Details

analyze4.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample11.0ms (1.4%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

128

valid

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify421.0ms (54%)

Algorithm

1×	egg-herbie

Rules

730×	`exp-diff_binary64_12743`
700×	`exp-prod_binary64_12747`
678×	`times-frac_binary64_12701`
586×	`div-sub_binary64_12700`
235×	`unsub-neg_binary64_12689`
222×	`associate--r-_binary64_12634`
192×	`associate--r+_binary64_12631`
191×	`associate-+r-_binary64_12629`
177×	`swap-sqr_binary64_12662`
174×	`associate--l-_binary64_12633`
137×	`associate--l+_binary64_12632`
128×	`associate-+l-_binary64_12630`
108×	`associate-/r/_binary64_12641`
103×	`pow-plus_binary64_12758`
97×	`distribute-rgt-in_binary64_12645`
93×	`exp-sum_binary64_12741`
81×	`distribute-rgt1-in_binary64_12651`
74×	`associate-/l*_binary64_12640`
71×	`distribute-rgt-neg-in_binary64_12653`
69×	`distribute-rgt-out--_binary64_12649` `distribute-rgt-out_binary64_12648`
67×	`cancel-sign-sub-inv_binary64_12661`
56×	`distribute-rgt-neg-out_binary64_12655`
50×	`associate-l_binary64_12636`
48×	`associate-r_binary64_12635`
43×	`distribute-frac-neg_binary64_12658` `distribute-lft-neg-out_binary64_12654`
41×	`distribute-lft-neg-in_binary64_12652`
40×	`sub-neg_binary64_12688`
37×	`distribute-neg-out_binary64_12657`
35×	`neg-sub0_binary64_12690` `sqr-pow_binary64_12667`
32×	`neg-mul-1_binary64_12691`
31×	`distribute-lft-in_binary64_12644`
30×	`pow-sqr_binary64_12668`
28×	`distribute-neg-in_binary64_12656` `distribute-lft-out--_binary64_12647` `distribute-lft-out_binary64_12646`
26×	`*-commutative_binary64_12626`
24×	`+-commutative_binary64_12625`
22×	`pow-base-1_binary64_12755`
20×	`exp-sqrt_binary64_12748`
14×	`associate-+r+_binary64_12627`
13×	`sqr-neg_binary64_12709` `associate-/r_binary64_12639` `associate-l/_binary64_12638`
11×	`unswap-sqr_binary64_12663`
10×	`exp-lft-sqr_binary64_12750` `exp-neg_binary64_12742` `remove-double-neg_binary64_12683`
9×	`mul0-lft_binary64_12677`
8×	`cube-prod_binary64_12723` `-rgt-identity_binary64_12685` `-lft-identity_binary64_12684` `mul0-rgt_binary64_12678` `count-2_binary64_12643`
7×	`+-inverses_binary64_12674` `associate-+l+_binary64_12628`
6×	`cube-unmult_binary64_12732` `/-rgt-identity_binary64_12686`
5×	`+-rgt-identity_binary64_12680` `difference-of-squares_binary64_12664`
4×	`sub0-neg_binary64_12682` `distribute-lft1-in_binary64_12650`
3×	`cube-div_binary64_12724` `+-lft-identity_binary64_12679` `cancel-sign-sub_binary64_12660` `distribute-neg-frac_binary64_12659`
2×	`div0_binary64_12676` `*-inverses_binary64_12675`
1×	`prod-exp_binary64_12744` `1-exp_binary64_12739` `exp-1-e_binary64_12738` `--rgt-identity_binary64_12681` `rgt-mult-inverse_binary64_12672` `difference-of-sqr--1_binary64_12666`
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` `exp-to-pow_binary64_12757` `unpow0_binary64_12754` `unpow1_binary64_12753` `unpow-1_binary64_12752` `exp-lft-cube_binary64_12751` `exp-cbrt_binary64_12749` `div-exp_binary64_12746` `rec-exp_binary64_12745` `e-exp-1_binary64_12740` `exp-0_binary64_12737` `rem-log-exp_binary64_12736` `rem-exp-log_binary64_12735` `cube-mult_binary64_12725` `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` `rem-sqrt-square_binary64_12708` `rem-square-sqrt_binary64_12707` `mul-1-neg_binary64_12687` `lft-mult-inverse_binary64_12673` `remove-double-div_binary64_12671` `difference-of-sqr-1_binary64_12665` `associate-/l/_binary64_12642` `associate-*r/_binary64_12637`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	13	7
2	20	7
3	31	7
4	59	7
5	95	7
6	192	7
7	542	7
8	1020	7
9	3612	7

prune3.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

Counts

3 → 1

Compiler

Compiled 15 to 11 computations (26.7% saved)

localize3.0ms (0.4%)

rewrite0.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify9.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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-lft-sqr_binary64_12750 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-diff_binary64_12743 exp-neg_binary64_12742 exp-sum_binary64_12741 e-exp-1_binary64_12740 1-exp_binary64_12739 exp-1-e_binary64_12738 exp-0_binary64_12737 rem-log-exp_binary64_12736 rem-exp-log_binary64_12735 cube-unmult_binary64_12732 cube-mult_binary64_12725 cube-div_binary64_12724 cube-prod_binary64_12723 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 times-frac_binary64_12701 div-sub_binary64_12700 neg-mul-1_binary64_12691 neg-sub0_binary64_12690 unsub-neg_binary64_12689 sub-neg_binary64_12688 mul-1-neg_binary64_12687 /-rgt-identity_binary64_12686 *-rgt-identity_binary64_12685 *-lft-identity_binary64_12684 remove-double-neg_binary64_12683 sub0-neg_binary64_12682 --rgt-identity_binary64_12681 +-rgt-identity_binary64_12680 +-lft-identity_binary64_12679 mul0-rgt_binary64_12678 mul0-lft_binary64_12677 div0_binary64_12676 *-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 swap-sqr_binary64_12662 cancel-sign-sub-inv_binary64_12661 cancel-sign-sub_binary64_12660 distribute-neg-frac_binary64_12659 distribute-frac-neg_binary64_12658 distribute-neg-out_binary64_12657 distribute-neg-in_binary64_12656 distribute-rgt-neg-out_binary64_12655 distribute-lft-neg-out_binary64_12654 distribute-rgt-neg-in_binary64_12653 distribute-lft-neg-in_binary64_12652 distribute-rgt1-in_binary64_12651 distribute-lft1-in_binary64_12650 distribute-rgt-out--_binary64_12649 distribute-rgt-out_binary64_12648 distribute-lft-out--_binary64_12647 distribute-lft-out_binary64_12646 distribute-rgt-in_binary64_12645 distribute-lft-in_binary64_12644 count-2_binary64_12643 associate-/l/_binary64_12642 associate-/r/_binary64_12641 associate-/l*_binary64_12640 associate-/r*_binary64_12639 associate-*l/_binary64_12638 associate-*r/_binary64_12637 associate-*l*_binary64_12636 associate-*r*_binary64_12635 associate--r-_binary64_12634 associate--l-_binary64_12633 associate--l+_binary64_12632 associate--r+_binary64_12631 associate-+l-_binary64_12630 associate-+r-_binary64_12629 associate-+l+_binary64_12628 associate-+r+_binary64_12627 *-commutative_binary64_12626 +-commutative_binary64_12625

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Error

Counts

1 → 1

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

2×	`neg-mul-1_binary64_12691` `neg-sub0_binary64_12690` `sub-neg_binary64_12688` `*-rgt-identity_binary64_12685` `+-commutative_binary64_12625`
1×	`1-exp_binary64_12739` `unsub-neg_binary64_12689` `distribute-rgt-neg-out_binary64_12655` `*-commutative_binary64_12626`
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` `*-lft-identity_binary64_12684` `remove-double-neg_binary64_12683` `sub0-neg_binary64_12682` `--rgt-identity_binary64_12681` `+-rgt-identity_binary64_12680` `+-lft-identity_binary64_12679` `cancel-sign-sub-inv_binary64_12661` `cancel-sign-sub_binary64_12660` `distribute-neg-frac_binary64_12659` `distribute-frac-neg_binary64_12658` `distribute-neg-out_binary64_12657` `distribute-neg-in_binary64_12656` `distribute-lft-neg-out_binary64_12654` `distribute-rgt-neg-in_binary64_12653` `distribute-lft-neg-in_binary64_12652`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	9	7
2	13	7
3	15	7
4	18	7
5	17	7

Proof

(=> (- f64 (+ f64 h0 h0) 1))
sub-neg_binary64_12688 =>
(+ f64 (+ f64 h0 h0) (=> (neg f64 1)))
neg-mul-1_binary64_12691 =>
(+ f64 (+ f64 h0 h0) (=> (* f64 -1 1)))
*-rgt-identity_binary64_12685 =>
(+ f64 (+ f64 h0 h0) -1)

end0.0ms (0%)

sample324.0ms (41.5%)

Algorithm

1×

intervals

Results

122.0ms

8000×

body

128

valid

Compiler

Compiled 16 to 14 computations (12.5% saved)

Details

analyze4.0ms (0.5%)

sample11.0ms (1.4%)

simplify421.0ms (54%)

prune3.0ms (0.3%)

localize3.0ms (0.4%)

rewrite0.0ms (0.1%)

series0.0ms (0%)

simplify9.0ms (1.1%)

prune1.0ms (0.2%)

simplify4.0ms (0.5%)

end0.0ms (0%)

sample324.0ms (41.5%)

Profiling