Details

analyze108.0ms (4.9%)

Algorithm

1×	search
2×	egg-herbie

Rules

686×	`times-frac_binary64`
548×	`unsub-neg_binary64`
524×	`distribute-rgt-in_binary64`
494×	`div-sub_binary64`
398×	`distribute-lft-in_binary64`
328×	`associate-/l/_binary64`
253×	`cancel-sign-sub-inv_binary64`
252×	`neg-mul-1_binary64`
226×	`neg-sub0_binary64`
144×	`sub-neg_binary64`
96×	`associate-/r/_binary64`
90×	`distribute-neg-frac_binary64`
88×	`associate-*l/_binary64`
77×	`distribute-neg-in_binary64`
76×	`distribute-lft-neg-out_binary64`
75×	`distribute-frac-neg_binary64`
72×	`distribute-rgt-neg-out_binary64`
70×	`distribute-rgt-neg-in_binary64` `associate--r+_binary64`
66×	`associate-*r/_binary64`
64×	`associate-/l*_binary64`
49×	`distribute-lft-neg-in_binary64`
31×	`*-commutative_binary64`
29×	`associate-+r+_binary64`
26×	`distribute-rgt-out--_binary64`
25×	`+-commutative_binary64`
24×	`mul0-rgt_binary64`
23×	`associate-r_binary64`
22×	`mul0-lft_binary64`
21×	`associate-l_binary64` `associate-+l+_binary64`
20×	`associate-/r*_binary64`
17×	`sub0-neg_binary64`
16×	`distribute-neg-out_binary64` `distribute-rgt-out_binary64`
14×	`associate-+l-_binary64`
12×	`sqr-neg_binary64` `+-lft-identity_binary64`
10×	`div0_binary64`
8×	`cube-prod_binary64`
6×	`cube-div_binary64` `+-rgt-identity_binary64` `associate--r-_binary64`
5×	`*-rgt-identity_binary64` `associate-+r-_binary64`
4×	`cube-unmult_binary64` `mul-1-neg_binary64` `*-inverses_binary64`
3×	`*-lft-identity_binary64` `remove-double-neg_binary64`
2×	`cube-neg_binary64` `/-rgt-identity_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-lft1-in_binary64` `associate--l+_binary64`
1×	`1-exp_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-mult_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `--rgt-identity_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `distribute-rgt1-in_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	39	34
2	96	34
3	210	34
4	466	34
5	1489	34
6	4308	34
7	4920	34
0	2	2
1	2	2

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)

sample25.0ms (1.2%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	4×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify75.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

624×	`neg-mul-1_binary64`
414×	`sub-neg_binary64`
381×	`distribute-frac-neg_binary64`
364×	`div-sub_binary64`
297×	`unsub-neg_binary64`
254×	`*-commutative_binary64`
253×	`times-frac_binary64`
204×	`neg-sub0_binary64`
190×	`cancel-sign-sub-inv_binary64` `distribute-rgt-in_binary64`
178×	`associate-/l*_binary64`
174×	`associate-/r/_binary64`
173×	`associate-*l/_binary64`
171×	`distribute-lft-in_binary64`
143×	`distribute-neg-frac_binary64`
137×	`cube-prod_binary64`
134×	`distribute-neg-out_binary64`
131×	`associate-/l/_binary64`
114×	`associate-l_binary64`
103×	`associate-*r/_binary64`
97×	`distribute-lft-neg-out_binary64`
96×	`distribute-rgt-neg-out_binary64`
91×	`distribute-rgt-neg-in_binary64` `associate-+l-_binary64`
89×	`distribute-rgt-out_binary64`
83×	`associate--r+_binary64`
79×	`associate-/r*_binary64`
78×	`associate-+l+_binary64`
70×	`associate-r_binary64`
66×	`distribute-lft-neg-in_binary64`
63×	`cube-div_binary64`
62×	`div0_binary64`
60×	`swap-sqr_binary64`
57×	`associate-+r+_binary64`
55×	`associate--l+_binary64`
50×	`remove-double-neg_binary64`
48×	`distribute-rgt-out--_binary64`
45×	`sqr-neg_binary64` `+-commutative_binary64`
43×	`sub0-neg_binary64`
38×	`associate-+r-_binary64`
34×	`mul0-rgt_binary64`
33×	`mul0-lft_binary64`
31×	`cube-neg_binary64`
29×	`unpow3_binary64` `cube-mult_binary64`
27×	`distribute-neg-in_binary64`
24×	`/-rgt-identity_binary64`
21×	`associate--r-_binary64`
19×	`associate--l-_binary64`
16×	`distribute-lft-out_binary64`
13×	`*-rgt-identity_binary64`
11×	`+-lft-identity_binary64` `cancel-sign-sub_binary64`
10×	`--rgt-identity_binary64` `unswap-sqr_binary64`
8×	`mul-1-neg_binary64`
7×	`*-lft-identity_binary64` `+-rgt-identity_binary64` `sqr-pow_binary64`
6×	`distribute-lft-out--_binary64`
5×	`distribute-rgt1-in_binary64`
4×	`remove-double-div_binary64`
3×	`+-inverses_binary64`
2×	`cube-unmult_binary64` `*-inverses_binary64` `lft-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-squares_binary64` `distribute-lft1-in_binary64`
1×	`unpow2_binary64` `pow-plus_binary64` `1-exp_binary64` `difference-of-sqr-1_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `rgt-mult-inverse_binary64` `pow-sqr_binary64` `count-2_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	22	17
2	54	17
3	115	17
4	245	17
5	646	17
6	1944	17
7	3229	17
8	4346	17
9	4836	17

prune3.0ms (0.1%)

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)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
29.8b	(/.f64 (.f64 b b) (.f64 a a))

rewrite43.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`prod-exp_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `cbrt-unprod_binary64` `add-sqr-sqrt_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `sqrt-prod_binary64`
2×	`add-log-exp_binary64`
1×	`frac-2neg_binary64` `times-frac_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/l_binary64` `associate-/r_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

2 → 34

Calls

2 calls:

10.0ms	(/.f64 (.f64 b b) (.f64 a a))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

Compiler

Compiled 615 to 257 computations (58.2% saved)

series45.0ms (2%)

Error

13.3b

Counts

2 → 12

Calls

2 calls:

23.0ms	(/.f64 (.f64 b b) (.f64 a a))
19.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))

Compiler

Compiled 275 to 275 computations (0% saved)

simplify112.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

533×	`times-frac_binary64`
377×	`cancel-sign-sub-inv_binary64`
330×	`associate-/l*_binary64`
326×	`unswap-sqr_binary64`
269×	`sub-neg_binary64`
241×	`*-commutative_binary64`
196×	`associate-*l/_binary64`
162×	`sqr-pow_binary64`
160×	`distribute-neg-in_binary64`
157×	`associate-/r*_binary64`
125×	`associate-*r/_binary64`
109×	`log-prod_binary64`
101×	`div-sub_binary64`
96×	`associate-l_binary64`
95×	`associate-/l/_binary64`
91×	`associate--r+_binary64`
87×	`associate-+l+_binary64`
86×	`associate--l+_binary64`
76×	`associate-r_binary64`
74×	`associate-/r/_binary64`
72×	`neg-mul-1_binary64`
70×	`cube-prod_binary64`
69×	`neg-sub0_binary64`
61×	`associate-+r+_binary64`
59×	`distribute-rgt-in_binary64`
58×	`distribute-lft-neg-in_binary64`
57×	`distribute-rgt-neg-in_binary64`
53×	`unsub-neg_binary64` `pow-sqr_binary64`
52×	`unpow3_binary64`
46×	`log-pow_binary64`
45×	`associate-+l-_binary64`
42×	`distribute-lft-in_binary64`
41×	`cube-mult_binary64`
36×	`log-div_binary64`
31×	`associate--r-_binary64`
28×	`+-commutative_binary64`
27×	`pow-plus_binary64`
26×	`cube-div_binary64` `associate--l-_binary64`
25×	`swap-sqr_binary64`
24×	`distribute-neg-frac_binary64`
22×	`exp-prod_binary64`
20×	`associate-+r-_binary64`
16×	`cube-unmult_binary64`
15×	`distribute-lft-out--_binary64`
14×	`+-rgt-identity_binary64`
13×	`*-rgt-identity_binary64`
12×	`*-lft-identity_binary64`
10×	`sub0-neg_binary64`
9×	`--rgt-identity_binary64` `div0_binary64`
8×	`unpow2_binary64` `count-2_binary64`
7×	`rem-sqrt-square_binary64` `distribute-rgt-out_binary64`
6×	`mul0-rgt_binary64` `mul0-lft_binary64` `distribute-neg-out_binary64` `distribute-lft-out_binary64`
5×	`remove-double-neg_binary64`
4×	`distribute-rgt-out--_binary64`
3×	`unpow1_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64`
2×	`unpow1/2_binary64` `exp-diff_binary64` `exp-sum_binary64` `+-lft-identity_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64`
1×	`1-exp_binary64` `rem-square-sqrt_binary64` `distribute-frac-neg_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64`

Counts

46 → 37

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	67	781
1	141	645
2	439	620
3	1827	605
4	2740	605
5	3842	518
6	4928	515
7	4992	515
8	4903	515

prune23.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	2	38

Error

Counts

38 → 2

Compiler

Compiled 265 to 191 computations (27.9% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))
0.4b	(pow.f64 (/.f64 b a) 2)
6.2b	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))

rewrite93.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`unpow-prod-down_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
19×	`log-pow_binary64`
18×	`exp-prod_binary64` `times-frac_binary64`
6×	`pow1_binary64` `add-exp-log_binary64`
3×	`log-prod_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `pow-unpow_binary64` `sqrt-prod_binary64`
2×	`div-inv_binary64` `unpow2_binary64` `sqr-pow_binary64` `pow-exp_binary64`
1×	`rem-log-exp_binary64` `pow-pow_binary64` `pow-to-exp_binary64` `div-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

3 → 72

Calls

3 calls:

6.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))
5.0ms	(pow.f64 (/.f64 b a) 2)
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))

Compiler

Compiled 1300 to 895 computations (31.2% saved)

series80.0ms (3.6%)

Error

Counts

3 → 18

Calls

3 calls:

42.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2)))
20.0ms	(pow.f64 (/.f64 b a) 2)
15.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 b a) 2))))))

Compiler

Compiled 455 to 451 computations (0.9% saved)

simplify86.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

698×	`associate-*l/_binary64`
408×	`associate-/l/_binary64`
391×	`associate-/r*_binary64`
253×	`log-pow_binary64`
196×	`exp-prod_binary64`
175×	`associate-/r/_binary64`
168×	`sqr-pow_binary64`
108×	`associate-l_binary64`
105×	`log-prod_binary64`
101×	`associate-r_binary64`
96×	`associate-*r/_binary64`
73×	`cube-prod_binary64`
70×	`distribute-rgt-neg-in_binary64`
69×	`distribute-lft-neg-in_binary64`
68×	`associate-/l*_binary64`
64×	`swap-sqr_binary64`
53×	`unswap-sqr_binary64`
51×	`cancel-sign-sub-inv_binary64`
48×	`rem-sqrt-square_binary64`
36×	`times-frac_binary64`
35×	`pow-sqr_binary64`
34×	`pow-plus_binary64`
32×	`log-div_binary64`
31×	`cube-unmult_binary64`
30×	`cube-div_binary64`
28×	`rem-log-exp_binary64` `distribute-rgt-in_binary64`
26×	`distribute-neg-frac_binary64`
24×	`*-commutative_binary64`
22×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64`
19×	`distribute-lft-in_binary64`
16×	`sub-neg_binary64`
14×	`*-rgt-identity_binary64`
10×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64` `*-lft-identity_binary64`
8×	`/-rgt-identity_binary64`
7×	`unpow3_binary64` `cube-mult_binary64`
6×	`distribute-lft-out_binary64`
5×	`exp-to-pow_binary64` `count-2_binary64`
4×	`distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-out_binary64`
3×	`rem-square-sqrt_binary64` `unsub-neg_binary64` `associate-+l-_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
2×	`rem-3cbrt-rft_binary64` `sub0-neg_binary64` `distribute-lft-out--_binary64` `associate-+r-_binary64` `+-commutative_binary64`
1×	`exp-sum_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `rem-3cbrt-lft_binary64` `+-rgt-identity_binary64` `difference-of-sqr-1_binary64` `distribute-neg-in_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `div-sub_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64`

Counts

90 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1169
1	230	996
2	465	958
3	1472	948
4	4813	948
5	5039	948

prune45.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	74	2	76

Error

Counts

76 → 2

Compiler

Compiled 732 to 469 computations (35.9% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))
0.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3))
0.0b	(pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3)
0.4b	(pow.f64 (/.f64 b a) 2)

rewrite116.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`unpow-prod-down_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
18×	`cbrt-prod_binary64`
15×	`sqrt-prod_binary64`
12×	`cube-prod_binary64`
9×	`times-frac_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
6×	`pow-unpow_binary64`
5×	`add-cbrt-cube_binary64`
4×	`pow-pow_binary64` `add-log-exp_binary64`
3×	`pow-exp_binary64` `sqr-pow_binary64`
2×	`pow-to-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`div-inv_binary64` `div-exp_binary64` `unpow2_binary64` `rem-cube-cbrt_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `rem-cbrt-cube_binary64` `rem-sqrt-square_binary64`

Counts

4 → 101

Calls

4 calls:

5.0ms	(pow.f64 (/.f64 b a) 2)
3.0ms	(pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3)
3.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))

Compiler

Compiled 1713 to 1287 computations (24.9% saved)

series102.0ms (4.6%)

Error

Counts

4 → 24

Calls

4 calls:

38.0ms	(pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3)
22.0ms	(pow.f64 (/.f64 b a) 2)
20.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2)))) 3))
19.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (pow.f64 (/.f64 b a) 2))))

Compiler

Compiled 675 to 671 computations (0.6% saved)

simplify108.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

491×	`associate-l_binary64`
425×	`associate-r_binary64`
411×	`log-prod_binary64`
371×	`exp-prod_binary64`
351×	`cube-prod_binary64`
340×	`unswap-sqr_binary64`
240×	`sqr-pow_binary64`
110×	`associate-*l/_binary64`
98×	`associate-*r/_binary64`
91×	`rem-sqrt-square_binary64`
69×	`associate-/l*_binary64`
65×	`pow-plus_binary64`
63×	`pow-sqr_binary64`
52×	`cube-unmult_binary64`
45×	`log-pow_binary64`
41×	`*-commutative_binary64`
37×	`associate-/r*_binary64`
36×	`times-frac_binary64`
32×	`log-div_binary64`
30×	`unpow3_binary64` `cube-div_binary64`
25×	`swap-sqr_binary64`
24×	`associate-/l/_binary64`
23×	`unpow1/2_binary64` `unpow1_binary64`
22×	`unpow2_binary64`
20×	`cube-mult_binary64`
19×	`*-rgt-identity_binary64`
17×	`sub-neg_binary64`
16×	`distribute-rgt-in_binary64` `associate-/r/_binary64`
14×	`*-lft-identity_binary64`
12×	`distribute-lft-in_binary64`
10×	`neg-mul-1_binary64` `neg-sub0_binary64`
8×	`/-rgt-identity_binary64`
7×	`associate-+l+_binary64` `associate-+r+_binary64`
6×	`rem-cbrt-cube_binary64` `distribute-neg-frac_binary64`
5×	`rem-square-sqrt_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
3×	`unsub-neg_binary64` `count-2_binary64` `associate-+l-_binary64`
2×	`rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `div-sub_binary64` `sub0-neg_binary64` `associate-+r-_binary64` `+-commutative_binary64`
1×	`1-exp_binary64` `rem-cube-cbrt_binary64` `+-rgt-identity_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-lft-out_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64`

Counts

125 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2272
1	273	2090
2	646	2049
3	2968	2044
4	4948	2044

prune40.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	97	2	99

Error

Counts

99 → 2

Compiler

Compiled 606 to 428 computations (29.4% saved)

regimes195.0ms (8.9%)

Accuracy

Total 0.0b remaining (39.2%)

Threshold costs 0.0b (39.2%)

Compiler

Compiled 1740 to 1509 computations (13.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`sub-neg_binary64` `+-commutative_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `*-commutative_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `unpow1_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	16	18
2	20	18
3	22	18
4	23	18
5	22	18

end1.0ms (0%)

Compiler: Compiled 11 to 11 computations (0% saved)

sample874.0ms (39.7%)

Algorithm

1×

intervals

Results

293.0ms	8000×	body	128	valid
159.0ms	8000×	pre	128	true
3.0ms	142×	pre	128	false

Compiler

Compiled 55 to 56 computations (-1.8% saved)

Details

analyze108.0ms (4.9%)

sample25.0ms (1.2%)

simplify75.0ms (3.4%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

rewrite43.0ms (2%)

series45.0ms (2%)

simplify112.0ms (5.1%)

prune23.0ms (1%)

localize8.0ms (0.4%)

rewrite93.0ms (4.2%)

series80.0ms (3.6%)

simplify86.0ms (3.9%)

prune45.0ms (2%)

localize9.0ms (0.4%)

rewrite116.0ms (5.3%)

series102.0ms (4.6%)

simplify108.0ms (4.9%)

prune40.0ms (1.8%)

regimes195.0ms (8.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample874.0ms (39.7%)

Profiling