Details

analyze36.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample24.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	6×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify167.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4836	17
1	4836	17

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

13.3b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize8.0ms (0.2%)

Local error

Found 6 expressions with local error:

27.2b	(/.f64 (.f64 b b) (.f64 a a))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
0.0b	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
0.0b	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
27.2b	(/.f64 (.f64 b b) (.f64 a a))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
10×	`add-sqr-sqrt_binary64_3169`
9×	`*-un-lft-identity_binary64_3147`
5×	`cancel-sign-sub-inv_binary64_3113` `add-log-exp_binary64_3186` `add-cube-cbrt_binary64_3182`
4×	`times-frac_binary64_3153` `pow1_binary64_3208` `prod-exp_binary64_3196` `difference-of-squares_binary64_3116` `cbrt-undiv_binary64_3181` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198`
3×	`sqrt-prod_binary64_3163`
2×	`div-inv_binary64_3144`
1×	`flip--_binary64_3122` `clear-num_binary64_3146` `flip3--_binary64_3151` `frac-2neg_binary64_3158` `associate-/r_binary64_3091` `sub-neg_binary64_3140` `rem-sqrt-square_binary64_3160` `distribute-lft-out--_binary64_3099` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `diff-log_binary64_3239` `associate-/l_binary64_3092`

Counts

3 → 55

Calls

6 calls:

8.0ms	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
7.0ms	(/.f64 (.f64 b b) (.f64 a a))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
0.0ms	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
0.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

series269.0ms (8.6%)

Counts

3 → 24

Calls

3 calls:

120.0ms	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
84.0ms	(/.f64 (.f64 b b) (.f64 a a))
65.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

Compiler

Compiled 438 to 444 computations (-1.4% saved)

simplify64.0ms (2%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5440	1064

prune80.0ms (2.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	2	80

Error

Counts

80 → 2

Compiler

Compiled 1075 to 493 computations (54.1% saved)

localize9.0ms (0.3%)

Local error

Found 6 expressions with local error:

0.4b	(*.f64 (/.f64 b a) (/.f64 b a))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
0.0b	(-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))
0.0b	(-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
0.4b	(*.f64 (/.f64 b a) (/.f64 b a))

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_3169`
40×	`times-frac_binary64_3153`
33×	`*-un-lft-identity_binary64_3147`
32×	`add-cube-cbrt_binary64_3182`
15×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
13×	`swap-sqr_binary64_3114` `associate-r_binary64_3087` `associate-l_binary64_3088`
11×	`pow1_binary64_3208`
5×	`add-log-exp_binary64_3186`
4×	`unswap-sqr_binary64_3115` `prod-exp_binary64_3196` `cbrt-undiv_binary64_3181` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `div-inv_binary64_3144`
3×	`sqrt-prod_binary64_3163`
2×	`difference-of-squares_binary64_3116`
1×	`-commutative_binary64_3078` `frac-times_binary64_3157` `flip--_binary64_3122` `cancel-sign-sub-inv_binary64_3113` `pow-prod-down_binary64_3218` `associate-l/_binary64_3090` `flip3--_binary64_3151` `sub-neg_binary64_3140` `rem-sqrt-square_binary64_3160` `pow-plus_binary64_3210` `sqrt-pow1_binary64_3165` `pow2_binary64_3228` `pow1/2_binary64_3227` `pow-prod-up_binary64_3217` `diff-log_binary64_3239` `associate-*r/_binary64_3089` `pow-sqr_binary64_3120`

Counts

3 → 94

Calls

6 calls:

12.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
3.0ms	(-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
0.0ms	(-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))
0.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))

series264.0ms (8.4%)

Counts

3 → 24

Calls

3 calls:

114.0ms	(-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))
82.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
67.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))

Compiler

Compiled 438 to 444 computations (-1.4% saved)

simplify75.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5055	1452

prune92.0ms (2.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	118	2	120

Error

Counts

120 → 2

Compiler

Compiled 1651 to 902 computations (45.4% saved)

localize15.0ms (0.5%)

Local error

Found 8 expressions with local error:

27.2b	(/.f64 (.f64 b b) (.f64 a a))
0.5b	(pow.f64 (/.f64 b a) 4)
0.0b	(/.f64 (-.f64 1 (pow.f64 (/.f64 b a) 4)) (+.f64 (/.f64 (.f64 b b) (.f64 a a)) 1))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 b a) 4)) (+.f64 (/.f64 (.f64 b b) (.f64 a a)) 1))))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 b a) 4)) (+.f64 (/.f64 (.f64 b b) (.f64 a a)) 1))))
0.0b	(/.f64 (-.f64 1 (pow.f64 (/.f64 b a) 4)) (+.f64 (/.f64 (.f64 b b) (.f64 a a)) 1))
0.5b	(pow.f64 (/.f64 b a) 4)
27.2b	(/.f64 (.f64 b b) (.f64 a a))

rewrite51.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64_3169`
87×	`*-un-lft-identity_binary64_3147`
68×	`times-frac_binary64_3153`
40×	`difference-of-squares_binary64_3116`
33×	`unpow-prod-down_binary64_3226`
31×	`add-cube-cbrt_binary64_3182`
21×	`add-exp-log_binary64_3185`
18×	`add-cbrt-cube_binary64_3183`
13×	`distribute-lft-out_binary64_3098` `associate-/l*_binary64_3092`
11×	`sqr-pow_binary64_3119`
6×	`pow1_binary64_3208` `div-exp_binary64_3198`
5×	`associate-/r*_binary64_3091` `distribute-lft-out--_binary64_3099` `cbrt-undiv_binary64_3181`
4×	`prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `add-log-exp_binary64_3186`
3×	`pow-unpow_binary64_3224` `sqrt-prod_binary64_3163` `div-inv_binary64_3144`
2×	`pow-exp_binary64_3215` `clear-num_binary64_3146` `frac-2neg_binary64_3158` `associate-/l/_binary64_3094` `associate-/r/_binary64_3093`
1×	`flip--_binary64_3122` `flip-+_binary64_3121` `flip3--_binary64_3151` `flip3-+_binary64_3150` `pow-to-exp_binary64_3216` `rem-sqrt-square_binary64_3160` `div-sub_binary64_3152` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `pow-pow_binary64_3219`

Counts

4 → 143

Calls

8 calls:

22.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 b a) 4)) (+.f64 (/.f64 (.f64 b b) (.f64 a a)) 1))
6.0ms	(/.f64 (.f64 b b) (.f64 a a))
5.0ms	(pow.f64 (/.f64 b a) 4)
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 b a) 4)) (+.f64 (/.f64 (.f64 b b) (.f64 a a)) 1))))
0.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 b a) 4)) (+.f64 (/.f64 (.f64 b b) (.f64 a a)) 1))))

series574.0ms (18.3%)

Counts

4 → 30

Calls

4 calls:

284.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 b a) 4)) (+.f64 (/.f64 (.f64 b b) (.f64 a a)) 1))
105.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 b a) 4)) (+.f64 (/.f64 (.f64 b b) (.f64 a a)) 1))))
93.0ms	(pow.f64 (/.f64 b a) 4)
92.0ms	(/.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 906 to 816 computations (9.9% saved)

simplify65.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5186	4241

prune215.0ms (6.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	173	2	175

Error

Counts

175 → 2

Compiler

Compiled 4335 to 2657 computations (38.7% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	141	221
1	141	221

regimes186.0ms (5.9%)

Compiler: Compiled 1379 to 1130 computations (18.1% saved)

bsearch0.0ms (0%)

regimes33.0ms (1.1%)

Accuracy

Total 0.0b remaining (59.6%)

Threshold costs 0.0b (59.6%)

Compiler

Compiled 72 to 92 computations (-27.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 12 to 11 computations (8.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	18
1	34	18

end0.0ms (0%)

sample850.0ms (27.1%)

Algorithm

1×

intervals

Results

282.0ms	8000×	body	128	valid
165.0ms	8000×	pre	128	true
2.0ms	118×	pre	128	false

Compiler

Compiled 173 to 143 computations (17.3% saved)

Pareto

0.0

Details

analyze36.0ms (1.1%)

sample24.0ms (0.8%)

simplify167.0ms (5.3%)

prune5.0ms (0.2%)

localize8.0ms (0.2%)

rewrite23.0ms (0.7%)

series269.0ms (8.6%)

simplify64.0ms (2%)

prune80.0ms (2.5%)

localize9.0ms (0.3%)

rewrite24.0ms (0.8%)

series264.0ms (8.4%)

simplify75.0ms (2.4%)

prune92.0ms (2.9%)

localize15.0ms (0.5%)

rewrite51.0ms (1.6%)

series574.0ms (18.3%)

simplify65.0ms (2.1%)

prune215.0ms (6.8%)

simplify6.0ms (0.2%)

regimes186.0ms (5.9%)

bsearch0.0ms (0%)

regimes33.0ms (1.1%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample850.0ms (27.1%)

Profiling