Details

Time bar (total: 4.9s)

analyze42.0ms (0.9%)

Algorithm
search
Search
TrueOtherFalseIter
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
18.7%81.2%0.1%5
65.6%34.3%0.1%6
76.5%23.4%0.1%7
82%18%0.1%8
87.8%12.1%0.1%9
90.7%9.2%0.1%10
93.8%6.1%0.1%11
95.3%4.6%0.1%12
96.8%3.1%0.1%13
97.6%2.3%0.1%14
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample22.0ms (0.5%)

Algorithm
intervals
Results
13.0ms256×body128valid
Compiler

Compiled 15 to 15 computations (0% saved)

simplify164.0ms (3.3%)

Algorithm
egg-herbie
Rules
*-commutative_binary64_31040
associate-/r/_binary64_31055 associate-/l*_binary64_31054
+-commutative_binary64_31039
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_31372 erf-erfc_binary64_31371 erf-odd_binary64_31370 if-if-and-not_binary64_31369 if-if-and_binary64_31368 if-if-or-not_binary64_31367 if-if-or_binary64_31366 if-not_binary64_31365 if-same_binary64_31364 if-false_binary64_31363 if-true_binary64_31362 not-gte_binary64_31361 not-lte_binary64_31360 not-gt_binary64_31359 not-lt_binary64_31358 gte-same_binary64_31357 lte-same_binary64_31356 gt-same_binary64_31355 lt-same_binary64_31354 sinh---cosh_binary64_31301 sinh-+-cosh_binary64_31300 sinh-cosh_binary64_31299 tanh-def-c_binary64_31298 tanh-def-b_binary64_31297 tanh-def-a_binary64_31296 cosh-def_binary64_31295 sinh-def_binary64_31294 tan-neg_binary64_31241 cos-neg_binary64_31240 sin-neg_binary64_31239 tan-0_binary64_31238 cos-0_binary64_31237 sin-0_binary64_31236 hang-m-tan_binary64_31235 hang-p-tan_binary64_31234 hang-m0-tan_binary64_31233 hang-p0-tan_binary64_31232 hang-0m-tan_binary64_31231 hang-0p-tan_binary64_31230 tan-+PI/2_binary64_31229 tan-+PI_binary64_31228 tan-PI_binary64_31227 tan-PI/3_binary64_31226 tan-PI/4_binary64_31225 tan-PI/6_binary64_31224 cos-+PI/2_binary64_31223 cos-+PI_binary64_31222 cos-PI_binary64_31221 cos-PI/2_binary64_31220 cos-PI/3_binary64_31219 cos-PI/4_binary64_31218 cos-PI/6_binary64_31217 sin-+PI/2_binary64_31216 sin-+PI_binary64_31215 sin-PI_binary64_31214 sin-PI/2_binary64_31213 sin-PI/3_binary64_31212 sin-PI/4_binary64_31211 sin-PI/6_binary64_31210 sub-1-sin_binary64_31209 sub-1-cos_binary64_31208 -1-add-sin_binary64_31207 -1-add-cos_binary64_31206 1-sub-sin_binary64_31205 1-sub-cos_binary64_31204 cos-sin-sum_binary64_31203 log-E_binary64_31199 log-pow_binary64_31198 log-rec_binary64_31197 log-div_binary64_31196 log-prod_binary64_31195 pow-base-0_binary64_31193 unpow1/3_binary64_31176 unpow3_binary64_31175 unpow2_binary64_31174 unpow1/2_binary64_31173 pow-plus_binary64_31172 exp-to-pow_binary64_31171 pow-base-1_binary64_31169 unpow0_binary64_31168 unpow1_binary64_31167 unpow-1_binary64_31166 exp-lft-cube_binary64_31165 exp-lft-sqr_binary64_31164 exp-cbrt_binary64_31163 exp-sqrt_binary64_31162 exp-prod_binary64_31161 div-exp_binary64_31160 rec-exp_binary64_31159 prod-exp_binary64_31158 exp-diff_binary64_31157 exp-neg_binary64_31156 exp-sum_binary64_31155 e-exp-1_binary64_31154 1-exp_binary64_31153 exp-1-e_binary64_31152 exp-0_binary64_31151 rem-log-exp_binary64_31150 rem-exp-log_binary64_31149 cube-unmult_binary64_31146 cube-mult_binary64_31139 cube-div_binary64_31138 cube-prod_binary64_31137 cube-neg_binary64_31136 rem-3cbrt-rft_binary64_31135 rem-3cbrt-lft_binary64_31134 rem-cbrt-cube_binary64_31133 rem-cube-cbrt_binary64_31132 sqr-abs_binary64_31124 sqr-neg_binary64_31123 rem-sqrt-square_binary64_31122 rem-square-sqrt_binary64_31121 times-frac_binary64_31115 div-sub_binary64_31114 neg-mul-1_binary64_31105 neg-sub0_binary64_31104 unsub-neg_binary64_31103 sub-neg_binary64_31102 mul-1-neg_binary64_31101 /-rgt-identity_binary64_31100 *-rgt-identity_binary64_31099 *-lft-identity_binary64_31098 remove-double-neg_binary64_31097 sub0-neg_binary64_31096 --rgt-identity_binary64_31095 +-rgt-identity_binary64_31094 +-lft-identity_binary64_31093 mul0-rgt_binary64_31092 mul0-lft_binary64_31091 div0_binary64_31090 *-inverses_binary64_31089 +-inverses_binary64_31088 lft-mult-inverse_binary64_31087 rgt-mult-inverse_binary64_31086 remove-double-div_binary64_31085 pow-sqr_binary64_31082 sqr-pow_binary64_31081 difference-of-sqr--1_binary64_31080 difference-of-sqr-1_binary64_31079 difference-of-squares_binary64_31078 unswap-sqr_binary64_31077 swap-sqr_binary64_31076 cancel-sign-sub-inv_binary64_31075 cancel-sign-sub_binary64_31074 distribute-neg-frac_binary64_31073 distribute-frac-neg_binary64_31072 distribute-neg-out_binary64_31071 distribute-neg-in_binary64_31070 distribute-rgt-neg-out_binary64_31069 distribute-lft-neg-out_binary64_31068 distribute-rgt-neg-in_binary64_31067 distribute-lft-neg-in_binary64_31066 distribute-rgt1-in_binary64_31065 distribute-lft1-in_binary64_31064 distribute-rgt-out--_binary64_31063 distribute-rgt-out_binary64_31062 distribute-lft-out--_binary64_31061 distribute-lft-out_binary64_31060 distribute-rgt-in_binary64_31059 distribute-lft-in_binary64_31058 count-2_binary64_31057 associate-/l/_binary64_31056 associate-/r*_binary64_31053 associate-*l/_binary64_31052 associate-*r/_binary64_31051 associate-*l*_binary64_31050 associate-*r*_binary64_31049 associate--r-_binary64_31048 associate--l-_binary64_31047 associate--l+_binary64_31046 associate--r+_binary64_31045 associate-+l-_binary64_31044 associate-+r-_binary64_31043 associate-+l+_binary64_31042 associate-+r+_binary64_31041
Counts
1 → 4
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11110
21510
31810
41910

prune9.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New134
Fresh101
Picked000
Done000
Total235
Error
0.0b
Counts
5 → 3
Compiler

Compiled 49 to 33 computations (32.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 x (+.f64 x y))
0.1b
(*.f64 (/.f64 x (+.f64 x y)) 100)

rewrite79.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
34×*-un-lft-identity_binary64_31109
25×add-sqr-sqrt_binary64_31131 times-frac_binary64_31115
20×add-cube-cbrt_binary64_31144
18×associate-*l*_binary64_31050
add-exp-log_binary64_31147 add-cbrt-cube_binary64_31145
distribute-lft-out_binary64_31060
pow1_binary64_31170 associate-/r/_binary64_31055 associate-/r*_binary64_31053
associate-*r*_binary64_31049 associate-/l*_binary64_31054
div-exp_binary64_31160 prod-exp_binary64_31158 add-log-exp_binary64_31148 cbrt-unprod_binary64_31142 cbrt-undiv_binary64_31143 unswap-sqr_binary64_31077 div-inv_binary64_31106 flip3-+_binary64_31112 flip-+_binary64_31083
pow-prod-down_binary64_31180 associate-*l/_binary64_31052 *-commutative_binary64_31040 frac-2neg_binary64_31120 clear-num_binary64_31108
Counts
2 → 70
Calls

2 calls:

11.0ms
(/.f64 x (+.f64 x y))
11.0ms
(*.f64 (/.f64 x (+.f64 x y)) 100)
Compiler

Compiled 1031 to 370 computations (64.1% saved)

series227.0ms (4.6%)

Error
0.0b
Counts
2 → 36
Calls

2 calls:

114.0ms
(*.f64 (/.f64 x (+.f64 x y)) 100)
84.0ms
(/.f64 x (+.f64 x y))
Compiler

Compiled 966 to 772 computations (20.1% saved)

simplify288.0ms (5.9%)

Algorithm
egg-herbie
Rules
569×cancel-sign-sub-inv_binary64_31075
316×associate-/l*_binary64_31054
303×associate-*l/_binary64_31052
283×associate-*l*_binary64_31050
273×times-frac_binary64_31115
220×associate-*r*_binary64_31049
213×associate-*r/_binary64_31051
207×distribute-rgt-neg-in_binary64_31067
205×distribute-rgt-in_binary64_31059
179×distribute-lft-neg-in_binary64_31066
173×distribute-neg-frac_binary64_31073
152×associate-/r*_binary64_31053
137×unswap-sqr_binary64_31077
131×sub-neg_binary64_31102
100×*-commutative_binary64_31040
97×associate-/r/_binary64_31055
93×distribute-rgt-out--_binary64_31063
89×associate-/l/_binary64_31056
58×sqr-pow_binary64_31081
53×neg-mul-1_binary64_31105
52×div-sub_binary64_31114 neg-sub0_binary64_31104
51×distribute-rgt-out_binary64_31062
45×*-rgt-identity_binary64_31099
44×unsub-neg_binary64_31103
43×*-lft-identity_binary64_31098
42×cube-div_binary64_31138
40×log-div_binary64_31196 +-commutative_binary64_31039
39×distribute-lft-in_binary64_31058
35×associate-+l-_binary64_31044
32×log-prod_binary64_31195
31×cube-prod_binary64_31137
30×distribute-lft-neg-out_binary64_31068 associate-+l+_binary64_31042
28×pow-sqr_binary64_31082 distribute-lft-out_binary64_31060
27×swap-sqr_binary64_31076 associate-+r-_binary64_31043
25×associate--l+_binary64_31046 associate-+r+_binary64_31041
23×/-rgt-identity_binary64_31100
19×distribute-lft-out--_binary64_31061
17×exp-prod_binary64_31161 sub0-neg_binary64_31096 difference-of-squares_binary64_31078
16×+-rgt-identity_binary64_31094
15×distribute-neg-out_binary64_31071
14×associate--r+_binary64_31045
13×pow-plus_binary64_31172 distribute-rgt1-in_binary64_31065
11×distribute-neg-in_binary64_31070
10×cube-unmult_binary64_31146
div-exp_binary64_31160 prod-exp_binary64_31158
exp-sqrt_binary64_31162
log-rec_binary64_31197 unpow3_binary64_31175 distribute-rgt-neg-out_binary64_31069
cube-mult_binary64_31139
exp-lft-sqr_binary64_31164 remove-double-div_binary64_31085
log-pow_binary64_31198 rec-exp_binary64_31159 cancel-sign-sub_binary64_31074
unpow2_binary64_31174 unpow1_binary64_31167 remove-double-neg_binary64_31097 associate--l-_binary64_31047
pow-base-1_binary64_31169 exp-diff_binary64_31157 1-exp_binary64_31153 exp-1-e_binary64_31152 rem-log-exp_binary64_31150 rem-sqrt-square_binary64_31122 --rgt-identity_binary64_31095 +-lft-identity_binary64_31093 mul0-rgt_binary64_31092 mul0-lft_binary64_31091 div0_binary64_31090 *-inverses_binary64_31089 rgt-mult-inverse_binary64_31086 difference-of-sqr--1_binary64_31080 distribute-frac-neg_binary64_31072 associate--r-_binary64_31048
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_31372 erf-erfc_binary64_31371 erf-odd_binary64_31370 if-if-and-not_binary64_31369 if-if-and_binary64_31368 if-if-or-not_binary64_31367 if-if-or_binary64_31366 if-not_binary64_31365 if-same_binary64_31364 if-false_binary64_31363 if-true_binary64_31362 not-gte_binary64_31361 not-lte_binary64_31360 not-gt_binary64_31359 not-lt_binary64_31358 gte-same_binary64_31357 lte-same_binary64_31356 gt-same_binary64_31355 lt-same_binary64_31354 sinh---cosh_binary64_31301 sinh-+-cosh_binary64_31300 sinh-cosh_binary64_31299 tanh-def-c_binary64_31298 tanh-def-b_binary64_31297 tanh-def-a_binary64_31296 cosh-def_binary64_31295 sinh-def_binary64_31294 tan-neg_binary64_31241 cos-neg_binary64_31240 sin-neg_binary64_31239 tan-0_binary64_31238 cos-0_binary64_31237 sin-0_binary64_31236 hang-m-tan_binary64_31235 hang-p-tan_binary64_31234 hang-m0-tan_binary64_31233 hang-p0-tan_binary64_31232 hang-0m-tan_binary64_31231 hang-0p-tan_binary64_31230 tan-+PI/2_binary64_31229 tan-+PI_binary64_31228 tan-PI_binary64_31227 tan-PI/3_binary64_31226 tan-PI/4_binary64_31225 tan-PI/6_binary64_31224 cos-+PI/2_binary64_31223 cos-+PI_binary64_31222 cos-PI_binary64_31221 cos-PI/2_binary64_31220 cos-PI/3_binary64_31219 cos-PI/4_binary64_31218 cos-PI/6_binary64_31217 sin-+PI/2_binary64_31216 sin-+PI_binary64_31215 sin-PI_binary64_31214 sin-PI/2_binary64_31213 sin-PI/3_binary64_31212 sin-PI/4_binary64_31211 sin-PI/6_binary64_31210 sub-1-sin_binary64_31209 sub-1-cos_binary64_31208 -1-add-sin_binary64_31207 -1-add-cos_binary64_31206 1-sub-sin_binary64_31205 1-sub-cos_binary64_31204 cos-sin-sum_binary64_31203 log-E_binary64_31199 pow-base-0_binary64_31193 unpow1/3_binary64_31176 unpow1/2_binary64_31173 exp-to-pow_binary64_31171 unpow0_binary64_31168 unpow-1_binary64_31166 exp-lft-cube_binary64_31165 exp-cbrt_binary64_31163 exp-neg_binary64_31156 exp-sum_binary64_31155 e-exp-1_binary64_31154 exp-0_binary64_31151 rem-exp-log_binary64_31149 cube-neg_binary64_31136 rem-3cbrt-rft_binary64_31135 rem-3cbrt-lft_binary64_31134 rem-cbrt-cube_binary64_31133 rem-cube-cbrt_binary64_31132 sqr-abs_binary64_31124 sqr-neg_binary64_31123 rem-square-sqrt_binary64_31121 mul-1-neg_binary64_31101 +-inverses_binary64_31088 lft-mult-inverse_binary64_31087 difference-of-sqr-1_binary64_31079 distribute-lft1-in_binary64_31064 count-2_binary64_31057
Counts
106 → 133
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01261526
13201430
29391358
331291340

prune121.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1312133
Fresh022
Picked011
Done000
Total1315136
Error
0b
Counts
136 → 5
Compiler

Compiled 2133 to 882 computations (58.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 (+.f64 x y) 100)
0.2b
(/.f64 x (/.f64 (+.f64 x y) 100))

rewrite129.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
108×times-frac_binary64_31115
92×*-un-lft-identity_binary64_31109
60×add-cube-cbrt_binary64_31144 add-sqr-sqrt_binary64_31131
19×associate-/r*_binary64_31053
16×distribute-lft-out_binary64_31060
add-exp-log_binary64_31147 add-cbrt-cube_binary64_31145
associate-/l*_binary64_31054
div-inv_binary64_31106
div-exp_binary64_31160 cbrt-undiv_binary64_31143
pow1_binary64_31170 add-log-exp_binary64_31148 frac-2neg_binary64_31120 clear-num_binary64_31108 associate-/l/_binary64_31056
associate-/r/_binary64_31055 flip3-+_binary64_31112 flip-+_binary64_31083
Counts
2 → 115
Calls

2 calls:

8.0ms
(/.f64 x (/.f64 (+.f64 x y) 100))
6.0ms
(/.f64 (+.f64 x y) 100)
Compiler

Compiled 1934 to 979 computations (49.4% saved)

series233.0ms (4.8%)

Error
0b
Counts
2 → 30
Calls

2 calls:

114.0ms
(/.f64 x (/.f64 (+.f64 x y) 100))
96.0ms
(/.f64 (+.f64 x y) 100)
Compiler

Compiled 729 to 592 computations (18.8% saved)

simplify394.0ms (8.1%)

Algorithm
egg-herbie
Rules
535×associate-/r/_binary64_31055
432×cancel-sign-sub-inv_binary64_31075
359×associate-*l/_binary64_31052
332×associate-/r*_binary64_31053
277×associate-*l*_binary64_31050
259×associate-*r/_binary64_31051
229×*-commutative_binary64_31040
168×associate-*r*_binary64_31049
154×distribute-neg-frac_binary64_31073
148×distribute-rgt-neg-in_binary64_31067
131×associate-/l/_binary64_31056
129×associate-/l*_binary64_31054
122×distribute-lft-neg-in_binary64_31066
100×distribute-rgt-out_binary64_31062
96×sub-neg_binary64_31102 unswap-sqr_binary64_31077
81×distribute-rgt-out--_binary64_31063
74×times-frac_binary64_31115
68×distribute-rgt-in_binary64_31059
61×div-sub_binary64_31114
57×distribute-lft-in_binary64_31058
55×neg-mul-1_binary64_31105
54×neg-sub0_binary64_31104
47×sqr-pow_binary64_31081
46×unsub-neg_binary64_31103
40×/-rgt-identity_binary64_31100 *-rgt-identity_binary64_31099
33×distribute-lft-neg-out_binary64_31068 +-commutative_binary64_31039
31×cube-prod_binary64_31137
29×log-prod_binary64_31195
28×log-div_binary64_31196 *-lft-identity_binary64_31098
27×cube-div_binary64_31138 pow-sqr_binary64_31082 swap-sqr_binary64_31076
21×associate-+l+_binary64_31042 associate-+r+_binary64_31041
20×associate-+l-_binary64_31044
19×associate-+r-_binary64_31043
16×div-exp_binary64_31160 prod-exp_binary64_31158
15×pow-plus_binary64_31172 exp-prod_binary64_31161
13×distribute-neg-in_binary64_31070 distribute-rgt1-in_binary64_31065 associate--l+_binary64_31046
12×sub0-neg_binary64_31096 distribute-neg-out_binary64_31071
10×cube-unmult_binary64_31146 distribute-rgt-neg-out_binary64_31069 associate--r+_binary64_31045
+-rgt-identity_binary64_31094
distribute-lft-out_binary64_31060
log-pow_binary64_31198 unpow3_binary64_31175 exp-sqrt_binary64_31162
rec-exp_binary64_31159 cube-mult_binary64_31139 distribute-frac-neg_binary64_31072
mul0-rgt_binary64_31092 mul0-lft_binary64_31091 remove-double-div_binary64_31085 associate--r-_binary64_31048 associate--l-_binary64_31047
unpow2_binary64_31174 unpow1_binary64_31167 exp-lft-sqr_binary64_31164 remove-double-neg_binary64_31097 difference-of-squares_binary64_31078 cancel-sign-sub_binary64_31074 distribute-lft-out--_binary64_31061
log-rec_binary64_31197 pow-base-1_binary64_31169 exp-diff_binary64_31157 1-exp_binary64_31153 rem-log-exp_binary64_31150 rem-sqrt-square_binary64_31122 --rgt-identity_binary64_31095 div0_binary64_31090 *-inverses_binary64_31089 rgt-mult-inverse_binary64_31086 distribute-lft1-in_binary64_31064 count-2_binary64_31057
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_31372 erf-erfc_binary64_31371 erf-odd_binary64_31370 if-if-and-not_binary64_31369 if-if-and_binary64_31368 if-if-or-not_binary64_31367 if-if-or_binary64_31366 if-not_binary64_31365 if-same_binary64_31364 if-false_binary64_31363 if-true_binary64_31362 not-gte_binary64_31361 not-lte_binary64_31360 not-gt_binary64_31359 not-lt_binary64_31358 gte-same_binary64_31357 lte-same_binary64_31356 gt-same_binary64_31355 lt-same_binary64_31354 sinh---cosh_binary64_31301 sinh-+-cosh_binary64_31300 sinh-cosh_binary64_31299 tanh-def-c_binary64_31298 tanh-def-b_binary64_31297 tanh-def-a_binary64_31296 cosh-def_binary64_31295 sinh-def_binary64_31294 tan-neg_binary64_31241 cos-neg_binary64_31240 sin-neg_binary64_31239 tan-0_binary64_31238 cos-0_binary64_31237 sin-0_binary64_31236 hang-m-tan_binary64_31235 hang-p-tan_binary64_31234 hang-m0-tan_binary64_31233 hang-p0-tan_binary64_31232 hang-0m-tan_binary64_31231 hang-0p-tan_binary64_31230 tan-+PI/2_binary64_31229 tan-+PI_binary64_31228 tan-PI_binary64_31227 tan-PI/3_binary64_31226 tan-PI/4_binary64_31225 tan-PI/6_binary64_31224 cos-+PI/2_binary64_31223 cos-+PI_binary64_31222 cos-PI_binary64_31221 cos-PI/2_binary64_31220 cos-PI/3_binary64_31219 cos-PI/4_binary64_31218 cos-PI/6_binary64_31217 sin-+PI/2_binary64_31216 sin-+PI_binary64_31215 sin-PI_binary64_31214 sin-PI/2_binary64_31213 sin-PI/3_binary64_31212 sin-PI/4_binary64_31211 sin-PI/6_binary64_31210 sub-1-sin_binary64_31209 sub-1-cos_binary64_31208 -1-add-sin_binary64_31207 -1-add-cos_binary64_31206 1-sub-sin_binary64_31205 1-sub-cos_binary64_31204 cos-sin-sum_binary64_31203 log-E_binary64_31199 pow-base-0_binary64_31193 unpow1/3_binary64_31176 unpow1/2_binary64_31173 exp-to-pow_binary64_31171 unpow0_binary64_31168 unpow-1_binary64_31166 exp-lft-cube_binary64_31165 exp-cbrt_binary64_31163 exp-neg_binary64_31156 exp-sum_binary64_31155 e-exp-1_binary64_31154 exp-1-e_binary64_31152 exp-0_binary64_31151 rem-exp-log_binary64_31149 cube-neg_binary64_31136 rem-3cbrt-rft_binary64_31135 rem-3cbrt-lft_binary64_31134 rem-cbrt-cube_binary64_31133 rem-cube-cbrt_binary64_31132 sqr-abs_binary64_31124 sqr-neg_binary64_31123 rem-square-sqrt_binary64_31121 mul-1-neg_binary64_31101 +-lft-identity_binary64_31093 +-inverses_binary64_31088 lft-mult-inverse_binary64_31087 difference-of-sqr--1_binary64_31080 difference-of-sqr-1_binary64_31079
Counts
145 → 445
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01912626
14422518
214822470
336532461

prune508.0ms (10.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New4450445
Fresh033
Picked011
Done011
Total4455450
Error
0b
Counts
450 → 5
Compiler

Compiled 8374 to 3561 computations (57.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 100 (+.f64 x y))
0.2b
(*.f64 (/.f64 100 (+.f64 x y)) x)

rewrite78.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
34×*-un-lft-identity_binary64_31109
25×add-sqr-sqrt_binary64_31131 times-frac_binary64_31115
20×add-cube-cbrt_binary64_31144
18×associate-*l*_binary64_31050
add-exp-log_binary64_31147 add-cbrt-cube_binary64_31145
distribute-lft-out_binary64_31060
pow1_binary64_31170 associate-/r/_binary64_31055 associate-/r*_binary64_31053
associate-*r*_binary64_31049 associate-/l*_binary64_31054
div-exp_binary64_31160 prod-exp_binary64_31158 add-log-exp_binary64_31148 cbrt-unprod_binary64_31142 cbrt-undiv_binary64_31143 unswap-sqr_binary64_31077 div-inv_binary64_31106 flip3-+_binary64_31112 flip-+_binary64_31083
pow-prod-down_binary64_31180 associate-*l/_binary64_31052 *-commutative_binary64_31040 frac-2neg_binary64_31120 clear-num_binary64_31108
Counts
2 → 70
Calls

2 calls:

10.0ms
(*.f64 (/.f64 100 (+.f64 x y)) x)
5.0ms
(/.f64 100 (+.f64 x y))
Compiler

Compiled 1031 to 532 computations (48.4% saved)

series240.0ms (4.9%)

Error
0b
Counts
2 → 36
Calls

2 calls:

113.0ms
(*.f64 (/.f64 100 (+.f64 x y)) x)
92.0ms
(/.f64 100 (+.f64 x y))
Compiler

Compiled 1182 to 955 computations (19.2% saved)

simplify337.0ms (6.9%)

Algorithm
egg-herbie
Rules
408×associate-/l*_binary64_31054
379×times-frac_binary64_31115
342×associate-*l*_binary64_31050
330×associate-*l/_binary64_31052
291×distribute-neg-frac_binary64_31073
281×distribute-rgt-neg-in_binary64_31067
253×associate-*r*_binary64_31049
231×associate-*r/_binary64_31051
186×unswap-sqr_binary64_31077
176×associate-/r*_binary64_31053
159×sub-neg_binary64_31102
134×associate-/r/_binary64_31055
129×associate-/l/_binary64_31056
114×*-commutative_binary64_31040
104×div-sub_binary64_31114
100×cancel-sign-sub-inv_binary64_31075
68×*-lft-identity_binary64_31098
64×neg-mul-1_binary64_31105 neg-sub0_binary64_31104
63×sqr-pow_binary64_31081
60×unsub-neg_binary64_31103
58×*-rgt-identity_binary64_31099
55×distribute-rgt-in_binary64_31059
50×+-commutative_binary64_31039
41×distribute-lft-in_binary64_31058
40×/-rgt-identity_binary64_31100 distribute-lft-neg-in_binary64_31066
38×log-div_binary64_31196
36×cube-div_binary64_31138 distribute-lft-neg-out_binary64_31068
34×associate-+l-_binary64_31044
32×log-prod_binary64_31195 pow-sqr_binary64_31082
30×cube-prod_binary64_31137
28×associate--l+_binary64_31046 associate-+r-_binary64_31043
26×associate-+l+_binary64_31042
24×swap-sqr_binary64_31076
23×associate-+r+_binary64_31041
19×exp-prod_binary64_31161 +-rgt-identity_binary64_31094
18×associate--r+_binary64_31045
17×sub0-neg_binary64_31096 distribute-rgt-out_binary64_31062
15×distribute-neg-out_binary64_31071 distribute-rgt-out--_binary64_31063
14×difference-of-squares_binary64_31078 distribute-neg-in_binary64_31070
13×pow-plus_binary64_31172
12×cube-unmult_binary64_31146 distribute-lft-out_binary64_31060
11×distribute-lft-out--_binary64_31061
div-exp_binary64_31160 prod-exp_binary64_31158
exp-sqrt_binary64_31162 remove-double-div_binary64_31085
log-rec_binary64_31197
unpow3_binary64_31175 cube-mult_binary64_31139 cancel-sign-sub_binary64_31074 distribute-rgt-neg-out_binary64_31069
exp-lft-sqr_binary64_31164 mul0-rgt_binary64_31092 mul0-lft_binary64_31091
log-pow_binary64_31198 rec-exp_binary64_31159 distribute-rgt1-in_binary64_31065
unpow2_binary64_31174 unpow1_binary64_31167 associate--l-_binary64_31047
exp-diff_binary64_31157 1-exp_binary64_31153 exp-1-e_binary64_31152 rem-log-exp_binary64_31150 rem-sqrt-square_binary64_31122 remove-double-neg_binary64_31097 +-lft-identity_binary64_31093 *-inverses_binary64_31089 rgt-mult-inverse_binary64_31086 distribute-frac-neg_binary64_31072
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_31372 erf-erfc_binary64_31371 erf-odd_binary64_31370 if-if-and-not_binary64_31369 if-if-and_binary64_31368 if-if-or-not_binary64_31367 if-if-or_binary64_31366 if-not_binary64_31365 if-same_binary64_31364 if-false_binary64_31363 if-true_binary64_31362 not-gte_binary64_31361 not-lte_binary64_31360 not-gt_binary64_31359 not-lt_binary64_31358 gte-same_binary64_31357 lte-same_binary64_31356 gt-same_binary64_31355 lt-same_binary64_31354 sinh---cosh_binary64_31301 sinh-+-cosh_binary64_31300 sinh-cosh_binary64_31299 tanh-def-c_binary64_31298 tanh-def-b_binary64_31297 tanh-def-a_binary64_31296 cosh-def_binary64_31295 sinh-def_binary64_31294 tan-neg_binary64_31241 cos-neg_binary64_31240 sin-neg_binary64_31239 tan-0_binary64_31238 cos-0_binary64_31237 sin-0_binary64_31236 hang-m-tan_binary64_31235 hang-p-tan_binary64_31234 hang-m0-tan_binary64_31233 hang-p0-tan_binary64_31232 hang-0m-tan_binary64_31231 hang-0p-tan_binary64_31230 tan-+PI/2_binary64_31229 tan-+PI_binary64_31228 tan-PI_binary64_31227 tan-PI/3_binary64_31226 tan-PI/4_binary64_31225 tan-PI/6_binary64_31224 cos-+PI/2_binary64_31223 cos-+PI_binary64_31222 cos-PI_binary64_31221 cos-PI/2_binary64_31220 cos-PI/3_binary64_31219 cos-PI/4_binary64_31218 cos-PI/6_binary64_31217 sin-+PI/2_binary64_31216 sin-+PI_binary64_31215 sin-PI_binary64_31214 sin-PI/2_binary64_31213 sin-PI/3_binary64_31212 sin-PI/4_binary64_31211 sin-PI/6_binary64_31210 sub-1-sin_binary64_31209 sub-1-cos_binary64_31208 -1-add-sin_binary64_31207 -1-add-cos_binary64_31206 1-sub-sin_binary64_31205 1-sub-cos_binary64_31204 cos-sin-sum_binary64_31203 log-E_binary64_31199 pow-base-0_binary64_31193 unpow1/3_binary64_31176 unpow1/2_binary64_31173 exp-to-pow_binary64_31171 pow-base-1_binary64_31169 unpow0_binary64_31168 unpow-1_binary64_31166 exp-lft-cube_binary64_31165 exp-cbrt_binary64_31163 exp-neg_binary64_31156 exp-sum_binary64_31155 e-exp-1_binary64_31154 exp-0_binary64_31151 rem-exp-log_binary64_31149 cube-neg_binary64_31136 rem-3cbrt-rft_binary64_31135 rem-3cbrt-lft_binary64_31134 rem-cbrt-cube_binary64_31133 rem-cube-cbrt_binary64_31132 sqr-abs_binary64_31124 sqr-neg_binary64_31123 rem-square-sqrt_binary64_31121 mul-1-neg_binary64_31101 --rgt-identity_binary64_31095 div0_binary64_31090 +-inverses_binary64_31088 lft-mult-inverse_binary64_31087 difference-of-sqr--1_binary64_31080 difference-of-sqr-1_binary64_31079 distribute-lft1-in_binary64_31064 count-2_binary64_31057 associate--r-_binary64_31048
Counts
106 → 189
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01421634
13681520
210991493
338931493

prune179.0ms (3.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1890189
Fresh022
Picked011
Done022
Total1895194
Error
0b
Counts
194 → 5
Compiler

Compiled 3235 to 1636 computations (49.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b
(*.f64 (/.f64 (*.f64 x (sqrt.f64 100)) (+.f64 x y)) (sqrt.f64 100))
0.2b
(/.f64 (*.f64 x (sqrt.f64 100)) (+.f64 x y))

rewrite97.0ms (2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
16×add-exp-log_binary64_31147 add-cbrt-cube_binary64_31145
14×*-un-lft-identity_binary64_31109
12×add-sqr-sqrt_binary64_31131
10×associate-*l*_binary64_31050
add-cube-cbrt_binary64_31144 times-frac_binary64_31115
associate-*r*_binary64_31049
prod-exp_binary64_31158 cbrt-unprod_binary64_31142
pow1_binary64_31170 div-exp_binary64_31160 cbrt-undiv_binary64_31143 associate-/r/_binary64_31055 associate-/r*_binary64_31053 sqrt-prod_binary64_31125
distribute-lft-out_binary64_31060
add-log-exp_binary64_31148 div-inv_binary64_31106 flip3-+_binary64_31112 flip-+_binary64_31083 unswap-sqr_binary64_31077
frac-2neg_binary64_31120 clear-num_binary64_31108 associate-/l*_binary64_31054 pow-prod-down_binary64_31180 associate-*l/_binary64_31052 *-commutative_binary64_31040
Counts
2 → 59
Calls

2 calls:

13.0ms
(*.f64 (/.f64 (*.f64 x (sqrt.f64 100)) (+.f64 x y)) (sqrt.f64 100))
7.0ms
(/.f64 (*.f64 x (sqrt.f64 100)) (+.f64 x y))
Compiler

Compiled 1133 to 716 computations (36.8% saved)

series233.0ms (4.8%)

Error
0b
Counts
2 → 36
Calls

2 calls:

102.0ms
(/.f64 (*.f64 x (sqrt.f64 100)) (+.f64 x y))
97.0ms
(*.f64 (/.f64 (*.f64 x (sqrt.f64 100)) (+.f64 x y)) (sqrt.f64 100))
Compiler

Compiled 1131 to 937 computations (17.2% saved)

simplify310.0ms (6.3%)

Algorithm
egg-herbie
Rules
473×cancel-sign-sub-inv_binary64_31075
285×*-commutative_binary64_31040
245×associate-/r*_binary64_31053
215×associate-/l/_binary64_31056
210×associate-/r/_binary64_31055
201×distribute-rgt-in_binary64_31059
193×distribute-rgt-neg-in_binary64_31067
180×sub-neg_binary64_31102
178×distribute-lft-neg-in_binary64_31066
177×distribute-lft-in_binary64_31058
130×unswap-sqr_binary64_31077
120×distribute-neg-frac_binary64_31073
108×associate-*l*_binary64_31050
93×distribute-rgt-out--_binary64_31063
88×associate-*l/_binary64_31052
84×associate-/l*_binary64_31054
80×associate-*r*_binary64_31049
77×neg-mul-1_binary64_31105
76×neg-sub0_binary64_31104
74×times-frac_binary64_31115
67×sqr-pow_binary64_31081
65×distribute-rgt-out_binary64_31062
64×distribute-lft-out_binary64_31060
56×associate-*r/_binary64_31051
54×log-div_binary64_31196 log-prod_binary64_31195
52×cube-div_binary64_31138
48×+-commutative_binary64_31039
46×cube-prod_binary64_31137
45×*-rgt-identity_binary64_31099 associate-+l-_binary64_31044
44×distribute-lft-out--_binary64_31061
43×div-sub_binary64_31114 swap-sqr_binary64_31076
41×associate-+l+_binary64_31042
35×associate-+r+_binary64_31041
32×associate-+r-_binary64_31043
30×pow-sqr_binary64_31082 associate--l+_binary64_31046
29×unsub-neg_binary64_31103
21×/-rgt-identity_binary64_31100 +-rgt-identity_binary64_31094
19×exp-prod_binary64_31161 sub0-neg_binary64_31096 distribute-lft-neg-out_binary64_31068
17×*-lft-identity_binary64_31098
16×associate--r+_binary64_31045
15×distribute-neg-in_binary64_31070
14×difference-of-squares_binary64_31078 distribute-rgt1-in_binary64_31065
13×unpow3_binary64_31175 cube-mult_binary64_31139
12×pow-plus_binary64_31172
10×associate--l-_binary64_31047
cube-unmult_binary64_31146
distribute-rgt-neg-out_binary64_31069
log-pow_binary64_31198 rem-sqrt-square_binary64_31122 cancel-sign-sub_binary64_31074
log-rec_binary64_31197 unpow2_binary64_31174 pow-base-1_binary64_31169 unpow1_binary64_31167 distribute-frac-neg_binary64_31072 distribute-lft1-in_binary64_31064 associate--r-_binary64_31048
exp-lft-sqr_binary64_31164 exp-sqrt_binary64_31162 div-exp_binary64_31160 rec-exp_binary64_31159 prod-exp_binary64_31158 exp-diff_binary64_31157 1-exp_binary64_31153 exp-1-e_binary64_31152 rem-log-exp_binary64_31150 rem-square-sqrt_binary64_31121 remove-double-neg_binary64_31097 --rgt-identity_binary64_31095 div0_binary64_31090 *-inverses_binary64_31089 rgt-mult-inverse_binary64_31086
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_31372 erf-erfc_binary64_31371 erf-odd_binary64_31370 if-if-and-not_binary64_31369 if-if-and_binary64_31368 if-if-or-not_binary64_31367 if-if-or_binary64_31366 if-not_binary64_31365 if-same_binary64_31364 if-false_binary64_31363 if-true_binary64_31362 not-gte_binary64_31361 not-lte_binary64_31360 not-gt_binary64_31359 not-lt_binary64_31358 gte-same_binary64_31357 lte-same_binary64_31356 gt-same_binary64_31355 lt-same_binary64_31354 sinh---cosh_binary64_31301 sinh-+-cosh_binary64_31300 sinh-cosh_binary64_31299 tanh-def-c_binary64_31298 tanh-def-b_binary64_31297 tanh-def-a_binary64_31296 cosh-def_binary64_31295 sinh-def_binary64_31294 tan-neg_binary64_31241 cos-neg_binary64_31240 sin-neg_binary64_31239 tan-0_binary64_31238 cos-0_binary64_31237 sin-0_binary64_31236 hang-m-tan_binary64_31235 hang-p-tan_binary64_31234 hang-m0-tan_binary64_31233 hang-p0-tan_binary64_31232 hang-0m-tan_binary64_31231 hang-0p-tan_binary64_31230 tan-+PI/2_binary64_31229 tan-+PI_binary64_31228 tan-PI_binary64_31227 tan-PI/3_binary64_31226 tan-PI/4_binary64_31225 tan-PI/6_binary64_31224 cos-+PI/2_binary64_31223 cos-+PI_binary64_31222 cos-PI_binary64_31221 cos-PI/2_binary64_31220 cos-PI/3_binary64_31219 cos-PI/4_binary64_31218 cos-PI/6_binary64_31217 sin-+PI/2_binary64_31216 sin-+PI_binary64_31215 sin-PI_binary64_31214 sin-PI/2_binary64_31213 sin-PI/3_binary64_31212 sin-PI/4_binary64_31211 sin-PI/6_binary64_31210 sub-1-sin_binary64_31209 sub-1-cos_binary64_31208 -1-add-sin_binary64_31207 -1-add-cos_binary64_31206 1-sub-sin_binary64_31205 1-sub-cos_binary64_31204 cos-sin-sum_binary64_31203 log-E_binary64_31199 pow-base-0_binary64_31193 unpow1/3_binary64_31176 unpow1/2_binary64_31173 exp-to-pow_binary64_31171 unpow0_binary64_31168 unpow-1_binary64_31166 exp-lft-cube_binary64_31165 exp-cbrt_binary64_31163 exp-neg_binary64_31156 exp-sum_binary64_31155 e-exp-1_binary64_31154 exp-0_binary64_31151 rem-exp-log_binary64_31149 cube-neg_binary64_31136 rem-3cbrt-rft_binary64_31135 rem-3cbrt-lft_binary64_31134 rem-cbrt-cube_binary64_31133 rem-cube-cbrt_binary64_31132 sqr-abs_binary64_31124 sqr-neg_binary64_31123 mul-1-neg_binary64_31101 +-lft-identity_binary64_31093 mul0-rgt_binary64_31092 mul0-lft_binary64_31091 +-inverses_binary64_31088 lft-mult-inverse_binary64_31087 remove-double-div_binary64_31085 difference-of-sqr--1_binary64_31080 difference-of-sqr-1_binary64_31079 distribute-neg-out_binary64_31071 count-2_binary64_31057
Counts
95 → 241
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01301620
13781461
213661407
329531353

prune266.0ms (5.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New2410241
Fresh011
Picked011
Done033
Total2415246
Error
0b
Counts
246 → 5
Compiler

Compiled 4378 to 2411 computations (44.9% saved)

regimes149.0ms (3%)

Accuracy

Total 0.2b remaining (99.3%)

Threshold costs 0.2b (99.3%)

Compiler

Compiled 842 to 683 computations (18.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64_31040 +-commutative_binary64_31039
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_31369 if-if-and_binary64_31368 if-if-or-not_binary64_31367 if-if-or_binary64_31366 if-not_binary64_31365 if-same_binary64_31364 if-false_binary64_31363 if-true_binary64_31362 tan-0_binary64_31238 cos-0_binary64_31237 sin-0_binary64_31236 unpow1_binary64_31167 e-exp-1_binary64_31154 1-exp_binary64_31153 exp-1-e_binary64_31152 exp-0_binary64_31151 sqr-abs_binary64_31124 sqr-neg_binary64_31123 neg-mul-1_binary64_31105 neg-sub0_binary64_31104 unsub-neg_binary64_31103 sub-neg_binary64_31102 mul-1-neg_binary64_31101 /-rgt-identity_binary64_31100 *-rgt-identity_binary64_31099 *-lft-identity_binary64_31098 remove-double-neg_binary64_31097 sub0-neg_binary64_31096 --rgt-identity_binary64_31095 +-rgt-identity_binary64_31094 +-lft-identity_binary64_31093 cancel-sign-sub-inv_binary64_31075 cancel-sign-sub_binary64_31074 distribute-neg-frac_binary64_31073 distribute-frac-neg_binary64_31072 distribute-neg-out_binary64_31071 distribute-neg-in_binary64_31070 distribute-rgt-neg-out_binary64_31069 distribute-lft-neg-out_binary64_31068 distribute-rgt-neg-in_binary64_31067 distribute-lft-neg-in_binary64_31066
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
1910
Proof
(* f64 (/ f64 h0 (+ f64 h0 h1)) 100)

end0.0ms (0%)

sample760.0ms (15.5%)

Algorithm
intervals
Results
200.0ms8000×body128valid
Compiler

Compiled 289 to 232 computations (19.7% saved)

Profiling

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