Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample13.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify96.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.3%)

Local error

Found 6 expressions with local error:

0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite27.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_3147`
26×	`add-sqr-sqrt_binary64_3169`
21×	`distribute-lft-out_binary64_3098`
18×	`times-frac_binary64_3153`
15×	`add-cube-cbrt_binary64_3182`
14×	`sqrt-prod_binary64_3163`
6×	`associate-/r*_binary64_3091`
5×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-log-exp_binary64_3186`
4×	`pow1_binary64_3208`
3×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `associate-/l*_binary64_3092`
2×	`associate-/r/_binary64_3093` `sqrt-div_binary64_3164`
1×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `rem-sqrt-square_binary64_3160` `+-commutative_binary64_3077` `cbrt-undiv_binary64_3181` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `div-exp_binary64_3198` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

3 → 71

Calls

6 calls:

8.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series63.0ms (3%)

Counts

3 → 13

Calls

3 calls:

35.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
14.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
13.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 236 to 200 computations (15.3% saved)

simplify91.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4842	1113
1	4842	1113

prune86.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	3	85

Error

Counts

85 → 3

Compiler

Compiled 1069 to 803 computations (24.9% saved)

localize7.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite47.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_3147`
51×	`add-sqr-sqrt_binary64_3169`
38×	`times-frac_binary64_3153`
33×	`distribute-lft-out_binary64_3098`
27×	`add-cube-cbrt_binary64_3182`
24×	`associate-r_binary64_3087`
20×	`sqrt-prod_binary64_3163`
17×	`add-exp-log_binary64_3185`
11×	`add-cbrt-cube_binary64_3183`
8×	`pow1_binary64_3208`
6×	`associate-/r*_binary64_3091` `add-log-exp_binary64_3186`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `prod-exp_binary64_3196` `div-exp_binary64_3198` `associate-/r/_binary64_3093`
3×	`unswap-sqr_binary64_3115` `associate-/l_binary64_3092` `associate-l*_binary64_3088`
2×	`cbrt-undiv_binary64_3181` `cbrt-unprod_binary64_3180` `1-exp_binary64_3191` `sqrt-div_binary64_3164` `rec-exp_binary64_3197` `div-inv_binary64_3144`
1×	`-commutative_binary64_3078` `clear-num_binary64_3146` `pow-prod-down_binary64_3218` `frac-2neg_binary64_3158` `inv-pow_binary64_3232` `rem-sqrt-square_binary64_3160` `+-commutative_binary64_3077` `pow-flip_binary64_3221` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `un-div-inv_binary64_3145` `associate-r/_binary64_3089` `sum-log_binary64_3238`

Counts

4 → 122

Calls

8 calls:

15.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

series97.0ms (4.7%)

Counts

4 → 19

Calls

4 calls:

37.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
25.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
18.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
16.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 403 to 346 computations (14.1% saved)

simplify94.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	6073	1773

prune125.0ms (6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	141	3	144

Error

Counts

144 → 3

Compiler

Compiled 2019 to 1663 computations (17.6% saved)

localize8.0ms (0.4%)

Local error

Found 8 expressions with local error:

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

rewrite62.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`*-un-lft-identity_binary64_3147`
92×	`add-sqr-sqrt_binary64_3169`
79×	`sqrt-prod_binary64_3163`
76×	`times-frac_binary64_3153`
57×	`distribute-lft-out_binary64_3098`
47×	`add-cube-cbrt_binary64_3182`
42×	`associate-r_binary64_3087`
11×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
7×	`pow1_binary64_3208`
6×	`unswap-sqr_binary64_3115` `associate-/r_binary64_3091` `add-log-exp_binary64_3186` `associate-/l_binary64_3092` `associate-l_binary64_3088`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `associate-/r/_binary64_3093`
2×	`prod-exp_binary64_3196` `cbrt-undiv_binary64_3181` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `sqrt-div_binary64_3164` `div-inv_binary64_3144`
1×	`-commutative_binary64_3078` `clear-num_binary64_3146` `pow-prod-down_binary64_3218` `frac-2neg_binary64_3158` `rem-sqrt-square_binary64_3160` `+-commutative_binary64_3077` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `associate-r/_binary64_3089` `sum-log_binary64_3238`

Counts

4 → 160

Calls

8 calls:

23.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

series106.0ms (5.1%)

Counts

4 → 14

Calls

4 calls:

44.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
38.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
12.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
12.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 412 to 323 computations (21.6% saved)

simplify90.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4939	2885
1	4939	2885

prune167.0ms (8.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	174	3	177

Error

Counts

177 → 3

Compiler

Compiled 3076 to 1918 computations (37.6% saved)

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	399
1	105	399

regimes71.0ms (3.4%)

Compiler: Compiled 532 to 444 computations (16.5% saved)

bsearch0.0ms (0%)

regimes20.0ms (1%)

Compiler: Compiled 39 to 38 computations (2.6% saved)

bsearch20.0ms (1%)

Steps

Iters	Range		Point
11	4.0458063928646034e-20	302.52702270046814	7.897555139426257e-06

Compiler

Compiled 1 to 1 computations (0% saved)

regimes12.0ms (0.6%)

Compiler: Compiled 33 to 32 computations (3% saved)

bsearch0.0ms (0%)

regimes10.0ms (0.5%)

Compiler: Compiled 15 to 17 computations (-13.3% saved)

bsearch0.0ms (0%)

regimes10.0ms (0.5%)

Accuracy

Total 0.2b remaining (99.3%)

Threshold costs 0.2b (99.3%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch3.0ms (0.2%)

Compiler: Compiled 36 to 32 computations (11.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	52
1	24	52

end0.0ms (0%)

sample721.0ms (34.8%)

Algorithm

1×

intervals

Results

228.0ms	7999×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 302 to 255 computations (15.6% saved)

Pareto

0.6478140687874746

Details

analyze3.0ms (0.1%)

sample13.0ms (0.6%)

simplify96.0ms (4.6%)

prune2.0ms (0.1%)

localize5.0ms (0.3%)

rewrite27.0ms (1.3%)

series63.0ms (3%)

simplify91.0ms (4.4%)

prune86.0ms (4.2%)

localize7.0ms (0.3%)

rewrite47.0ms (2.3%)

series97.0ms (4.7%)

simplify94.0ms (4.6%)

prune125.0ms (6%)

localize8.0ms (0.4%)

rewrite62.0ms (3%)

series106.0ms (5.1%)

simplify90.0ms (4.4%)

prune167.0ms (8.1%)

simplify10.0ms (0.5%)

regimes71.0ms (3.4%)

bsearch0.0ms (0%)

regimes20.0ms (1%)

bsearch20.0ms (1%)

regimes12.0ms (0.6%)

bsearch0.0ms (0%)

regimes10.0ms (0.5%)

bsearch0.0ms (0%)

regimes10.0ms (0.5%)

bsearch3.0ms (0.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample721.0ms (34.8%)

Profiling