Details

analyze362.0ms (5.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5348	82
0	2	2
1	2	2

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)

sample58.0ms (0.9%)

Algorithm

1×

intervals

Results

21.0ms	56×	body	1024	valid
10.0ms	141×	body	128	valid
8.0ms	36×	body	512	valid
6.0ms	9×	body	2048	valid
2.0ms	14×	body	256	valid
1.0ms	7×	body	128	invalid
1.0ms	7×	body	128	overflowed

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5212	41

prune7.0ms (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

Merged error: 28.5b

Counts

2 → 1

Compiler

Compiled 56 to 48 computations (14.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(*.f64 (-.f64 1 eps) x)
0.0b	(*.f64 (+.f64 1 eps) x)
2.5b	(-.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)))))

rewrite82.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_769`
76×	`exp-neg_binary64_807` `frac-times_binary64_770`
57×	`exp-diff_binary64_808` `neg-sub0_binary64_755`
42×	`associate-*l/_binary64_703`
38×	`associate-*r/_binary64_702`
34×	`add-sqr-sqrt_binary64_782`
32×	`flip--_binary64_735` `flip3--_binary64_764`
28×	`flip3-+_binary64_763` `flip-+_binary64_734`
24×	`-un-lft-identity_binary64_760` `associate-l*_binary64_701`
19×	`un-div-inv_binary64_758`
10×	`add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
9×	`add-exp-log_binary64_798` `associate-r_binary64_700`
8×	`difference-of-squares_binary64_729`
6×	`add-log-exp_binary64_799` `times-frac_binary64_766`
3×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`diff-log_binary64_852` `distribute-lft-out_binary64_711` `cancel-sign-sub-inv_binary64_726` `div-inv_binary64_757` `sub-neg_binary64_753`

Counts

4 → 175

Calls

4 calls:

19.0ms	(-.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)))))
15.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
7.0ms	(*.f64 (-.f64 1 eps) x)
7.0ms	(*.f64 (+.f64 1 eps) x)

series196.0ms (3%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(-.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)))))
36.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
22.0ms	(*.f64 (-.f64 1 eps) x)
16.0ms	(*.f64 (+.f64 1 eps) x)

simplify180.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4978	8961
1	4978	8961

prune593.0ms (9.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	3	188

Merged error: 1.0b

Counts

188 → 3

Compiler

Compiled 8635 to 6654 computations (22.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
6.0b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_782`
12×	`associate-l_binary64_701`
7×	`add-exp-log_binary64_798` `add-log-exp_binary64_799`
6×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
4×	`unswap-sqr_binary64_728` `add-cbrt-cube_binary64_796` `cube-prod_binary64_788` `unpow-prod-down_binary64_839`
3×	`prod-exp_binary64_809` `associate-r_binary64_700`
2×	`diff-log_binary64_852` `sqr-pow_binary64_732` `pow1_binary64_821`
1×	`cube-mult_binary64_790` `unpow3_binary64_826` `cancel-sign-sub-inv_binary64_726` `pow-exp_binary64_828` `difference-of-squares_binary64_729` `pow-to-exp_binary64_829` `sum-log_binary64_851` `cbrt-unprod_binary64_793` `associate--l+_binary64_697` `sub-neg_binary64_753` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

2 → 46

Calls

2 calls:

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

series41.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

22.0ms	(*.f64 (pow.f64 x 3) 2/3)
19.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4879	687
1	4879	687

prune63.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	48	4	52
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	49	6	55

Merged error: 1.0b

Counts

55 → 6

Compiler

Compiled 1119 to 838 computations (25.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 x 2/3)
6.0b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 x 2/3)) 2) (.f64 x x))
42.6b	(cbrt.f64 (pow.f64 x 3))
42.6b	(cbrt.f64 (pow.f64 x 3))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_791`
15×	`add-sqr-sqrt_binary64_782`
12×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
9×	`add-log-exp_binary64_799`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `cube-prod_binary64_788` `pow1_binary64_821` `unpow-prod-down_binary64_839`
3×	`associate-r_binary64_700` `associate-l_binary64_701`
2×	`pow1/3_binary64_842` `cube-mult_binary64_790` `rem-cbrt-cube_binary64_784` `diff-log_binary64_852` `unpow3_binary64_826` `sqr-pow_binary64_732`
1×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `cancel-sign-sub-inv_binary64_726` `difference-of-squares_binary64_729` `sum-log_binary64_851` `cbrt-unprod_binary64_793` `associate--l+_binary64_697` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 75

Calls

4 calls:

20.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 x 2/3)) 2) (.f64 x x))
4.0ms	(*.f64 x 2/3)
3.0ms	(cbrt.f64 (pow.f64 x 3))
2.0ms	(cbrt.f64 (pow.f64 x 3))

series62.0ms (1%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 x 2/3)) 2) (.f64 x x))
13.0ms	(cbrt.f64 (pow.f64 x 3))
11.0ms	(cbrt.f64 (pow.f64 x 3))
10.0ms	(*.f64 x 2/3)

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	6109	767

prune108.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 1.0b

Counts

93 → 6

Compiler

Compiled 2149 to 1487 computations (30.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))
6.0b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 (.f64 x (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3))) 2) (.f64 x x))
42.6b	(cbrt.f64 (pow.f64 x 3))
42.6b	(cbrt.f64 (pow.f64 x 3))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`cbrt-prod_binary64_791`
27×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
11×	`pow1_binary64_821`
9×	`add-log-exp_binary64_799`
8×	`pow1/3_binary64_842`
6×	`add-exp-log_binary64_798` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701` `cube-prod_binary64_788` `unpow-prod-down_binary64_839`
4×	`unswap-sqr_binary64_728` `add-cbrt-cube_binary64_796`
2×	`cube-mult_binary64_790` `rem-cbrt-cube_binary64_784` `diff-log_binary64_852` `unpow3_binary64_826` `pow-sqr_binary64_733` `sqr-pow_binary64_732` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831`
1×	`pow2_binary64_841` `prod-exp_binary64_809` `cancel-sign-sub-inv_binary64_726` `pow-plus_binary64_823` `difference-of-squares_binary64_729` `sum-log_binary64_851` `cbrt-unprod_binary64_793` `associate--l+_binary64_697` `sub-neg_binary64_753` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 97

Calls

4 calls:

25.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 (.f64 x (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3))) 2) (.f64 x x))
6.0ms	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))
2.0ms	(cbrt.f64 (pow.f64 x 3))
2.0ms	(cbrt.f64 (pow.f64 x 3))

series67.0ms (1%)

Counts

4 → 10

Calls

4 calls:

45.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 x 3)) (cbrt.f64 (pow.f64 x 3))) (.f64 (.f64 x (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3))) 2) (.f64 x x))
11.0ms	(cbrt.f64 (pow.f64 x 3))
11.0ms	(cbrt.f64 (pow.f64 x 3))
0.0ms	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4927	1013
1	4927	1013

prune176.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	107	6	113

Merged error: 1.0b

Counts

113 → 6

Compiler

Compiled 3100 to 2362 computations (23.8% saved)

regimes551.0ms (8.5%)

Compiler: Compiled 8188 to 6776 computations (17.2% saved)

bsearch84.0ms (1.3%)

Steps

Iters	Range		Point
10	0.4521184382831142	727311487548.9751	328.7748566827125

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	251	99
1	251	99

end0.0ms (0%)

sample3.4s (52.6%)

Algorithm

1×

intervals

Results

782.0ms	1976×	body	1024	valid
328.0ms	4308×	body	128	valid
236.0ms	1013×	body	512	valid
137.0ms	201×	body	2048	valid
74.0ms	502×	body	256	valid
20.0ms	221×	body	128	invalid
13.0ms	183×	body	128	overflowed
13.0ms	27×	body	1024	invalid
3.0ms	13×	body	512	invalid
0.0ms	2×	body	256	invalid

Compiler

Compiled 2112 to 1747 computations (17.3% saved)

Details

analyze362.0ms (5.6%)

sample58.0ms (0.9%)

simplify71.0ms (1.1%)

prune7.0ms (0.1%)

localize17.0ms (0.3%)

rewrite82.0ms (1.3%)

series196.0ms (3%)

simplify180.0ms (2.8%)

prune593.0ms (9.2%)

localize7.0ms (0.1%)

rewrite20.0ms (0.3%)

series41.0ms (0.6%)

simplify58.0ms (0.9%)

prune63.0ms (1%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series62.0ms (1%)

simplify67.0ms (1%)

prune108.0ms (1.7%)

localize15.0ms (0.2%)

rewrite48.0ms (0.7%)

series67.0ms (1%)

simplify68.0ms (1.1%)

prune176.0ms (2.7%)

regimes551.0ms (8.5%)

bsearch84.0ms (1.3%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample3.4s (52.6%)

Profiling