4890	1428
1	4890	1428

prune194.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	124	4	128

Merged error: 0.3b

Counts

128 → 4

Compiler

Compiled 3261 to 2629 computations (19.4% saved)

regimes97.0ms (1.8%)

Compiler: Compiled 556 to 472 computations (15.1% saved)

bsearch90.0ms (1.7%)

Steps

Iters	Range		Point
10	2.0717416958964465e-05	435548.6755890104	27.34141034853695

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	187	66
1	187	66

end0.0ms (0%)

sample2.1s (38.4%)

Algorithm

1×

intervals

Results

865.0ms	2002×	body	1024	valid
341.0ms	4223×	body	128	valid
255.0ms	1034×	body	512	valid
156.0ms	214×	body	2048	valid
81.0ms	527×	body	256	valid
19.0ms	223×	body	128	invalid
13.0ms	176×	body	128	overflowed
10.0ms	24×	body	1024	invalid
3.0ms	11×	body	512	invalid
1.0ms	7×	body	256	invalid

Compiler

Compiled 184 to 156 computations (15.2% saved)

Details

analyze223.0ms (4.1%)

sample66.0ms (1.2%)

simplify223.0ms (4.1%)

prune10.0ms (0.2%)

localize17.0ms (0.3%)

rewrite70.0ms (1.3%)

series367.0ms (6.8%)

simplify120.0ms (2.2%)

prune844.0ms (15.6%)

localize8.0ms (0.1%)

rewrite27.0ms (0.5%)

series188.0ms (3.5%)

simplify72.0ms (1.3%)

prune95.0ms (1.8%)

localize8.0ms (0.1%)

rewrite18.0ms (0.3%)

series83.0ms (1.5%)

simplify54.0ms (1%)

prune53.0ms (1%)

localize11.0ms (0.2%)

rewrite62.0ms (1.1%)

series264.0ms (4.9%)

simplify68.0ms (1.3%)

prune194.0ms (3.6%)

regimes97.0ms (1.8%)

bsearch90.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (38.4%)

Profiling