Details

analyze396.0ms (14.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample26.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms	87×	body	1024	valid
3.0ms	42×	body	512	valid
2.0ms	101×	body	128	valid
1.0ms	21×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune2.0ms (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: 41.2b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.7b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.7b	(-.f64 (exp.f64 x) 1)

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_782`
30×	`*-un-lft-identity_binary64_760`
21×	`times-frac_binary64_766`
15×	`add-cube-cbrt_binary64_795`
10×	`difference-of-squares_binary64_729`
7×	`associate-/r*_binary64_704`
5×	`difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712`
4×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `associate-/l*_binary64_705`
2×	`associate-/r/_binary64_706` `pow1_binary64_821` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

2 → 63

Calls

2 calls:

7.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.0ms	(-.f64 (exp.f64 x) 1)

series51.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

37.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
13.0ms	(-.f64 (exp.f64 x) 1)

simplify79.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4915	1129
1	4915	1129

prune70.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

Compiler

Compiled 981 to 490 computations (50.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
0.1b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.1b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.4b	(*.f64 x 1/6)

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
17×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
15×	`add-cbrt-cube_binary64_796`
14×	`add-exp-log_binary64_798`
13×	`pow1_binary64_821`
9×	`associate-l_binary64_701` `times-frac_binary64_766`
7×	`associate-r_binary64_700`
6×	`associate-*r/_binary64_702`
5×	`prod-exp_binary64_809` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
4×	`add-log-exp_binary64_799`
3×	`flip3-+_binary64_763` `associate-/r_binary64_704` `flip-+_binary64_734` `associate-/l_binary64_705` `*-commutative_binary64_691`
2×	`unswap-sqr_binary64_728` `associate-/r/_binary64_706`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 93

Calls

4 calls:

8.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
7.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)

series113.0ms (4%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
34.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
26.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
11.0ms	(*.f64 x 1/6)

simplify101.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4908	1844
1	4908	1844

prune102.0ms (3.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Merged error: 0b

Counts

109 → 4

Compiler

Compiled 2201 to 1369 computations (37.8% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
0.4b	(*.f64 x 1/12)

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_799`
6×	`add-sqr-sqrt_binary64_782`
4×	`*-un-lft-identity_binary64_760` `add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`associate-r_binary64_700` `sum-log_binary64_851` `associate-l_binary64_701`
1×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-+r+_binary64_692` `+-commutative_binary64_690` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

2 → 31

Calls

2 calls:

9.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
4.0ms	(*.f64 x 1/12)

series20.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

11.0ms	(*.f64 x 1/12)
9.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))

simplify85.0ms (3%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4872	417
1	4872	417

prune32.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	37	4	41

Merged error: 0b

Counts

41 → 4

Compiler

Compiled 542 to 430 computations (20.7% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (+.f64 (.f64 x 1/6) 1/2))
0.2b	(pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 (*.f64 x 1/6) 1/2))))) 3)
0.4b	(*.f64 x 1/6)
26.2b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 (*.f64 x 1/6) 1/2))))) 3))

rewrite39.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_782`
38×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
36×	`cbrt-prod_binary64_791` `times-frac_binary64_766`
30×	`cube-prod_binary64_788` `unpow-prod-down_binary64_839`
11×	`add-cbrt-cube_binary64_796`
10×	`add-exp-log_binary64_798`
9×	`pow1_binary64_821`
8×	`associate-/r/_binary64_706`
6×	`associate-r_binary64_700` `associate-l_binary64_701`
5×	`flip3-+_binary64_763` `flip-+_binary64_734`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757`
3×	`pow-unpow_binary64_837`
2×	`cube-mult_binary64_790` `unswap-sqr_binary64_728` `prod-exp_binary64_809` `unpow3_binary64_826` `pow-exp_binary64_828` `rem-cube-cbrt_binary64_783` `cube-div_binary64_789` `associate-r/_binary64_702` `sqr-pow_binary64_732` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `-commutative_binary64_691`
1×	`pow1/3_binary64_842` `rem-cbrt-cube_binary64_784` `cbrt-undiv_binary64_794` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `pow-to-exp_binary64_829` `cbrt-div_binary64_792` `div-exp_binary64_811` `pow-pow_binary64_832`

Counts

4 → 136

Calls

4 calls:

7.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 (*.f64 x 1/6) 1/2))))) 3))
7.0ms	(pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 (*.f64 x 1/6) 1/2))))) 3)
7.0ms	(.f64 x (+.f64 (.f64 x 1/6) 1/2))
4.0ms	(*.f64 x 1/6)

series128.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 (*.f64 x 1/6) 1/2))))) 3)
37.0ms	(.f64 x (+.f64 (.f64 x 1/6) 1/2))
26.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 (*.f64 x 1/6) 1/2))))) 3))
10.0ms	(*.f64 x 1/6)

simplify90.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4993	4158
1	4993	4158

prune182.0ms (6.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	148	4	152

Merged error: 0b

Counts

152 → 4

Compiler

Compiled 3808 to 2512 computations (34% saved)

regimes104.0ms (3.7%)

Compiler: Compiled 1069 to 761 computations (28.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms (0%)

sample1.1s (38.6%)

Algorithm

1×

intervals

Results

375.0ms	2664×	body	1024	valid
102.0ms	1319×	body	512	valid
73.0ms	3023×	body	128	valid
49.0ms	305×	body	2048	valid
34.0ms	689×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 296 to 216 computations (27% saved)

Details

analyze396.0ms (14.1%)

sample26.0ms (0.9%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite16.0ms (0.6%)

series51.0ms (1.8%)

simplify79.0ms (2.8%)

prune70.0ms (2.5%)

localize9.0ms (0.3%)

rewrite32.0ms (1.1%)

series113.0ms (4%)

simplify101.0ms (3.6%)

prune102.0ms (3.6%)

localize8.0ms (0.3%)

rewrite14.0ms (0.5%)

series20.0ms (0.7%)

simplify85.0ms (3%)

prune32.0ms (1.1%)

localize14.0ms (0.5%)

rewrite39.0ms (1.4%)

series128.0ms (4.5%)

simplify90.0ms (3.2%)

prune182.0ms (6.5%)

regimes104.0ms (3.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (38.6%)

Profiling