Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify171.0ms (7.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

prune2.0ms (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: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite57.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_3110`
41×	`times-frac_binary64_3116`
40×	`add-sqr-sqrt_binary64_3131`
24×	`add-cube-cbrt_binary64_3142`
12×	`distribute-lft-out_binary64_3063`
11×	`associate-/r*_binary64_3056`
9×	`add-exp-log_binary64_3145`
8×	`difference-of-squares_binary64_3079`
7×	`add-cbrt-cube_binary64_3143`
6×	`distribute-lft-out--_binary64_3064` `associate-/l*_binary64_3057`
5×	`add-log-exp_binary64_3146`
4×	`difference-of-sqr-1_binary64_3080` `pow1_binary64_3168` `associate-/r/_binary64_3058`
3×	`div-exp_binary64_3158` `div-inv_binary64_3107`
2×	`cbrt-undiv_binary64_3141` `clear-num_binary64_3109` `flip3-+_binary64_3113` `frac-2neg_binary64_3121` `flip-+_binary64_3084`
1×	`frac-add_binary64_3118` `+-commutative_binary64_3042` `1-exp_binary64_3151` `rec-exp_binary64_3157` `inv-pow_binary64_3192` `sum-log_binary64_3198` `pow-flip_binary64_3181` `flip3--_binary64_3114` `flip--_binary64_3085`

Counts

3 → 100

Calls

3 calls:

34.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

series103.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

59.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
25.0ms	(/.f64 x (+.f64 x 1))
20.0ms	(/.f64 1 (-.f64 x 1))

simplify63.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5076	1579

prune102.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	3	110

Merged error: 0b

Counts

110 → 3

Compiler

Compiled 1893 to 1391 computations (26.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite79.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`*-un-lft-identity_binary64_3110`
40×	`times-frac_binary64_3116`
28×	`distribute-lft-out_binary64_3063`
23×	`add-cube-cbrt_binary64_3142` `add-sqr-sqrt_binary64_3131`
10×	`add-exp-log_binary64_3145`
9×	`exp-prod_binary64_3159` `add-log-exp_binary64_3146`
8×	`associate-/r*_binary64_3056` `add-cbrt-cube_binary64_3143`
6×	`associate-/l*_binary64_3057`
5×	`pow1_binary64_3168`
4×	`associate-/r/_binary64_3058` `div-inv_binary64_3107`
3×	`div-exp_binary64_3158` `flip3-+_binary64_3113` `flip-+_binary64_3084`
2×	`cbrt-undiv_binary64_3141` `clear-num_binary64_3109` `sum-log_binary64_3198` `frac-2neg_binary64_3121` `rem-exp-log_binary64_3147`
1×	`frac-add_binary64_3118` `+-commutative_binary64_3042` `exp-sum_binary64_3153` `1-exp_binary64_3151` `rec-exp_binary64_3157` `inv-pow_binary64_3192` `pow-flip_binary64_3181`

Counts

4 → 107

Calls

4 calls:

29.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
28.0ms	(exp.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))
6.0ms	(/.f64 x (+.f64 1 x))
6.0ms	(/.f64 1 (+.f64 -1 x))

series196.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(exp.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))))
57.0ms	(+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x)))
26.0ms	(/.f64 x (+.f64 1 x))
18.0ms	(/.f64 1 (+.f64 -1 x))

simplify69.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4967	1686
1	4967	1686

prune123.0ms (5.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	119	3	122

Merged error: 0b

Counts

122 → 3

Compiler

Compiled 2235 to 1710 computations (23.5% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 -1 x))
0.0b	(+.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3)) (/.f64 x (+.f64 x 1)))
0.1b	(pow.f64 (/.f64 1 (+.f64 -1 x)) 3)
19.5b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3))

rewrite94.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64_3110`
60×	`times-frac_binary64_3116`
47×	`add-cube-cbrt_binary64_3142` `add-sqr-sqrt_binary64_3131`
42×	`cbrt-prod_binary64_3138`
36×	`cube-prod_binary64_3135` `unpow-prod-down_binary64_3186`
17×	`distribute-lft-out_binary64_3063`
13×	`add-exp-log_binary64_3145`
10×	`associate-/r/_binary64_3058`
9×	`add-cbrt-cube_binary64_3143`
7×	`pow1_binary64_3168`
6×	`add-log-exp_binary64_3146` `flip3-+_binary64_3113` `flip-+_binary64_3084`
5×	`div-inv_binary64_3107`
4×	`div-exp_binary64_3158` `pow-exp_binary64_3175` `associate-/r*_binary64_3056`
3×	`cube-div_binary64_3136` `pow-pow_binary64_3179` `pow-unpow_binary64_3184` `associate-/l*_binary64_3057`
2×	`rem-cube-cbrt_binary64_3132` `cbrt-undiv_binary64_3141` `1-exp_binary64_3151` `rec-exp_binary64_3157` `cbrt-div_binary64_3139` `inv-pow_binary64_3192` `pow-flip_binary64_3181` `unpow3_binary64_3173` `sqr-pow_binary64_3082` `cube-mult_binary64_3137`
1×	`frac-add_binary64_3118` `+-commutative_binary64_3042` `clear-num_binary64_3109` `sum-log_binary64_3198` `pow1/3_binary64_3189` `rem-cbrt-cube_binary64_3133` `frac-2neg_binary64_3121` `pow-to-exp_binary64_3176`

Counts

4 → 162

Calls

4 calls:

49.0ms	(+.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3)) (/.f64 x (+.f64 x 1)))
11.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3))
9.0ms	(pow.f64 (/.f64 1 (+.f64 -1 x)) 3)
6.0ms	(/.f64 1 (+.f64 -1 x))

series113.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(+.f64 (cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3)) (/.f64 x (+.f64 x 1)))
22.0ms	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 -1 x)) 3))
22.0ms	(pow.f64 (/.f64 1 (+.f64 -1 x)) 3)
16.0ms	(/.f64 1 (+.f64 -1 x))

simplify75.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5084	2384

prune187.0ms (7.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	174	3	177

Merged error: 0b

Counts

177 → 3

Compiler

Compiled 3150 to 2472 computations (21.5% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 1 (+.f64 -1 x))
0.0b	(+.f64 (log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x)))) (/.f64 x (+.f64 x 1)))
3.5b	(log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x))))

rewrite63.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64_3110`
36×	`times-frac_binary64_3116`
32×	`add-cube-cbrt_binary64_3142` `add-sqr-sqrt_binary64_3131`
20×	`log-pow_binary64_3196`
18×	`exp-prod_binary64_3159`
13×	`distribute-lft-out_binary64_3063`
10×	`add-exp-log_binary64_3145`
8×	`associate-/r*_binary64_3056` `add-cbrt-cube_binary64_3143`
7×	`pow1_binary64_3168`
6×	`associate-/r/_binary64_3058` `log-prod_binary64_3193` `associate-/l*_binary64_3057`
5×	`add-log-exp_binary64_3146`
4×	`flip3-+_binary64_3113` `flip-+_binary64_3084`
3×	`div-exp_binary64_3158` `associate-+l+_binary64_3045` `div-inv_binary64_3107`
2×	`cbrt-undiv_binary64_3141` `clear-num_binary64_3109` `frac-2neg_binary64_3121`
1×	`+-commutative_binary64_3042` `1-exp_binary64_3151` `rec-exp_binary64_3157` `inv-pow_binary64_3192` `sum-log_binary64_3198` `pow-flip_binary64_3181` `rem-log-exp_binary64_3148`

Counts

4 → 116

Calls

4 calls:

33.0ms	(+.f64 (log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x)))) (/.f64 x (+.f64 x 1)))
9.0ms	(log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x))))
6.0ms	(/.f64 1 (+.f64 -1 x))
5.0ms	(/.f64 x (+.f64 x 1))

series181.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(+.f64 (log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x)))) (/.f64 x (+.f64 x 1)))
33.0ms	(log.f64 (exp.f64 (/.f64 1 (+.f64 -1 x))))
24.0ms	(/.f64 x (+.f64 x 1))
16.0ms	(/.f64 1 (+.f64 -1 x))

simplify105.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4910	1699
1	4910	1699

prune130.0ms (5.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	128	3	131

Merged error: 0b

Counts

131 → 3

Compiler

Compiled 2366 to 1814 computations (23.3% saved)

regimes12.0ms (0.5%)

Compiler: Compiled 42 to 36 computations (14.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	20
1	15	20

end0.0ms (0%)

sample418.0ms (17.4%)

Algorithm

1×

intervals

Results

232.0ms

8000×

body

128

valid

Compiler

Compiled 65 to 56 computations (13.8% saved)

Details

analyze4.0ms (0.2%)

sample12.0ms (0.5%)

simplify171.0ms (7.1%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

rewrite57.0ms (2.4%)

series103.0ms (4.3%)

simplify63.0ms (2.6%)

prune102.0ms (4.3%)

localize10.0ms (0.4%)

rewrite79.0ms (3.3%)

series196.0ms (8.2%)

simplify69.0ms (2.9%)

prune123.0ms (5.1%)

localize9.0ms (0.4%)

rewrite94.0ms (3.9%)

series113.0ms (4.7%)

simplify75.0ms (3.1%)

prune187.0ms (7.8%)

localize12.0ms (0.5%)

rewrite63.0ms (2.6%)

series181.0ms (7.5%)

simplify105.0ms (4.4%)

prune130.0ms (5.4%)

regimes12.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample418.0ms (17.4%)

Profiling