Details

analyze12.0ms (0.1%)

Algorithm

1×

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
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample20.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify1.3s (11.9%)

Algorithm

1×	egg-herbie

Rules

908×	`sub-neg_binary64_12688`
684×	`distribute-lft-out--_binary64_12647`
583×	`distribute-rgt-out_binary64_12648`
515×	`distribute-rgt-out--_binary64_12649`
293×	`cancel-sign-sub-inv_binary64_12661`
221×	`associate-/r/_binary64_12641`
206×	`div-sub_binary64_12700`
180×	`times-frac_binary64_12701`
150×	`associate-/r*_binary64_12639`
65×	`distribute-rgt-in_binary64_12645`
64×	`distribute-rgt-neg-in_binary64_12653` `associate-/l*_binary64_12640`
55×	`*-commutative_binary64_12626`
53×	`distribute-lft-neg-in_binary64_12652`
50×	`neg-mul-1_binary64_12691`
47×	`unsub-neg_binary64_12689`
46×	`neg-sub0_binary64_12690`
38×	`associate-r_binary64_12635`
37×	`distribute-lft-in_binary64_12644`
28×	`distribute-rgt1-in_binary64_12651`
27×	`associate-l_binary64_12636`
24×	`distribute-neg-frac_binary64_12659`
22×	`associate-/l/_binary64_12642`
17×	`associate-+l-_binary64_12630` `+-commutative_binary64_12625`
13×	`distribute-neg-in_binary64_12656`
10×	`associate--r+_binary64_12631`
9×	`associate-+r-_binary64_12629` `associate-+r+_binary64_12627`
8×	`distribute-lft-neg-out_binary64_12654` `distribute-lft-out_binary64_12646`
7×	`sub0-neg_binary64_12682` `associate-+l+_binary64_12628`
6×	`--rgt-identity_binary64_12681` `+-rgt-identity_binary64_12680` `mul0-rgt_binary64_12678`
5×	`+-lft-identity_binary64_12679` `mul0-lft_binary64_12677` `div0_binary64_12676` `distribute-lft1-in_binary64_12650` `count-2_binary64_12643`
4×	`distribute-rgt-neg-out_binary64_12655`
3×	`remove-double-neg_binary64_12683` `swap-sqr_binary64_12662` `associate--r-_binary64_12634`
2×	`exp-sum_binary64_12741`
1×	`exp-lft-sqr_binary64_12750` `exp-diff_binary64_12743` `1-exp_binary64_12739` `cube-unmult_binary64_12732` `cube-prod_binary64_12723` `distribute-frac-neg_binary64_12658`
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_12958` `erf-erfc_binary64_12957` `erf-odd_binary64_12956` `if-if-and-not_binary64_12955` `if-if-and_binary64_12954` `if-if-or-not_binary64_12953` `if-if-or_binary64_12952` `if-not_binary64_12951` `if-same_binary64_12950` `if-false_binary64_12949` `if-true_binary64_12948` `not-gte_binary64_12947` `not-lte_binary64_12946` `not-gt_binary64_12945` `not-lt_binary64_12944` `gte-same_binary64_12943` `lte-same_binary64_12942` `gt-same_binary64_12941` `lt-same_binary64_12940` `sinh---cosh_binary64_12887` `sinh-+-cosh_binary64_12886` `sinh-cosh_binary64_12885` `tanh-def-c_binary64_12884` `tanh-def-b_binary64_12883` `tanh-def-a_binary64_12882` `cosh-def_binary64_12881` `sinh-def_binary64_12880` `tan-neg_binary64_12827` `cos-neg_binary64_12826` `sin-neg_binary64_12825` `tan-0_binary64_12824` `cos-0_binary64_12823` `sin-0_binary64_12822` `hang-m-tan_binary64_12821` `hang-p-tan_binary64_12820` `hang-m0-tan_binary64_12819` `hang-p0-tan_binary64_12818` `hang-0m-tan_binary64_12817` `hang-0p-tan_binary64_12816` `tan-+PI/2_binary64_12815` `tan-+PI_binary64_12814` `tan-PI_binary64_12813` `tan-PI/3_binary64_12812` `tan-PI/4_binary64_12811` `tan-PI/6_binary64_12810` `cos-+PI/2_binary64_12809` `cos-+PI_binary64_12808` `cos-PI_binary64_12807` `cos-PI/2_binary64_12806` `cos-PI/3_binary64_12805` `cos-PI/4_binary64_12804` `cos-PI/6_binary64_12803` `sin-+PI/2_binary64_12802` `sin-+PI_binary64_12801` `sin-PI_binary64_12800` `sin-PI/2_binary64_12799` `sin-PI/3_binary64_12798` `sin-PI/4_binary64_12797` `sin-PI/6_binary64_12796` `sub-1-sin_binary64_12795` `sub-1-cos_binary64_12794` `-1-add-sin_binary64_12793` `-1-add-cos_binary64_12792` `1-sub-sin_binary64_12791` `1-sub-cos_binary64_12790` `cos-sin-sum_binary64_12789` `log-E_binary64_12785` `log-pow_binary64_12784` `log-rec_binary64_12783` `log-div_binary64_12782` `log-prod_binary64_12781` `pow-base-0_binary64_12779` `unpow1/3_binary64_12762` `unpow3_binary64_12761` `unpow2_binary64_12760` `unpow1/2_binary64_12759` `pow-plus_binary64_12758` `exp-to-pow_binary64_12757` `pow-base-1_binary64_12755` `unpow0_binary64_12754` `unpow1_binary64_12753` `unpow-1_binary64_12752` `exp-lft-cube_binary64_12751` `exp-cbrt_binary64_12749` `exp-sqrt_binary64_12748` `exp-prod_binary64_12747` `div-exp_binary64_12746` `rec-exp_binary64_12745` `prod-exp_binary64_12744` `exp-neg_binary64_12742` `e-exp-1_binary64_12740` `exp-1-e_binary64_12738` `exp-0_binary64_12737` `rem-log-exp_binary64_12736` `rem-exp-log_binary64_12735` `cube-mult_binary64_12725` `cube-div_binary64_12724` `cube-neg_binary64_12722` `rem-3cbrt-rft_binary64_12721` `rem-3cbrt-lft_binary64_12720` `rem-cbrt-cube_binary64_12719` `rem-cube-cbrt_binary64_12718` `sqr-abs_binary64_12710` `sqr-neg_binary64_12709` `rem-sqrt-square_binary64_12708` `rem-square-sqrt_binary64_12707` `mul-1-neg_binary64_12687` `/-rgt-identity_binary64_12686` `-rgt-identity_binary64_12685` `-lft-identity_binary64_12684` `-inverses_binary64_12675` `+-inverses_binary64_12674` `lft-mult-inverse_binary64_12673` `rgt-mult-inverse_binary64_12672` `remove-double-div_binary64_12671` `pow-sqr_binary64_12668` `sqr-pow_binary64_12667` `difference-of-sqr--1_binary64_12666` `difference-of-sqr-1_binary64_12665` `difference-of-squares_binary64_12664` `unswap-sqr_binary64_12663` `cancel-sign-sub_binary64_12660` `distribute-neg-out_binary64_12657` `associate-l/_binary64_12638` `associate-*r/_binary64_12637` `associate--l-_binary64_12633` `associate--l+_binary64_12632`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	21	28
2	47	28
3	94	28
4	181	28
5	282	28
6	528	28
7	4082	28

prune4.0ms (0%)

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

Error

31.9b

Counts

2 → 1

Compiler

Compiled 38 to 24 computations (36.8% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

3.9b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))
31.3b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))

rewrite89.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

31.9b

Rules

10×	`add-cube-cbrt_binary64_12730` `add-sqr-sqrt_binary64_12717` `*-un-lft-identity_binary64_12695`
9×	`times-frac_binary64_12701`
4×	`add-exp-log_binary64_12733` `add-log-exp_binary64_12734` `add-cbrt-cube_binary64_12731`
3×	`associate-/l_binary64_12640` `associate-/r_binary64_12639`
2×	`pow1_binary64_12756` `flip3--_binary64_12699` `associate-/l/_binary64_12642` `flip--_binary64_12670` `associate-/r/_binary64_12641`
1×	`div-exp_binary64_12746` `cbrt-undiv_binary64_12729` `frac-2neg_binary64_12706` `div-sub_binary64_12700` `clear-num_binary64_12694` `div-inv_binary64_12692` `flip3-+_binary64_12698` `flip-+_binary64_12669` `diff-log_binary64_12787` `sub-neg_binary64_12688` `cancel-sign-sub-inv_binary64_12661`

Counts

2 → 44

Calls

2 calls:

9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
4.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

Compiler

Compiled 1537 to 800 computations (48% saved)

series471.0ms (4.3%)

Error

0.6b

Counts

2 → 30

Calls

2 calls:

251.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
189.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) y))

Compiler

Compiled 1029 to 834 computations (19% saved)

simplify323.0ms (3%)

Algorithm

1×	egg-herbie

Rules

438×	`associate-l_binary64_12636`
427×	`cancel-sign-sub-inv_binary64_12661`
363×	`associate-r_binary64_12635`
242×	`div-sub_binary64_12700`
211×	`unswap-sqr_binary64_12663`
206×	`associate-/l*_binary64_12640`
167×	`times-frac_binary64_12701`
152×	`associate-*l/_binary64_12638`
137×	`distribute-rgt-in_binary64_12645`
127×	`distribute-lft-in_binary64_12644`
126×	`associate-*r/_binary64_12637`
122×	`associate-/r*_binary64_12639`
118×	`sqr-pow_binary64_12667`
115×	`exp-prod_binary64_12747`
114×	`sub-neg_binary64_12688`
105×	`associate-/l/_binary64_12642`
91×	`*-commutative_binary64_12626`
84×	`associate-/r/_binary64_12641`
83×	`distribute-rgt-neg-in_binary64_12653`
79×	`neg-sub0_binary64_12690`
76×	`cube-prod_binary64_12723`
75×	`neg-mul-1_binary64_12691`
71×	`distribute-lft-neg-in_binary64_12652`
65×	`pow-sqr_binary64_12668`
63×	`unsub-neg_binary64_12689`
42×	`distribute-neg-frac_binary64_12659`
40×	`swap-sqr_binary64_12662`
37×	`cube-div_binary64_12724`
36×	`+-commutative_binary64_12625`
32×	`difference-of-squares_binary64_12664` `associate-+l+_binary64_12628`
25×	`*-lft-identity_binary64_12684`
20×	`pow-plus_binary64_12758`
18×	`exp-sum_binary64_12741` `associate-+l-_binary64_12630`
17×	`/-rgt-identity_binary64_12686` `distribute-lft-neg-out_binary64_12654`
16×	`distribute-rgt-out_binary64_12648`
15×	`*-rgt-identity_binary64_12685`
14×	`exp-diff_binary64_12743` `cube-unmult_binary64_12732` `associate-+r-_binary64_12629` `associate-+r+_binary64_12627`
12×	`unpow3_binary64_12761`
11×	`sub0-neg_binary64_12682` `+-rgt-identity_binary64_12680`
10×	`log-div_binary64_12782` `log-prod_binary64_12781` `div-exp_binary64_12746` `associate--r+_binary64_12631`
9×	`prod-exp_binary64_12744` `cube-mult_binary64_12725` `mul0-lft_binary64_12677`
8×	`mul0-rgt_binary64_12678` `associate--l+_binary64_12632`
7×	`distribute-neg-in_binary64_12656` `distribute-lft-out_binary64_12646`
6×	`distribute-rgt-neg-out_binary64_12655`
5×	`exp-sqrt_binary64_12748` `remove-double-neg_binary64_12683`
4×	`exp-lft-sqr_binary64_12750`
3×	`rec-exp_binary64_12745` `mul-1-neg_binary64_12687`
2×	`unpow2_binary64_12760` `unpow1_binary64_12753` `sqr-neg_binary64_12709` `*-inverses_binary64_12675` `associate--r-_binary64_12634`
1×	`log-pow_binary64_12784` `log-rec_binary64_12783` `1-exp_binary64_12739` `rem-log-exp_binary64_12736` `cube-neg_binary64_12722` `rgt-mult-inverse_binary64_12672` `distribute-rgt-out--_binary64_12649` `associate--l-_binary64_12633`
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_12958` `erf-erfc_binary64_12957` `erf-odd_binary64_12956` `if-if-and-not_binary64_12955` `if-if-and_binary64_12954` `if-if-or-not_binary64_12953` `if-if-or_binary64_12952` `if-not_binary64_12951` `if-same_binary64_12950` `if-false_binary64_12949` `if-true_binary64_12948` `not-gte_binary64_12947` `not-lte_binary64_12946` `not-gt_binary64_12945` `not-lt_binary64_12944` `gte-same_binary64_12943` `lte-same_binary64_12942` `gt-same_binary64_12941` `lt-same_binary64_12940` `sinh---cosh_binary64_12887` `sinh-+-cosh_binary64_12886` `sinh-cosh_binary64_12885` `tanh-def-c_binary64_12884` `tanh-def-b_binary64_12883` `tanh-def-a_binary64_12882` `cosh-def_binary64_12881` `sinh-def_binary64_12880` `tan-neg_binary64_12827` `cos-neg_binary64_12826` `sin-neg_binary64_12825` `tan-0_binary64_12824` `cos-0_binary64_12823` `sin-0_binary64_12822` `hang-m-tan_binary64_12821` `hang-p-tan_binary64_12820` `hang-m0-tan_binary64_12819` `hang-p0-tan_binary64_12818` `hang-0m-tan_binary64_12817` `hang-0p-tan_binary64_12816` `tan-+PI/2_binary64_12815` `tan-+PI_binary64_12814` `tan-PI_binary64_12813` `tan-PI/3_binary64_12812` `tan-PI/4_binary64_12811` `tan-PI/6_binary64_12810` `cos-+PI/2_binary64_12809` `cos-+PI_binary64_12808` `cos-PI_binary64_12807` `cos-PI/2_binary64_12806` `cos-PI/3_binary64_12805` `cos-PI/4_binary64_12804` `cos-PI/6_binary64_12803` `sin-+PI/2_binary64_12802` `sin-+PI_binary64_12801` `sin-PI_binary64_12800` `sin-PI/2_binary64_12799` `sin-PI/3_binary64_12798` `sin-PI/4_binary64_12797` `sin-PI/6_binary64_12796` `sub-1-sin_binary64_12795` `sub-1-cos_binary64_12794` `-1-add-sin_binary64_12793` `-1-add-cos_binary64_12792` `1-sub-sin_binary64_12791` `1-sub-cos_binary64_12790` `cos-sin-sum_binary64_12789` `log-E_binary64_12785` `pow-base-0_binary64_12779` `unpow1/3_binary64_12762` `unpow1/2_binary64_12759` `exp-to-pow_binary64_12757` `pow-base-1_binary64_12755` `unpow0_binary64_12754` `unpow-1_binary64_12752` `exp-lft-cube_binary64_12751` `exp-cbrt_binary64_12749` `exp-neg_binary64_12742` `e-exp-1_binary64_12740` `exp-1-e_binary64_12738` `exp-0_binary64_12737` `rem-exp-log_binary64_12735` `rem-3cbrt-rft_binary64_12721` `rem-3cbrt-lft_binary64_12720` `rem-cbrt-cube_binary64_12719` `rem-cube-cbrt_binary64_12718` `sqr-abs_binary64_12710` `rem-sqrt-square_binary64_12708` `rem-square-sqrt_binary64_12707` `--rgt-identity_binary64_12681` `+-lft-identity_binary64_12679` `div0_binary64_12676` `+-inverses_binary64_12674` `lft-mult-inverse_binary64_12673` `remove-double-div_binary64_12671` `difference-of-sqr--1_binary64_12666` `difference-of-sqr-1_binary64_12665` `cancel-sign-sub_binary64_12660` `distribute-frac-neg_binary64_12658` `distribute-neg-out_binary64_12657` `distribute-rgt1-in_binary64_12651` `distribute-lft1-in_binary64_12650` `distribute-lft-out--_binary64_12647` `count-2_binary64_12643`

Counts

74 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	2132
1	300	1982
2	1030	1977
3	3606	1977

prune297.0ms (2.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	199	3	202

Error

0.2b

Counts

202 → 3

Compiler

Compiled 6144 to 3260 computations (46.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 (/.f64 y x) (/.f64 y x))
0.5b	(/.f64 1/2 (*.f64 (/.f64 y x) (/.f64 y x)))

rewrite125.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

44×	`add-sqr-sqrt_binary64_12717`
43×	`times-frac_binary64_12701`
32×	`add-exp-log_binary64_12733` `add-cbrt-cube_binary64_12731` `add-cube-cbrt_binary64_12730` `*-un-lft-identity_binary64_12695`
13×	`div-exp_binary64_12746` `cbrt-undiv_binary64_12729` `swap-sqr_binary64_12662` `associate-l_binary64_12636` `associate-r_binary64_12635`
9×	`pow1_binary64_12756`
8×	`prod-exp_binary64_12744` `cbrt-unprod_binary64_12728`
5×	`div-inv_binary64_12692`
4×	`unswap-sqr_binary64_12663`
3×	`associate-/r/_binary64_12641` `associate-/l*_binary64_12640`
2×	`add-log-exp_binary64_12734` `frac-times_binary64_12705` `associate-l/_binary64_12638` `associate-r/_binary64_12637`
1×	`frac-2neg_binary64_12706` `clear-num_binary64_12694` `associate-/r_binary64_12639` `pow2_binary64_12776` `pow-prod-down_binary64_12766` `pow-prod-up_binary64_12765` `pow-plus_binary64_12758` `pow-sqr_binary64_12668` `-commutative_binary64_12626`

Counts

2 → 97

Calls

2 calls:

12.0ms	(*.f64 (/.f64 y x) (/.f64 y x))
8.0ms	(/.f64 1/2 (*.f64 (/.f64 y x) (/.f64 y x)))

Compiler

Compiled 1881 to 720 computations (61.7% saved)

series296.0ms (2.7%)

Error

0.2b

Counts

2 → 12

Calls

2 calls:

156.0ms	(/.f64 1/2 (*.f64 (/.f64 y x) (/.f64 y x)))
130.0ms	(*.f64 (/.f64 y x) (/.f64 y x))

Compiler

Compiled 396 to 374 computations (5.6% saved)

simplify439.0ms (4%)

Algorithm

1×	egg-herbie

Rules

350×	`unswap-sqr_binary64_12663`
232×	`*-commutative_binary64_12626`
216×	`log-prod_binary64_12781`
212×	`exp-prod_binary64_12747`
211×	`distribute-rgt-in_binary64_12645`
175×	`distribute-lft-in_binary64_12644`
159×	`associate-/l_binary64_12640` `associate-l/_binary64_12638`
129×	`associate-*r/_binary64_12637`
122×	`swap-sqr_binary64_12662`
117×	`associate--r+_binary64_12631`
112×	`cube-prod_binary64_12723`
107×	`cancel-sign-sub-inv_binary64_12661`
100×	`log-div_binary64_12782`
98×	`sqr-pow_binary64_12667`
97×	`times-frac_binary64_12701` `associate--l+_binary64_12632`
96×	`associate-l_binary64_12636`
94×	`associate-+l+_binary64_12628`
92×	`associate-r_binary64_12635`
82×	`associate-/r*_binary64_12639`
81×	`associate-+r+_binary64_12627`
75×	`distribute-rgt-neg-in_binary64_12653`
74×	`cube-div_binary64_12724`
69×	`distribute-lft-neg-in_binary64_12652`
62×	`associate--l-_binary64_12633`
59×	`associate-+l-_binary64_12630`
56×	`sub-neg_binary64_12688`
52×	`unpow3_binary64_12761` `associate-/l/_binary64_12642` `associate-/r/_binary64_12641`
45×	`*-rgt-identity_binary64_12685`
43×	`associate--r-_binary64_12634`
42×	`distribute-neg-in_binary64_12656`
40×	`pow-plus_binary64_12758`
36×	`*-lft-identity_binary64_12684`
34×	`associate-+r-_binary64_12629`
33×	`log-pow_binary64_12784` `neg-mul-1_binary64_12691`
31×	`pow-sqr_binary64_12668`
30×	`neg-sub0_binary64_12690`
29×	`distribute-neg-frac_binary64_12659`
22×	`cube-mult_binary64_12725`
21×	`exp-to-pow_binary64_12757` `distribute-rgt-out_binary64_12648`
20×	`div-sub_binary64_12700`
19×	`+-commutative_binary64_12625`
17×	`prod-exp_binary64_12744` `distribute-lft-neg-out_binary64_12654`
16×	`div-exp_binary64_12746` `/-rgt-identity_binary64_12686`
15×	`unsub-neg_binary64_12689`
14×	`cube-unmult_binary64_12732`
13×	`log-rec_binary64_12783`
11×	`distribute-rgt-neg-out_binary64_12655`
10×	`distribute-rgt-out--_binary64_12649`
9×	`rem-sqrt-square_binary64_12708` `distribute-lft-out_binary64_12646`
6×	`distribute-neg-out_binary64_12657` `distribute-rgt1-in_binary64_12651`
5×	`exp-lft-sqr_binary64_12750` `count-2_binary64_12643`
4×	`pow-base-1_binary64_12755` `rec-exp_binary64_12745` `exp-sum_binary64_12741` `remove-double-neg_binary64_12683`
3×	`unpow1_binary64_12753` `exp-sqrt_binary64_12748`
2×	`unpow2_binary64_12760` `rem-3cbrt-rft_binary64_12721` `rem-3cbrt-lft_binary64_12720` `rem-square-sqrt_binary64_12707` `mul0-lft_binary64_12677` `distribute-lft1-in_binary64_12650` `distribute-lft-out--_binary64_12647`
1×	`unpow1/2_binary64_12759` `exp-diff_binary64_12743` `1-exp_binary64_12739` `exp-1-e_binary64_12738` `rem-log-exp_binary64_12736` `sub0-neg_binary64_12682` `mul0-rgt_binary64_12678` `*-inverses_binary64_12675`
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_12958` `erf-erfc_binary64_12957` `erf-odd_binary64_12956` `if-if-and-not_binary64_12955` `if-if-and_binary64_12954` `if-if-or-not_binary64_12953` `if-if-or_binary64_12952` `if-not_binary64_12951` `if-same_binary64_12950` `if-false_binary64_12949` `if-true_binary64_12948` `not-gte_binary64_12947` `not-lte_binary64_12946` `not-gt_binary64_12945` `not-lt_binary64_12944` `gte-same_binary64_12943` `lte-same_binary64_12942` `gt-same_binary64_12941` `lt-same_binary64_12940` `sinh---cosh_binary64_12887` `sinh-+-cosh_binary64_12886` `sinh-cosh_binary64_12885` `tanh-def-c_binary64_12884` `tanh-def-b_binary64_12883` `tanh-def-a_binary64_12882` `cosh-def_binary64_12881` `sinh-def_binary64_12880` `tan-neg_binary64_12827` `cos-neg_binary64_12826` `sin-neg_binary64_12825` `tan-0_binary64_12824` `cos-0_binary64_12823` `sin-0_binary64_12822` `hang-m-tan_binary64_12821` `hang-p-tan_binary64_12820` `hang-m0-tan_binary64_12819` `hang-p0-tan_binary64_12818` `hang-0m-tan_binary64_12817` `hang-0p-tan_binary64_12816` `tan-+PI/2_binary64_12815` `tan-+PI_binary64_12814` `tan-PI_binary64_12813` `tan-PI/3_binary64_12812` `tan-PI/4_binary64_12811` `tan-PI/6_binary64_12810` `cos-+PI/2_binary64_12809` `cos-+PI_binary64_12808` `cos-PI_binary64_12807` `cos-PI/2_binary64_12806` `cos-PI/3_binary64_12805` `cos-PI/4_binary64_12804` `cos-PI/6_binary64_12803` `sin-+PI/2_binary64_12802` `sin-+PI_binary64_12801` `sin-PI_binary64_12800` `sin-PI/2_binary64_12799` `sin-PI/3_binary64_12798` `sin-PI/4_binary64_12797` `sin-PI/6_binary64_12796` `sub-1-sin_binary64_12795` `sub-1-cos_binary64_12794` `-1-add-sin_binary64_12793` `-1-add-cos_binary64_12792` `1-sub-sin_binary64_12791` `1-sub-cos_binary64_12790` `cos-sin-sum_binary64_12789` `log-E_binary64_12785` `pow-base-0_binary64_12779` `unpow1/3_binary64_12762` `unpow0_binary64_12754` `unpow-1_binary64_12752` `exp-lft-cube_binary64_12751` `exp-cbrt_binary64_12749` `exp-neg_binary64_12742` `e-exp-1_binary64_12740` `exp-0_binary64_12737` `rem-exp-log_binary64_12735` `cube-neg_binary64_12722` `rem-cbrt-cube_binary64_12719` `rem-cube-cbrt_binary64_12718` `sqr-abs_binary64_12710` `sqr-neg_binary64_12709` `mul-1-neg_binary64_12687` `--rgt-identity_binary64_12681` `+-rgt-identity_binary64_12680` `+-lft-identity_binary64_12679` `div0_binary64_12676` `+-inverses_binary64_12674` `lft-mult-inverse_binary64_12673` `rgt-mult-inverse_binary64_12672` `remove-double-div_binary64_12671` `difference-of-sqr--1_binary64_12666` `difference-of-sqr-1_binary64_12665` `difference-of-squares_binary64_12664` `cancel-sign-sub_binary64_12660` `distribute-frac-neg_binary64_12658`

Counts

109 → 269

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	1906
1	411	1525
2	1469	1456
3	2085	1443
4	4809	1443

prune241.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	269	3	272

Error

0.2b

Counts

272 → 3

Compiler

Compiled 4735 to 1989 computations (58% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.9b	(-.f64 (.f64 x x) (.f64 y (*.f64 y 4)))
31.3b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
31.3b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
31.3b	(/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y 4))) (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))

rewrite452.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

28×	`add-cube-cbrt_binary64_12730` `add-sqr-sqrt_binary64_12717` `*-un-lft-identity_binary64_12695`
27×	`times-frac_binary64_12701`
10×	`add-exp-log_binary64_12733` `add-cbrt-cube_binary64_12731`
9×	`associate-/l_binary64_12640` `associate-/r_binary64_12639`
6×	`add-log-exp_binary64_12734` `associate-/l/_binary64_12642` `associate-/r/_binary64_12641`
4×	`pow1_binary64_12756` `flip3--_binary64_12699` `flip--_binary64_12670`
3×	`div-exp_binary64_12746` `cbrt-undiv_binary64_12729` `frac-2neg_binary64_12706` `div-sub_binary64_12700` `clear-num_binary64_12694` `div-inv_binary64_12692` `flip3-+_binary64_12698` `flip-+_binary64_12669`
1×	`diff-log_binary64_12787` `sub-neg_binary64_12688` `cancel-sign-sub-inv_binary64_12661`

Counts

4 → 108

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y 4))) (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))
9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
9.0ms	(-.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

Compiler

Compiled 8553 to 4518 computations (47.2% saved)

series1.2s (11.4%)

Error

0.2b

Counts

4 → 66

Calls

4 calls:

309.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y 4))) (+.f64 (.f64 x x) (.f64 y (.f64 y 4))))
274.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
267.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) y)) (+.f64 (.f64 x x) (.f64 (.f64 y 4) y)))
206.0ms	(-.f64 (.f64 x x) (.f64 y (*.f64 y 4)))

Compiler

Compiled 8388 to 5208 computations (37.9% saved)

simplify797.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

332×	`cancel-sign-sub-inv_binary64_12661`
281×	`div-sub_binary64_12700`
233×	`associate-/l*_binary64_12640`
225×	`distribute-neg-frac_binary64_12659`
207×	`associate-*l/_binary64_12638`
174×	`times-frac_binary64_12701`
161×	`associate-*r/_binary64_12637`
153×	`distribute-rgt-in_binary64_12645`
143×	`distribute-lft-in_binary64_12644`
140×	`*-commutative_binary64_12626`
136×	`associate-/r*_binary64_12639`
135×	`unswap-sqr_binary64_12663`
127×	`associate-/l/_binary64_12642`
124×	`sqr-pow_binary64_12667`
119×	`sub-neg_binary64_12688`
109×	`distribute-rgt-neg-in_binary64_12653`
101×	`associate-/r/_binary64_12641`
93×	`neg-mul-1_binary64_12691` `neg-sub0_binary64_12690`
92×	`exp-prod_binary64_12747` `distribute-lft-neg-in_binary64_12652`
80×	`associate-l_binary64_12636`
75×	`associate-r_binary64_12635`
69×	`unsub-neg_binary64_12689`
66×	`pow-sqr_binary64_12668`
56×	`cube-prod_binary64_12723`
49×	`cube-div_binary64_12724` `associate-+l+_binary64_12628`
36×	`swap-sqr_binary64_12662`
35×	`+-commutative_binary64_12625`
33×	`difference-of-squares_binary64_12664`
29×	`distribute-rgt-out_binary64_12648`
27×	`associate-+r+_binary64_12627`
24×	`exp-sum_binary64_12741`
21×	`distribute-lft-neg-out_binary64_12654`
20×	`/-rgt-identity_binary64_12686`
19×	`pow-plus_binary64_12758`
18×	`associate-+l-_binary64_12630`
15×	`unpow3_binary64_12761` `*-rgt-identity_binary64_12685`
14×	`exp-diff_binary64_12743` `associate-+r-_binary64_12629`
12×	`cube-mult_binary64_12725` `mul0-lft_binary64_12677`
11×	`log-div_binary64_12782` `sub0-neg_binary64_12682` `+-rgt-identity_binary64_12680` `mul0-rgt_binary64_12678`
10×	`log-prod_binary64_12781` `div-exp_binary64_12746` `distribute-neg-in_binary64_12656` `associate--r+_binary64_12631`
9×	`prod-exp_binary64_12744` `*-lft-identity_binary64_12684`
8×	`associate--l+_binary64_12632`
7×	`distribute-lft-out_binary64_12646`
6×	`cube-unmult_binary64_12732` `remove-double-neg_binary64_12683`
5×	`exp-sqrt_binary64_12748` `distribute-rgt-neg-out_binary64_12655`
4×	`exp-lft-sqr_binary64_12750`
3×	`rec-exp_binary64_12745`
2×	`unpow2_binary64_12760` `unpow1_binary64_12753` `*-inverses_binary64_12675` `associate--r-_binary64_12634`
1×	`log-pow_binary64_12784` `log-rec_binary64_12783` `1-exp_binary64_12739` `rem-log-exp_binary64_12736` `cube-neg_binary64_12722` `sqr-neg_binary64_12709` `rgt-mult-inverse_binary64_12672` `cancel-sign-sub_binary64_12660` `distribute-rgt-out--_binary64_12649` `associate--l-_binary64_12633`
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_12958` `erf-erfc_binary64_12957` `erf-odd_binary64_12956` `if-if-and-not_binary64_12955` `if-if-and_binary64_12954` `if-if-or-not_binary64_12953` `if-if-or_binary64_12952` `if-not_binary64_12951` `if-same_binary64_12950` `if-false_binary64_12949` `if-true_binary64_12948` `not-gte_binary64_12947` `not-lte_binary64_12946` `not-gt_binary64_12945` `not-lt_binary64_12944` `gte-same_binary64_12943` `lte-same_binary64_12942` `gt-same_binary64_12941` `lt-same_binary64_12940` `sinh---cosh_binary64_12887` `sinh-+-cosh_binary64_12886` `sinh-cosh_binary64_12885` `tanh-def-c_binary64_12884` `tanh-def-b_binary64_12883` `tanh-def-a_binary64_12882` `cosh-def_binary64_12881` `sinh-def_binary64_12880` `tan-neg_binary64_12827` `cos-neg_binary64_12826` `sin-neg_binary64_12825` `tan-0_binary64_12824` `cos-0_binary64_12823` `sin-0_binary64_12822` `hang-m-tan_binary64_12821` `hang-p-tan_binary64_12820` `hang-m0-tan_binary64_12819` `hang-p0-tan_binary64_12818` `hang-0m-tan_binary64_12817` `hang-0p-tan_binary64_12816` `tan-+PI/2_binary64_12815` `tan-+PI_binary64_12814` `tan-PI_binary64_12813` `tan-PI/3_binary64_12812` `tan-PI/4_binary64_12811` `tan-PI/6_binary64_12810` `cos-+PI/2_binary64_12809` `cos-+PI_binary64_12808` `cos-PI_binary64_12807` `cos-PI/2_binary64_12806` `cos-PI/3_binary64_12805` `cos-PI/4_binary64_12804` `cos-PI/6_binary64_12803` `sin-+PI/2_binary64_12802` `sin-+PI_binary64_12801` `sin-PI_binary64_12800` `sin-PI/2_binary64_12799` `sin-PI/3_binary64_12798` `sin-PI/4_binary64_12797` `sin-PI/6_binary64_12796` `sub-1-sin_binary64_12795` `sub-1-cos_binary64_12794` `-1-add-sin_binary64_12793` `-1-add-cos_binary64_12792` `1-sub-sin_binary64_12791` `1-sub-cos_binary64_12790` `cos-sin-sum_binary64_12789` `log-E_binary64_12785` `pow-base-0_binary64_12779` `unpow1/3_binary64_12762` `unpow1/2_binary64_12759` `exp-to-pow_binary64_12757` `pow-base-1_binary64_12755` `unpow0_binary64_12754` `unpow-1_binary64_12752` `exp-lft-cube_binary64_12751` `exp-cbrt_binary64_12749` `exp-neg_binary64_12742` `e-exp-1_binary64_12740` `exp-1-e_binary64_12738` `exp-0_binary64_12737` `rem-exp-log_binary64_12735` `rem-3cbrt-rft_binary64_12721` `rem-3cbrt-lft_binary64_12720` `rem-cbrt-cube_binary64_12719` `rem-cube-cbrt_binary64_12718` `sqr-abs_binary64_12710` `rem-sqrt-square_binary64_12708` `rem-square-sqrt_binary64_12707` `mul-1-neg_binary64_12687` `--rgt-identity_binary64_12681` `+-lft-identity_binary64_12679` `div0_binary64_12676` `+-inverses_binary64_12674` `lft-mult-inverse_binary64_12673` `remove-double-div_binary64_12671` `difference-of-sqr--1_binary64_12666` `difference-of-sqr-1_binary64_12665` `distribute-frac-neg_binary64_12658` `distribute-neg-out_binary64_12657` `distribute-rgt1-in_binary64_12651` `distribute-lft1-in_binary64_12650` `distribute-lft-out--_binary64_12647` `count-2_binary64_12643`

Counts

174 → 403

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	5620
1	329	5233
2	1159	5227
3	3203	5227

prune2.1s (19.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	403	0	403
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	403	3	406

Error

0.2b

Counts

406 → 3

Compiler

Compiled 29312 to 15698 computations (46.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 8 (.f64 (/.f64 y x) (/.f64 y x)))
0.2b	(*.f64 (/.f64 y x) (/.f64 y x))

rewrite118.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

44×	`add-sqr-sqrt_binary64_12717`
40×	`times-frac_binary64_12701`
32×	`add-exp-log_binary64_12733` `add-cbrt-cube_binary64_12731`
31×	`add-cube-cbrt_binary64_12730` `*-un-lft-identity_binary64_12695`
16×	`associate-l_binary64_12636`
14×	`pow1_binary64_12756` `associate-r_binary64_12635`
13×	`prod-exp_binary64_12744` `cbrt-unprod_binary64_12728` `swap-sqr_binary64_12662`
8×	`div-exp_binary64_12746` `cbrt-undiv_binary64_12729`
5×	`unswap-sqr_binary64_12663` `associate-*r/_binary64_12637`
4×	`pow-prod-down_binary64_12766` `div-inv_binary64_12692`
2×	`add-log-exp_binary64_12734` `frac-times_binary64_12705` `associate-l/_binary64_12638` `-commutative_binary64_12626`
1×	`pow2_binary64_12776` `pow-prod-up_binary64_12765` `pow-plus_binary64_12758` `pow-sqr_binary64_12668`

Counts

2 → 95

Calls

2 calls:

11.0ms	(*.f64 (/.f64 y x) (/.f64 y x))
9.0ms	(.f64 8 (.f64 (/.f64 y x) (/.f64 y x)))

Compiler

Compiled 1848 to 699 computations (62.2% saved)

series272.0ms (2.5%)

Error

0.2b

Counts

2 → 12

Calls

2 calls:

141.0ms	(.f64 8 (.f64 (/.f64 y x) (/.f64 y x)))
122.0ms	(*.f64 (/.f64 y x) (/.f64 y x))

Compiler

Compiled 396 to 374 computations (5.6% saved)

simplify487.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

537×	`associate-/l/_binary64_12642`
447×	`unswap-sqr_binary64_12663`
299×	`associate-/r*_binary64_12639`
270×	`distribute-rgt-in_binary64_12645`
258×	`associate-/r/_binary64_12641`
250×	`*-commutative_binary64_12626`
153×	`associate-*l/_binary64_12638`
148×	`associate-r_binary64_12635`
146×	`associate-*r/_binary64_12637`
141×	`log-div_binary64_12782`
139×	`associate-l_binary64_12636`
138×	`log-prod_binary64_12781` `cube-div_binary64_12724`
130×	`swap-sqr_binary64_12662`
120×	`cube-prod_binary64_12723` `associate-/l*_binary64_12640`
109×	`exp-prod_binary64_12747`
106×	`sqr-pow_binary64_12667`
76×	`*-lft-identity_binary64_12684`
61×	`*-rgt-identity_binary64_12685`
53×	`cancel-sign-sub-inv_binary64_12661`
47×	`times-frac_binary64_12701`
38×	`pow-sqr_binary64_12668`
34×	`sub-neg_binary64_12688`
25×	`associate-+l+_binary64_12628`
22×	`unpow3_binary64_12761` `distribute-rgt-out_binary64_12648`
21×	`distribute-neg-in_binary64_12656`
20×	`cube-mult_binary64_12725` `associate-+r+_binary64_12627`
19×	`pow-plus_binary64_12758`
18×	`distribute-lft-in_binary64_12644`
16×	`div-exp_binary64_12746` `prod-exp_binary64_12744` `unsub-neg_binary64_12689`
15×	`cube-unmult_binary64_12732` `neg-mul-1_binary64_12691`
13×	`exp-sqrt_binary64_12748`
12×	`log-pow_binary64_12784` `exp-lft-sqr_binary64_12750` `neg-sub0_binary64_12690` `associate-+l-_binary64_12630` `associate-+r-_binary64_12629`
11×	`/-rgt-identity_binary64_12686`
10×	`distribute-lft-neg-in_binary64_12652` `distribute-rgt-out--_binary64_12649` `+-commutative_binary64_12625`
9×	`log-rec_binary64_12783` `rem-sqrt-square_binary64_12708`
8×	`distribute-lft-neg-out_binary64_12654` `associate--r+_binary64_12631`
7×	`distribute-rgt1-in_binary64_12651` `associate--l+_binary64_12632`
6×	`distribute-rgt-neg-out_binary64_12655` `distribute-rgt-neg-in_binary64_12653`
5×	`distribute-lft-out_binary64_12646`
4×	`rec-exp_binary64_12745` `count-2_binary64_12643` `associate--r-_binary64_12634` `associate--l-_binary64_12633`
3×	`exp-sum_binary64_12741` `rem-3cbrt-rft_binary64_12721` `rem-3cbrt-lft_binary64_12720` `rem-square-sqrt_binary64_12707`
2×	`unpow2_binary64_12760` `unpow1_binary64_12753` `distribute-lft1-in_binary64_12650` `distribute-lft-out--_binary64_12647`
1×	`pow-base-1_binary64_12755` `exp-diff_binary64_12743` `1-exp_binary64_12739` `exp-1-e_binary64_12738` `rem-log-exp_binary64_12736` `remove-double-neg_binary64_12683` `sub0-neg_binary64_12682` `mul0-lft_binary64_12677` `*-inverses_binary64_12675` `remove-double-div_binary64_12671` `distribute-neg-out_binary64_12657`
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_12958` `erf-erfc_binary64_12957` `erf-odd_binary64_12956` `if-if-and-not_binary64_12955` `if-if-and_binary64_12954` `if-if-or-not_binary64_12953` `if-if-or_binary64_12952` `if-not_binary64_12951` `if-same_binary64_12950` `if-false_binary64_12949` `if-true_binary64_12948` `not-gte_binary64_12947` `not-lte_binary64_12946` `not-gt_binary64_12945` `not-lt_binary64_12944` `gte-same_binary64_12943` `lte-same_binary64_12942` `gt-same_binary64_12941` `lt-same_binary64_12940` `sinh---cosh_binary64_12887` `sinh-+-cosh_binary64_12886` `sinh-cosh_binary64_12885` `tanh-def-c_binary64_12884` `tanh-def-b_binary64_12883` `tanh-def-a_binary64_12882` `cosh-def_binary64_12881` `sinh-def_binary64_12880` `tan-neg_binary64_12827` `cos-neg_binary64_12826` `sin-neg_binary64_12825` `tan-0_binary64_12824` `cos-0_binary64_12823` `sin-0_binary64_12822` `hang-m-tan_binary64_12821` `hang-p-tan_binary64_12820` `hang-m0-tan_binary64_12819` `hang-p0-tan_binary64_12818` `hang-0m-tan_binary64_12817` `hang-0p-tan_binary64_12816` `tan-+PI/2_binary64_12815` `tan-+PI_binary64_12814` `tan-PI_binary64_12813` `tan-PI/3_binary64_12812` `tan-PI/4_binary64_12811` `tan-PI/6_binary64_12810` `cos-+PI/2_binary64_12809` `cos-+PI_binary64_12808` `cos-PI_binary64_12807` `cos-PI/2_binary64_12806` `cos-PI/3_binary64_12805` `cos-PI/4_binary64_12804` `cos-PI/6_binary64_12803` `sin-+PI/2_binary64_12802` `sin-+PI_binary64_12801` `sin-PI_binary64_12800` `sin-PI/2_binary64_12799` `sin-PI/3_binary64_12798` `sin-PI/4_binary64_12797` `sin-PI/6_binary64_12796` `sub-1-sin_binary64_12795` `sub-1-cos_binary64_12794` `-1-add-sin_binary64_12793` `-1-add-cos_binary64_12792` `1-sub-sin_binary64_12791` `1-sub-cos_binary64_12790` `cos-sin-sum_binary64_12789` `log-E_binary64_12785` `pow-base-0_binary64_12779` `unpow1/3_binary64_12762` `unpow1/2_binary64_12759` `exp-to-pow_binary64_12757` `unpow0_binary64_12754` `unpow-1_binary64_12752` `exp-lft-cube_binary64_12751` `exp-cbrt_binary64_12749` `exp-neg_binary64_12742` `e-exp-1_binary64_12740` `exp-0_binary64_12737` `rem-exp-log_binary64_12735` `cube-neg_binary64_12722` `rem-cbrt-cube_binary64_12719` `rem-cube-cbrt_binary64_12718` `sqr-abs_binary64_12710` `sqr-neg_binary64_12709` `div-sub_binary64_12700` `mul-1-neg_binary64_12687` `--rgt-identity_binary64_12681` `+-rgt-identity_binary64_12680` `+-lft-identity_binary64_12679` `mul0-rgt_binary64_12678` `div0_binary64_12676` `+-inverses_binary64_12674` `lft-mult-inverse_binary64_12673` `rgt-mult-inverse_binary64_12672` `difference-of-sqr--1_binary64_12666` `difference-of-sqr-1_binary64_12665` `difference-of-squares_binary64_12664` `cancel-sign-sub_binary64_12660` `distribute-neg-frac_binary64_12659` `distribute-frac-neg_binary64_12658`

Counts

107 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	1843
1	386	1490
2	1346	1410
3	3123	1325

prune224.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	238	4	242

Error

0.2b

Counts

242 → 4

Compiler

Compiled 4306 to 1667 computations (61.3% saved)

regimes378.0ms (3.5%)

Accuracy

Total 14.6b remaining (98.7%)

Threshold costs 0b (0%)

Compiler

Compiled 2704 to 1822 computations (32.6% saved)

bsearch105.0ms (1%)

Steps

Iters	Range		Point
9	1.9245248108512554e+93	2.9871896888805264e+98	2.3603932586440707e+93
10	8940940.886897527	1.6924302778817275e+25	1.1479425156598322e+25
9	6.434120008777964e-109	6.143071788487509e-103	1.5090468438504177e-108
8	-1990583705354130.8	-373286383877.15765	-203696801868708.62

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`neg-mul-1_binary64_12691` `neg-sub0_binary64_12690`
18×	`*-commutative_binary64_12626`
14×	`+-commutative_binary64_12625`
13×	`distribute-rgt-neg-in_binary64_12653`
12×	`sub-neg_binary64_12688` `distribute-lft-neg-in_binary64_12652`
9×	`distribute-rgt-neg-out_binary64_12655` `distribute-lft-neg-out_binary64_12654`
8×	`*-lft-identity_binary64_12684`
7×	`unsub-neg_binary64_12689` `cancel-sign-sub-inv_binary64_12661`
5×	`*-rgt-identity_binary64_12685`
2×	`distribute-neg-frac_binary64_12659`
1×	`1-exp_binary64_12739`
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_12955` `if-if-and_binary64_12954` `if-if-or-not_binary64_12953` `if-if-or_binary64_12952` `if-not_binary64_12951` `if-same_binary64_12950` `if-false_binary64_12949` `if-true_binary64_12948` `tan-0_binary64_12824` `cos-0_binary64_12823` `sin-0_binary64_12822` `unpow1_binary64_12753` `e-exp-1_binary64_12740` `exp-1-e_binary64_12738` `exp-0_binary64_12737` `sqr-abs_binary64_12710` `sqr-neg_binary64_12709` `mul-1-neg_binary64_12687` `/-rgt-identity_binary64_12686` `remove-double-neg_binary64_12683` `sub0-neg_binary64_12682` `--rgt-identity_binary64_12681` `+-rgt-identity_binary64_12680` `+-lft-identity_binary64_12679` `cancel-sign-sub_binary64_12660` `distribute-frac-neg_binary64_12658` `distribute-neg-out_binary64_12657` `distribute-neg-in_binary64_12656`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	131
1	56	131
2	72	131
3	93	131
4	127	131
5	142	131
6	150	131
7	153	131

Proof

(if real (<= f64 h0 -1629574414949669/8) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0)))) (if real (<= f64 h0 7980515386491239/5288447750321988791615322464262168318627237463714249754277190362195246329890490766601513683517722278780729696200186866434048) (=> (- f64 (/ f64 1/2 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))) 1)) (if real (<= f64 h0 11479425156598322123767808) (- f64 (/ f64 (* f64 h0 h0) (+ f64 (* f64 h0 h0) (* f64 (* f64 h1 4) h1))) (/ f64 (* f64 h1 4) (/ f64 (+ f64 (* f64 h0 h0) (* f64 h1 (* f64 h1 4))) h1))) (if real (<= f64 h0 2360393258644070726213713923902290724382879567626611148931215486194655003562465094340551114752) (+ f64 -1 (* f64 (/ f64 1/2 h1) (/ f64 h0 (/ f64 h1 h0)))) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))))))))
sub-neg_binary64_12688 =>
(if real (<= f64 h0 -1629574414949669/8) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0)))) (if real (<= f64 h0 7980515386491239/5288447750321988791615322464262168318627237463714249754277190362195246329890490766601513683517722278780729696200186866434048) (+ f64 (/ f64 1/2 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))) (neg f64 1)) (if real (<= f64 h0 11479425156598322123767808) (- f64 (/ f64 (* f64 h0 h0) (+ f64 (* f64 h0 h0) (* f64 (* f64 h1 4) h1))) (/ f64 (* f64 h1 4) (/ f64 (+ f64 (* f64 h0 h0) (* f64 h1 (* f64 h1 4))) h1))) (if real (<= f64 h0 2360393258644070726213713923902290724382879567626611148931215486194655003562465094340551114752) (+ f64 -1 (* f64 (/ f64 1/2 h1) (/ f64 h0 (/ f64 h1 h0)))) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))))))))
<= *-commutative_binary64_12626
(if real (<= f64 h0 -1629574414949669/8) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0)))) (if real (<= f64 h0 7980515386491239/5288447750321988791615322464262168318627237463714249754277190362195246329890490766601513683517722278780729696200186866434048) (+ f64 (/ f64 1/2 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))) (=> (neg f64 1))) (if real (<= f64 h0 11479425156598322123767808) (- f64 (/ f64 (* f64 h0 h0) (+ f64 (* f64 h0 h0) (<= (* f64 h1 (* f64 h1 4))))) (/ f64 (* f64 h1 4) (/ f64 (+ f64 (* f64 h0 h0) (* f64 h1 (* f64 h1 4))) h1))) (if real (<= f64 h0 2360393258644070726213713923902290724382879567626611148931215486194655003562465094340551114752) (+ f64 -1 (* f64 (/ f64 1/2 h1) (/ f64 h0 (/ f64 h1 h0)))) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))))))))
neg-mul-1_binary64_12691 =>
(if real (<= f64 h0 -1629574414949669/8) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0)))) (if real (<= f64 h0 7980515386491239/5288447750321988791615322464262168318627237463714249754277190362195246329890490766601513683517722278780729696200186866434048) (+ f64 (/ f64 1/2 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))) (=> (* f64 -1 1))) (if real (<= f64 h0 11479425156598322123767808) (- f64 (/ f64 (* f64 h0 h0) (+ f64 (* f64 h0 h0) (* f64 h1 (* f64 h1 4)))) (/ f64 (* f64 h1 4) (/ f64 (+ f64 (* f64 h0 h0) (* f64 h1 (* f64 h1 4))) h1))) (if real (<= f64 h0 2360393258644070726213713923902290724382879567626611148931215486194655003562465094340551114752) (+ f64 -1 (* f64 (/ f64 1/2 h1) (/ f64 h0 (/ f64 h1 h0)))) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))))))))
*-rgt-identity_binary64_12685 =>
(if real (<= f64 h0 -1629574414949669/8) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0)))) (if real (<= f64 h0 7980515386491239/5288447750321988791615322464262168318627237463714249754277190362195246329890490766601513683517722278780729696200186866434048) (+ f64 (/ f64 1/2 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))) -1) (if real (<= f64 h0 11479425156598322123767808) (- f64 (/ f64 (* f64 h0 h0) (+ f64 (* f64 h0 h0) (* f64 h1 (* f64 h1 4)))) (/ f64 (* f64 h1 4) (/ f64 (+ f64 (* f64 h0 h0) (* f64 h1 (* f64 h1 4))) h1))) (if real (<= f64 h0 2360393258644070726213713923902290724382879567626611148931215486194655003562465094340551114752) (+ f64 -1 (* f64 (/ f64 1/2 h1) (/ f64 h0 (/ f64 h1 h0)))) (- f64 1 (* f64 8 (* f64 (/ f64 h1 h0) (/ f64 h1 h0))))))))

end0.0ms (0%)

sample999.0ms (9.2%)

Algorithm

1×

intervals

Results

342.0ms

8000×

body

128

valid

Compiler

Compiled 598 to 383 computations (36% saved)

Details

analyze12.0ms (0.1%)

sample20.0ms (0.2%)

simplify1.3s (11.9%)

prune4.0ms (0%)

localize8.0ms (0.1%)

rewrite89.0ms (0.8%)

series471.0ms (4.3%)

simplify323.0ms (3%)

prune297.0ms (2.7%)

localize8.0ms (0.1%)

rewrite125.0ms (1.1%)

series296.0ms (2.7%)

simplify439.0ms (4%)

prune241.0ms (2.2%)

localize18.0ms (0.2%)

rewrite452.0ms (4.2%)

series1.2s (11.4%)

simplify797.0ms (7.3%)

prune2.1s (19.6%)

localize6.0ms (0.1%)

rewrite118.0ms (1.1%)

series272.0ms (2.5%)

simplify487.0ms (4.5%)

prune224.0ms (2.1%)

regimes378.0ms (3.5%)

bsearch105.0ms (1%)

simplify13.0ms (0.1%)

end0.0ms (0%)

sample999.0ms (9.2%)

Profiling