Details

Time bar (total: 3.1s)

analyze501.0ms (16.3%)

Algorithm
search
egg-herbie
Rules
376×distribute-rgt-in_binary64
360×unsub-neg_binary64
336×sub-neg_binary64
225×associate-+r+_binary64
220×distribute-lft-in_binary64
207×associate-+l+_binary64
195×associate-+l-_binary64
174×associate--r+_binary64
147×distribute-neg-in_binary64
132×cancel-sign-sub-inv_binary64
102×associate--r-_binary64
99×neg-mul-1_binary64 distribute-lft-neg-out_binary64
93×associate--l+_binary64
81×neg-sub0_binary64 distribute-rgt-neg-out_binary64
75×sub0-neg_binary64 distribute-rgt-neg-in_binary64
66×associate-+r-_binary64
60×distribute-neg-out_binary64
57×*-rgt-identity_binary64 associate-*l*_binary64
55×*-commutative_binary64
51×associate-*r*_binary64
37×+-commutative_binary64
36×distribute-rgt-out_binary64
33×distribute-rgt-out--_binary64
21×*-lft-identity_binary64 remove-double-neg_binary64
18×mul0-rgt_binary64 mul0-lft_binary64 cancel-sign-sub_binary64 associate--l-_binary64
15×+-rgt-identity_binary64 distribute-lft-neg-in_binary64
12×--rgt-identity_binary64
+-lft-identity_binary64 distribute-lft-out--_binary64
1-exp_binary64 swap-x-y
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-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_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 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01640
12840
28040
317440
439440
572040
698840
7183240
8140040
9148140
10148140
11148740
12148740
13142940
033
133
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
0%99.9%0.1%5
0%99.9%0.1%6
21.8%78%0.1%7
26.5%73.3%0.1%8
36.7%63.2%0.1%9
41.3%49.9%8.7%10
47.2%43.3%9.5%11
54.4%35.5%10.1%12
57.9%27.4%14.7%13
61.7%23.2%15.1%14
Symmetry

(sort x y)

Compiler

Compiled 8 to 8 computations (0% saved)

sample22.0ms (0.7%)

Algorithm
intervals
Results
6.0ms256×body128valid
0.0ms13×body128invalid
Compiler

Compiled 15 to 18 computations (-20% saved)

simplify35.0ms (1.1%)

Algorithm
egg-herbie
Rules
145×distribute-rgt-in_binary64
135×cancel-sign-sub-inv_binary64
117×sub-neg_binary64
114×associate--r+_binary64
105×unsub-neg_binary64
78×distribute-lft-in_binary64
75×associate-+r+_binary64
72×associate-+l-_binary64
69×associate-+l+_binary64
62×distribute-neg-in_binary64
46×associate--r-_binary64
39×neg-mul-1_binary64
37×neg-sub0_binary64
36×distribute-lft-neg-out_binary64
27×distribute-rgt-neg-out_binary64 associate-*l*_binary64
26×associate--l+_binary64 *-commutative_binary64
25×*-rgt-identity_binary64 sub0-neg_binary64
24×associate-*r*_binary64
20×distribute-neg-out_binary64 distribute-rgt-neg-in_binary64
16×distribute-rgt-out--_binary64
14×associate-+r-_binary64 +-commutative_binary64
12×distribute-rgt-out_binary64
11×remove-double-neg_binary64
10×mul0-rgt_binary64 mul0-lft_binary64
*-lft-identity_binary64
+-rgt-identity_binary64 distribute-lft-neg-in_binary64
--rgt-identity_binary64
associate--l-_binary64
+-lft-identity_binary64 distribute-lft-out--_binary64
mul-1-neg_binary64
1-exp_binary64
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-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_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 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 /-rgt-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11410
23210
36610
416210
528710
638710
767110
862310
961210
1061210
1156910

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.0b
Counts
1 → 1
Compiler

Compiled 7 to 7 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(*.f64 (+.f64 x y) (-.f64 1 z))

rewrite51.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
10×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
cancel-sign-sub-inv_binary64 associate-*r*_binary64
add-cube-cbrt_binary64
frac-times_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-*l*_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 flip3-+_binary64 flip--_binary64 flip-+_binary64
sub-neg_binary64 associate-*l/_binary64 associate-*r/_binary64 difference-of-squares_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 distribute-lft-out_binary64 distribute-lft-out--_binary64 *-commutative_binary64
Counts
1 → 38
Calls

1 calls:

10.0ms
(*.f64 (+.f64 x y) (-.f64 1 z))
Compiler

Compiled 584 to 289 computations (50.5% saved)

series36.0ms (1.2%)

Error
0.0b
Counts
1 → 18
Calls

1 calls:

30.0ms
(*.f64 (+.f64 x y) (-.f64 1 z))
Compiler

Compiled 276 to 215 computations (22.1% saved)

simplify77.0ms (2.5%)

Algorithm
egg-herbie
Rules
619×distribute-rgt-in_binary64
579×distribute-lft-in_binary64
426×unsub-neg_binary64
274×distribute-lft-neg-out_binary64
273×distribute-rgt-neg-out_binary64
223×exp-prod_binary64
219×*-commutative_binary64
164×exp-sum_binary64
140×exp-diff_binary64
115×cancel-sign-sub-inv_binary64
94×associate-*l*_binary64
92×sub-neg_binary64 associate-+l+_binary64
90×exp-neg_binary64
89×neg-sub0_binary64
85×neg-mul-1_binary64
80×associate-*r*_binary64
76×associate-+r+_binary64
71×distribute-neg-out_binary64
64×*-lft-identity_binary64 distribute-rgt-neg-in_binary64
63×*-rgt-identity_binary64
50×distribute-lft-neg-in_binary64
37×sqr-pow_binary64 +-commutative_binary64
24×associate-+l-_binary64
21×mul0-rgt_binary64 mul0-lft_binary64
18×unswap-sqr_binary64
17×swap-sqr_binary64 associate-+r-_binary64
15×cube-prod_binary64
14×distribute-neg-in_binary64
13×distribute-rgt-out_binary64
12×cancel-sign-sub_binary64
10×distribute-rgt-out--_binary64
log-prod_binary64 sub0-neg_binary64 associate--l+_binary64
+-rgt-identity_binary64
associate--r+_binary64
pow-sqr_binary64
unpow3_binary64 cube-unmult_binary64
unpow1/2_binary64 difference-of-sqr-1_binary64 distribute-lft-out_binary64
cube-mult_binary64 div-sub_binary64 distribute-rgt1-in_binary64
mul-1-neg_binary64 difference-of-squares_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64
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 pow-base-0_binary64 unpow1/3_binary64 unpow2_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 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 times-frac_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
56 → 50
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
098846
1287732
2897732
32775732
44512732
54978732

prune33.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New46450
Fresh000
Picked101
Done000
Total47451
Error
0b
Counts
51 → 4
Compiler

Compiled 457 to 247 computations (46% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (+.f64 y x) (neg.f64 (*.f64 z (+.f64 y x))))
0.0b
(*.f64 z (+.f64 y x))

rewrite57.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
14×*-un-lft-identity_binary64
12×add-log-exp_binary64
add-sqr-sqrt_binary64 flip3-+_binary64 associate-*r/_binary64 flip-+_binary64 sum-log_binary64
distribute-lft-out_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 associate-*r*_binary64 distribute-neg-frac_binary64 frac-add_binary64
associate-*l*_binary64 distribute-lft-neg-in_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64 neg-log_binary64 distribute-rgt-out_binary64 distribute-neg-in_binary64 associate-+r+_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64 unsub-neg_binary64 distribute-rgt1-in_binary64 neg-sub0_binary64 associate-+r-_binary64 associate-+l+_binary64 +-commutative_binary64
Counts
2 → 51
Calls

2 calls:

7.0ms
(+.f64 (+.f64 y x) (neg.f64 (*.f64 z (+.f64 y x))))
6.0ms
(*.f64 z (+.f64 y x))
Compiler

Compiled 884 to 228 computations (74.2% saved)

series75.0ms (2.4%)

Error
0b
Counts
2 → 33
Calls

2 calls:

35.0ms
(+.f64 (+.f64 y x) (neg.f64 (*.f64 z (+.f64 y x))))
25.0ms
(*.f64 z (+.f64 y x))
Compiler

Compiled 605 to 437 computations (27.8% saved)

simplify100.0ms (3.2%)

Algorithm
egg-herbie
Rules
596×unsub-neg_binary64
409×times-frac_binary64
394×associate-+l+_binary64
354×*-commutative_binary64
329×associate-+r+_binary64
223×neg-sub0_binary64
210×neg-mul-1_binary64
165×distribute-rgt-in_binary64
163×associate--r+_binary64
157×cancel-sign-sub-inv_binary64
150×distribute-lft-in_binary64
142×exp-sum_binary64
137×associate-*l*_binary64
127×associate-*r*_binary64
118×distribute-lft-neg-out_binary64
113×distribute-rgt-neg-in_binary64
112×exp-prod_binary64
111×+-commutative_binary64
105×exp-diff_binary64
104×distribute-rgt-neg-out_binary64 associate--l+_binary64
92×distribute-lft-neg-in_binary64
83×distribute-neg-in_binary64
80×distribute-rgt-out_binary64
73×sub-neg_binary64
64×associate-+l-_binary64
47×cube-prod_binary64
43×log-prod_binary64
33×associate-+r-_binary64
28×sqr-pow_binary64 distribute-rgt-out--_binary64
21×associate--r-_binary64
18×associate--l-_binary64
17×distribute-rgt1-in_binary64
16×div-exp_binary64 *-lft-identity_binary64
15×prod-exp_binary64
14×div-sub_binary64 *-rgt-identity_binary64 swap-sqr_binary64
13×rec-exp_binary64 mul0-rgt_binary64 mul0-lft_binary64
11×unpow3_binary64
10×cube-mult_binary64 cube-neg_binary64
distribute-lft-out_binary64 associate-/r*_binary64
mul-1-neg_binary64 remove-double-neg_binary64 associate-/l*_binary64
sqr-neg_binary64 unswap-sqr_binary64
cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64
pow-plus_binary64 sub0-neg_binary64 +-rgt-identity_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
cube-unmult_binary64 associate-*r/_binary64
rem-sqrt-square_binary64
unpow1/2_binary64 exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 /-rgt-identity_binary64 --rgt-identity_binary64 +-lft-identity_binary64 pow-sqr_binary64 associate-*l/_binary64
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 pow-base-0_binary64 unpow1/3_binary64 unpow2_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 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_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 distribute-neg-frac_binary64 distribute-frac-neg_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64
Counts
84 → 66
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01231168
13641003
21498960
33819960
44759960
55164960

prune42.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New65166
Fresh123
Picked101
Done000
Total67370
Error
0b
Counts
70 → 3
Compiler

Compiled 622 to 235 computations (62.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 x (-.f64 y (*.f64 y z)))
0.0b
(-.f64 y (*.f64 y z))
0.0b
(+.f64 (+.f64 x (-.f64 y (*.f64 y z))) (neg.f64 (*.f64 x z)))

rewrite49.0ms (1.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
28×add-log-exp_binary64
12×sum-log_binary64
10×*-un-lft-identity_binary64
diff-log_binary64 distribute-lft-out_binary64
neg-log_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 associate-+r-_binary64
flip3-+_binary64 flip-+_binary64 +-commutative_binary64 sub-neg_binary64 cancel-sign-sub-inv_binary64 associate-+r+_binary64
unsub-neg_binary64 associate-+l-_binary64 neg-sub0_binary64 associate-+l+_binary64 flip3--_binary64 flip--_binary64
Counts
3 → 50
Calls

3 calls:

9.0ms
(+.f64 (+.f64 x (-.f64 y (*.f64 y z))) (neg.f64 (*.f64 x z)))
5.0ms
(+.f64 x (-.f64 y (*.f64 y z)))
3.0ms
(-.f64 y (*.f64 y z))
Compiler

Compiled 929 to 184 computations (80.2% saved)

series101.0ms (3.3%)

Error
0b
Counts
3 → 45
Calls

3 calls:

37.0ms
(+.f64 (+.f64 x (-.f64 y (*.f64 y z))) (neg.f64 (*.f64 x z)))
27.0ms
(+.f64 x (-.f64 y (*.f64 y z)))
16.0ms
(-.f64 y (*.f64 y z))
Compiler

Compiled 919 to 648 computations (29.5% saved)

simplify106.0ms (3.5%)

Algorithm
egg-herbie
Rules
587×associate-*l*_binary64
553×associate-*r*_binary64
334×associate-+l+_binary64
262×associate-+r+_binary64
224×cancel-sign-sub-inv_binary64
169×times-frac_binary64
125×exp-sum_binary64
108×associate--r+_binary64
99×associate--l+_binary64
95×exp-prod_binary64
93×exp-diff_binary64 distribute-lft-neg-out_binary64
92×distribute-rgt-neg-out_binary64
90×distribute-rgt-neg-in_binary64
88×sub-neg_binary64
85×distribute-rgt-in_binary64
77×distribute-lft-in_binary64
71×distribute-lft-neg-in_binary64
68×cube-prod_binary64
65×associate-+l-_binary64
56×unsub-neg_binary64
47×*-commutative_binary64
44×associate-+r-_binary64
43×neg-sub0_binary64
41×distribute-rgt-out_binary64
37×distribute-neg-in_binary64
36×+-commutative_binary64
34×sqr-pow_binary64 associate--r-_binary64
33×neg-mul-1_binary64
30×unpow3_binary64
29×log-prod_binary64 distribute-lft-out_binary64
25×associate--l-_binary64
17×prod-exp_binary64 swap-sqr_binary64
16×distribute-rgt-out--_binary64
14×associate-/l*_binary64 associate-*r/_binary64
13×cube-mult_binary64
12×distribute-lft-out--_binary64
11×cube-neg_binary64
10×div-exp_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 associate-*l/_binary64
cancel-sign-sub_binary64
cube-unmult_binary64 sqr-neg_binary64 remove-double-neg_binary64 associate-/r*_binary64
+-rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 difference-of-squares_binary64
mul-1-neg_binary64 unswap-sqr_binary64
*-rgt-identity_binary64
pow-plus_binary64 sub0-neg_binary64 +-lft-identity_binary64 distribute-lft1-in_binary64
*-lft-identity_binary64 --rgt-identity_binary64 pow-sqr_binary64 associate-/l/_binary64
rec-exp_binary64 1-exp_binary64 exp-1-e_binary64 /-rgt-identity_binary64
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 pow-base-0_binary64 unpow1/3_binary64 unpow2_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-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_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 div-sub_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 distribute-neg-frac_binary64 distribute-frac-neg_binary64 count-2_binary64 associate-/r/_binary64
Counts
95 → 78
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01051243
12931117
210651017
344101017
449811017
549501017

prune30.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New78078
Fresh022
Picked011
Done000
Total78381
Error
0b
Counts
81 → 3
Compiler

Compiled 585 to 191 computations (67.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (-.f64 1 z))
0.0b
(sqrt.f64 (-.f64 1 z))
0.1b
(*.f64 (+.f64 y x) (sqrt.f64 (-.f64 1 z)))
0.1b
(*.f64 (*.f64 (+.f64 y x) (sqrt.f64 (-.f64 1 z))) (sqrt.f64 (-.f64 1 z)))

rewrite150.0ms (4.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
46×sqrt-div_binary64
32×frac-times_binary64
29×add-sqr-sqrt_binary64
25×*-un-lft-identity_binary64 sqrt-prod_binary64
23×flip3--_binary64 flip--_binary64
18×associate-*r*_binary64
16×associate-*l/_binary64
13×pow1_binary64
12×flip3-+_binary64 flip-+_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64
10×associate-*r/_binary64
difference-of-squares_binary64
associate-*l*_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 distribute-lft-out--_binary64
*-commutative_binary64 unswap-sqr_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
distribute-lft-out_binary64
Counts
4 → 120
Calls

4 calls:

16.0ms
(*.f64 (*.f64 (+.f64 y x) (sqrt.f64 (-.f64 1 z))) (sqrt.f64 (-.f64 1 z)))
10.0ms
(*.f64 (+.f64 y x) (sqrt.f64 (-.f64 1 z)))
4.0ms
(sqrt.f64 (-.f64 1 z))
3.0ms
(sqrt.f64 (-.f64 1 z))
Compiler

Compiled 2780 to 1756 computations (36.8% saved)

series112.0ms (3.6%)

Error
0b
Counts
4 → 48
Calls

4 calls:

44.0ms
(*.f64 (+.f64 y x) (sqrt.f64 (-.f64 1 z)))
29.0ms
(*.f64 (*.f64 (+.f64 y x) (sqrt.f64 (-.f64 1 z))) (sqrt.f64 (-.f64 1 z)))
12.0ms
(sqrt.f64 (-.f64 1 z))
9.0ms
(sqrt.f64 (-.f64 1 z))
Compiler

Compiled 1334 to 1065 computations (20.2% saved)

simplify128.0ms (4.1%)

Algorithm
egg-herbie
Rules
580×associate--l+_binary64
498×sub-neg_binary64
373×*-commutative_binary64
268×cancel-sign-sub-inv_binary64
251×distribute-neg-in_binary64
250×associate-*l*_binary64
219×associate--l-_binary64
217×associate--r+_binary64
201×associate-+l+_binary64
181×distribute-rgt-neg-in_binary64
173×associate-*r*_binary64
147×+-commutative_binary64
146×distribute-lft-neg-in_binary64
139×associate-+r+_binary64
134×unsub-neg_binary64
101×neg-sub0_binary64
99×neg-mul-1_binary64
97×distribute-rgt-in_binary64
92×distribute-lft-in_binary64
78×distribute-rgt-out_binary64
69×exp-prod_binary64
59×sqr-pow_binary64
58×exp-sum_binary64
49×distribute-rgt-out--_binary64
47×distribute-lft-out_binary64
41×associate-+l-_binary64
37×distribute-lft-neg-out_binary64
32×unswap-sqr_binary64
27×exp-diff_binary64
26×*-lft-identity_binary64
25×swap-sqr_binary64 associate-+r-_binary64
19×*-rgt-identity_binary64
18×sub0-neg_binary64
17×log-prod_binary64
15×cube-prod_binary64 distribute-rgt-neg-out_binary64
13×+-rgt-identity_binary64
12×associate--r-_binary64
11×pow-sqr_binary64 associate-/l*_binary64
10×distribute-neg-out_binary64 distribute-rgt1-in_binary64
distribute-lft-out--_binary64
rem-sqrt-square_binary64
cube-unmult_binary64 cancel-sign-sub_binary64
rem-square-sqrt_binary64
unpow3_binary64 difference-of-sqr-1_binary64
unpow1/2_binary64 cube-mult_binary64
pow-plus_binary64 div-sub_binary64 mul-1-neg_binary64 difference-of-squares_binary64 count-2_binary64 associate-/l/_binary64 associate-*r/_binary64
unpow2_binary64 unpow1_binary64 1-exp_binary64 exp-1-e_binary64 associate-/r/_binary64 associate-/r*_binary64
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 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-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_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 times-frac_binary64 /-rgt-identity_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 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-lft1-in_binary64 associate-*l/_binary64
Counts
168 → 125
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01933069
15162806
216392779
329812749
454142749

prune76.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1250125
Fresh011
Picked011
Done011
Total1253128
Error
0b
Counts
128 → 3
Compiler

Compiled 1810 to 1049 computations (42% saved)

regimes676.0ms (22%)

Accuracy

Total 0.0b remaining (26.8%)

Threshold costs 0.0b (26.8%)

Compiler

Compiled 6275 to 5479 computations (12.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
neg-mul-1_binary64 neg-sub0_binary64 sub-neg_binary64
distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
unsub-neg_binary64
distribute-neg-in_binary64
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 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-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-rgt-neg-out_binary64 distribute-lft-neg-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01016
12316
24216
35416
46216
56516
66516

end6.0ms (0.2%)

Remove

(sort x y)

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample585.0ms (19%)

Algorithm
intervals
Results
207.0ms8000×body128valid
13.0ms570×body128invalid
Compiler

Compiled 52 to 57 computations (-9.6% saved)

Profiling

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