Details

analyze1.2s (8.8%)

Algorithm

1×	search
2×	egg-herbie

Rules

520×	`sub-neg_binary64`
373×	`div-sub_binary64`
267×	`log-prod_binary64`
240×	`associate-/r*_binary64`
225×	`sqr-pow_binary64`
204×	`difference-of-squares_binary64`
202×	`distribute-rgt-in_binary64`
195×	`associate-/l*_binary64`
192×	`cancel-sign-sub-inv_binary64`
173×	`distribute-lft-in_binary64`
168×	`*-commutative_binary64`
155×	`associate-/l/_binary64`
145×	`neg-mul-1_binary64`
135×	`neg-sub0_binary64` `pow-sqr_binary64`
126×	`unsub-neg_binary64`
116×	`times-frac_binary64`
112×	`distribute-rgt-neg-in_binary64` `associate-l_binary64`
105×	`distribute-lft-neg-in_binary64`
104×	`associate-*r/_binary64`
103×	`exp-prod_binary64`
101×	`associate-r_binary64`
99×	`associate-*l/_binary64`
80×	`unswap-sqr_binary64`
75×	`associate-/r/_binary64`
69×	`log-div_binary64`
62×	`*-lft-identity_binary64`
53×	`+-commutative_binary64`
46×	`div0_binary64` `distribute-neg-in_binary64`
44×	`*-rgt-identity_binary64` `distribute-neg-frac_binary64` `distribute-rgt-neg-out_binary64`
43×	`exp-diff_binary64`
40×	`sub0-neg_binary64`
38×	`associate--r+_binary64`
35×	`distribute-lft-neg-out_binary64`
29×	`prod-exp_binary64` `exp-sum_binary64`
23×	`exp-sqrt_binary64` `associate-+l-_binary64`
21×	`remove-double-neg_binary64`
20×	`rem-sqrt-square_binary64` `associate-+r+_binary64`
19×	`associate-+l+_binary64`
18×	`cube-prod_binary64`
16×	`cube-unmult_binary64` `associate-+r-_binary64`
15×	`unpow3_binary64` `/-rgt-identity_binary64` `+-rgt-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64`
14×	`pow-plus_binary64`
13×	`exp-lft-sqr_binary64`
12×	`associate--r-_binary64`
11×	`+-lft-identity_binary64` `distribute-frac-neg_binary64`
10×	`--rgt-identity_binary64`
9×	`associate--l+_binary64`
6×	`div-exp_binary64` `rec-exp_binary64`
5×	`cube-mult_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64`
2×	`sqr-neg_binary64` `distribute-lft-out--_binary64`
1×	`unpow2_binary64` `unpow-1_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-div_binary64` `cube-neg_binary64` `fabs-mul_binary64` `rem-square-sqrt_binary64` `distribute-lft-out_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `mul-1-neg_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` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate--l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	292	55
4	689	55
5	1392	55
6	3381	55
7	4578	55
8	4212	55
9	4795	55
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample218.0ms (1.6%)

Algorithm

1×

intervals

Results

66.0ms	132×	body	1024	valid
53.0ms	113×	body	1024	nan
25.0ms	66×	body	512	nan
19.0ms	55×	body	512	valid
17.0ms	15×	body	2048	valid
9.0ms	39×	body	256	valid
7.0ms	31×	body	256	nan
2.0ms	15×	body	128	valid
1.0ms	1×	body	2048	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

520×	`sub-neg_binary64`
373×	`div-sub_binary64`
267×	`log-prod_binary64`
240×	`associate-/r*_binary64`
225×	`sqr-pow_binary64`
204×	`difference-of-squares_binary64`
202×	`distribute-rgt-in_binary64`
195×	`associate-/l*_binary64`
192×	`cancel-sign-sub-inv_binary64`
173×	`distribute-lft-in_binary64`
168×	`*-commutative_binary64`
155×	`associate-/l/_binary64`
145×	`neg-mul-1_binary64`
135×	`neg-sub0_binary64` `pow-sqr_binary64`
126×	`unsub-neg_binary64`
116×	`times-frac_binary64`
112×	`distribute-rgt-neg-in_binary64` `associate-l_binary64`
105×	`distribute-lft-neg-in_binary64`
104×	`associate-*r/_binary64`
103×	`exp-prod_binary64`
101×	`associate-r_binary64`
99×	`associate-*l/_binary64`
80×	`unswap-sqr_binary64`
75×	`associate-/r/_binary64`
69×	`log-div_binary64`
62×	`*-lft-identity_binary64`
53×	`+-commutative_binary64`
46×	`div0_binary64` `distribute-neg-in_binary64`
44×	`*-rgt-identity_binary64` `distribute-neg-frac_binary64` `distribute-rgt-neg-out_binary64`
43×	`exp-diff_binary64`
40×	`sub0-neg_binary64`
38×	`associate--r+_binary64`
35×	`distribute-lft-neg-out_binary64`
29×	`prod-exp_binary64` `exp-sum_binary64`
23×	`exp-sqrt_binary64` `associate-+l-_binary64`
21×	`remove-double-neg_binary64`
20×	`rem-sqrt-square_binary64` `associate-+r+_binary64`
19×	`associate-+l+_binary64`
18×	`cube-prod_binary64`
16×	`cube-unmult_binary64` `associate-+r-_binary64`
15×	`unpow3_binary64` `/-rgt-identity_binary64` `+-rgt-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64`
14×	`pow-plus_binary64`
13×	`exp-lft-sqr_binary64`
12×	`associate--r-_binary64`
11×	`+-lft-identity_binary64` `distribute-frac-neg_binary64`
10×	`--rgt-identity_binary64`
9×	`associate--l+_binary64`
6×	`div-exp_binary64` `rec-exp_binary64`
5×	`cube-mult_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64`
2×	`sqr-neg_binary64` `distribute-lft-out--_binary64`
1×	`unpow2_binary64` `unpow-1_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-div_binary64` `cube-neg_binary64` `fabs-mul_binary64` `rem-square-sqrt_binary64` `distribute-lft-out_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `mul-1-neg_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` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate--l-_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	64
1	49	61
2	117	59
3	292	55
4	689	55
5	1392	55
6	3381	55
7	4578	55
8	4212	55
9	4795	55

prune12.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

62.2b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
1.0b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
5.5b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite413.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

62.1b

Rules

75×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`unpow-prod-down_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`sqr-pow_binary64` `cancel-sign-sub-inv_binary64` `associate-/r*_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `associate-r_binary64`
4×	`associate-/l*_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
3×	`div-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
2×	`flip3--_binary64` `flip--_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `frac-2neg_binary64` `clear-num_binary64` `flip3-+_binary64` `flip-+_binary64`

Counts

4 → 141

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 5775 to 3852 computations (33.3% saved)

series84.0ms (0.6%)

Error

1.7b

Counts

4 → 12

Calls

4 calls:

27.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
22.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
14.0ms	(*.f64 (/.f64 PI.f64 4) f)
10.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1112 to 841 computations (24.4% saved)

simplify235.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

586×	`associate-l_binary64`
539×	`associate-r_binary64`
488×	`times-frac_binary64`
231×	`associate-*l/_binary64`
203×	`exp-prod_binary64`
198×	`*-commutative_binary64`
187×	`associate-/l*_binary64`
178×	`associate-*r/_binary64`
142×	`distribute-rgt-in_binary64`
131×	`distribute-lft-in_binary64`
88×	`associate-/l/_binary64`
81×	`cube-prod_binary64`
79×	`cancel-sign-sub-inv_binary64`
69×	`associate-/r*_binary64`
67×	`unpow3_binary64`
61×	`neg-mul-1_binary64`
59×	`log-prod_binary64`
57×	`sqr-pow_binary64`
56×	`div-sub_binary64` `distribute-rgt-neg-in_binary64`
49×	`sub-neg_binary64` `associate-/r/_binary64` `+-commutative_binary64`
48×	`log-div_binary64`
44×	`distribute-lft-neg-in_binary64`
43×	`unswap-sqr_binary64`
37×	`distribute-rgt-out_binary64`
33×	`associate-+l+_binary64`
32×	`neg-sub0_binary64`
29×	`cube-div_binary64`
23×	`pow-sqr_binary64` `distribute-lft-neg-out_binary64`
22×	`associate-+r+_binary64`
21×	`exp-sum_binary64`
20×	`cube-unmult_binary64` `associate-+l-_binary64` `associate-+r-_binary64`
18×	`*-rgt-identity_binary64`
16×	`swap-sqr_binary64` `distribute-rgt-neg-out_binary64`
12×	`cube-mult_binary64`
10×	`exp-diff_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
9×	`*-lft-identity_binary64`
8×	`prod-exp_binary64` `fabs-mul_binary64` `unsub-neg_binary64` `distribute-rgt-out--_binary64`
7×	`distribute-neg-frac_binary64` `distribute-lft-out_binary64`
6×	`pow-plus_binary64` `distribute-neg-in_binary64`
5×	`log-rec_binary64` `exp-sqrt_binary64` `associate--l-_binary64`
4×	`pow-base-1_binary64` `/-rgt-identity_binary64` `count-2_binary64` `associate--r+_binary64`
3×	`fabs-sqr_binary64` `+-rgt-identity_binary64` `distribute-neg-out_binary64`
2×	`div-exp_binary64` `rec-exp_binary64` `rem-square-sqrt_binary64` `distribute-rgt1-in_binary64` `associate--r-_binary64`
1×	`unpow1/2_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `*-inverses_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `exp-to-pow_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `mul-1-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_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` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64`

Counts

153 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	5769
1	467	5390
2	1153	5388
3	3693	5376
4	4903	5376
5	4959	5376

prune147.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	5	138

Error

1.6b

Counts

138 → 5

Compiler

Compiled 4524 to 3042 computations (32.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.4b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
1.0b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))

rewrite237.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

36×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64` `add-exp-log_binary64`
24×	`add-cube-cbrt_binary64` `times-frac_binary64`
20×	`associate-l_binary64`
19×	`associate-r_binary64`
16×	`add-cbrt-cube_binary64`
12×	`pow1_binary64`
8×	`log-prod_binary64` `prod-exp_binary64`
5×	`div-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
4×	`rem-log-exp_binary64` `add-log-exp_binary64`
3×	`div-inv_binary64` `pow-prod-down_binary64` `*-commutative_binary64`
2×	`log-pow_binary64` `cbrt-undiv_binary64`
1×	`log-div_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `associate-l/_binary64`

Counts

4 → 104

Calls

4 calls:

10.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))
10.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
4.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 3268 to 2192 computations (32.9% saved)

series96.0ms (0.7%)

Error

1.4b

Counts

4 → 12

Calls

4 calls:

38.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
29.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))
9.0ms	(*.f64 (/.f64 PI.f64 4) f)
8.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 782 to 619 computations (20.8% saved)

simplify190.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

382×	`associate-/l*_binary64`
346×	`log-div_binary64`
305×	`associate-*l/_binary64`
268×	`*-commutative_binary64`
264×	`associate-*r/_binary64`
198×	`exp-diff_binary64`
192×	`sub-neg_binary64`
189×	`associate-/r*_binary64` `associate--r+_binary64`
186×	`times-frac_binary64`
167×	`associate-+l-_binary64`
155×	`associate-l_binary64`
129×	`log-prod_binary64`
118×	`associate-r_binary64`
103×	`sqr-pow_binary64`
102×	`associate--l+_binary64`
98×	`exp-prod_binary64`
88×	`associate-/l/_binary64`
82×	`/-rgt-identity_binary64`
60×	`associate-/r/_binary64`
57×	`distribute-rgt-in_binary64`
56×	`*-lft-identity_binary64`
55×	`distribute-lft-in_binary64`
52×	`*-rgt-identity_binary64`
49×	`div-sub_binary64`
48×	`distribute-neg-in_binary64`
47×	`exp-sum_binary64`
46×	`associate--r-_binary64`
44×	`cube-div_binary64`
43×	`+-commutative_binary64`
36×	`cube-prod_binary64` `associate-+l+_binary64`
35×	`log-rec_binary64`
33×	`swap-sqr_binary64` `associate-+r-_binary64`
32×	`distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `associate--l-_binary64`
30×	`associate-+r+_binary64`
28×	`unsub-neg_binary64`
26×	`pow-sqr_binary64`
25×	`neg-mul-1_binary64`
24×	`neg-sub0_binary64`
20×	`unpow3_binary64`
19×	`unswap-sqr_binary64`
16×	`exp-to-pow_binary64`
15×	`log-pow_binary64`
12×	`+-rgt-identity_binary64`
9×	`cancel-sign-sub-inv_binary64` `distribute-neg-frac_binary64`
8×	`unpow1/2_binary64` `rem-exp-log_binary64` `cube-unmult_binary64`
6×	`rec-exp_binary64` `cube-mult_binary64`
5×	`prod-exp_binary64` `remove-double-div_binary64`
3×	`sub0-neg_binary64` `count-2_binary64`
2×	`exp-sqrt_binary64` `div-exp_binary64` `rem-sqrt-square_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
1×	`log-E_binary64` `pow-plus_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `distribute-neg-out_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64`

Counts

116 → 88

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	217	3480
1	461	3038
2	1396	2997
3	3401	2997
4	4659	2993
5	4917	2993
6	5062	2993

prune156.0ms (1.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	77	16	93

Error

1.3b

Counts

93 → 16

Compiler

Compiled 2839 to 1898 computations (33.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(.f64 f (.f64 PI.f64 1/2))
0.3b	(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) -4) PI.f64)
1.0b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))

rewrite189.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

26×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
12×	`pow1_binary64`
11×	`add-cube-cbrt_binary64`
8×	`log-prod_binary64` `prod-exp_binary64`
7×	`times-frac_binary64`
6×	`associate-l_binary64`
5×	`div-exp_binary64` `cbrt-unprod_binary64`
4×	`rem-log-exp_binary64` `add-log-exp_binary64` `pow-prod-down_binary64` `associate-r_binary64`
3×	`associate-/r*_binary64`
2×	`div-inv_binary64` `cbrt-undiv_binary64` `*-commutative_binary64`
1×	`log-pow_binary64` `log-div_binary64` `distribute-lft-out_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l*_binary64` `unswap-sqr_binary64`

Counts

4 → 78

Calls

4 calls:

10.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))
7.0ms	(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) -4) PI.f64)
5.0ms	(.f64 f (.f64 PI.f64 1/2))
4.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 2376 to 1490 computations (37.3% saved)

series96.0ms (0.7%)

Error

1.3b

Counts

4 → 12

Calls

4 calls:

35.0ms	(/.f64 (.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))) -4) PI.f64)
31.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2))))
10.0ms	(*.f64 PI.f64 f)
9.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 782 to 605 computations (22.6% saved)

simplify179.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

616×	`times-frac_binary64`
391×	`associate-/l*_binary64`
291×	`sub-neg_binary64`
278×	`*-commutative_binary64`
223×	`log-div_binary64`
219×	`prod-exp_binary64`
201×	`associate-/r*_binary64`
173×	`associate-/l/_binary64`
159×	`div-sub_binary64`
139×	`associate-l_binary64`
127×	`exp-diff_binary64`
117×	`log-prod_binary64` `associate-r_binary64`
107×	`exp-prod_binary64`
103×	`sqr-pow_binary64`
91×	`associate--r-_binary64`
83×	`distribute-neg-in_binary64` `associate-*l/_binary64`
82×	`associate--l-_binary64`
73×	`exp-sum_binary64`
71×	`associate-/r/_binary64`
54×	`associate-*r/_binary64`
53×	`associate--r+_binary64`
47×	`distribute-rgt-in_binary64`
45×	`/-rgt-identity_binary64`
43×	`distribute-lft-in_binary64`
41×	`+-commutative_binary64`
36×	`associate-+r-_binary64`
34×	`neg-mul-1_binary64` `neg-sub0_binary64`
33×	`pow-sqr_binary64`
29×	`exp-to-pow_binary64` `swap-sqr_binary64`
28×	`unsub-neg_binary64` `associate-+l-_binary64`
27×	`cube-prod_binary64` `*-lft-identity_binary64`
24×	`*-rgt-identity_binary64` `associate-+l+_binary64`
22×	`associate-+r+_binary64`
20×	`cancel-sign-sub-inv_binary64` `distribute-lft-neg-out_binary64`
19×	`distribute-neg-frac_binary64` `distribute-rgt-neg-out_binary64`
18×	`log-pow_binary64` `unswap-sqr_binary64`
14×	`cube-div_binary64`
13×	`log-rec_binary64` `+-rgt-identity_binary64`
12×	`distribute-rgt-neg-in_binary64`
11×	`rem-exp-log_binary64`
10×	`distribute-lft-neg-in_binary64`
8×	`unpow1/2_binary64` `cube-unmult_binary64` `associate--l+_binary64`
7×	`unpow3_binary64` `pow-plus_binary64` `rec-exp_binary64` `sub0-neg_binary64`
4×	`cube-mult_binary64`
3×	`unpow-1_binary64` `div-exp_binary64` `remove-double-neg_binary64` `count-2_binary64`
2×	`exp-sqrt_binary64` `rem-sqrt-square_binary64`
1×	`log-E_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `--rgt-identity_binary64` `remove-double-div_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64`

Counts

90 → 60

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	2654
1	367	2227
2	1246	2191
3	3592	2191
4	4696	2191
5	4944	2191
6	4964	2191
7	5210	2191

prune100.0ms (0.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	61	15	76

Error

1.3b

Counts

76 → 15

Compiler

Compiled 1831 to 1180 computations (35.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(*.f64 PI.f64 f)
0.4b	(.f64 (+.f64 (neg.f64 (log.f64 f)) (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) PI.f64)))) (/.f64 -4 PI.f64))
2.9b	(log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))

rewrite207.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

25×	`pow1_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
19×	`add-exp-log_binary64` `associate-r_binary64`
18×	`associate-l_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
11×	`log-pow_binary64`
10×	`times-frac_binary64`
9×	`distribute-lft-out_binary64`
7×	`pow-prod-down_binary64`
6×	`prod-exp_binary64` `distribute-rgt-neg-in_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
3×	`rem-log-exp_binary64` `*-commutative_binary64`
2×	`associate-r/_binary64` `div-exp_binary64` `flip3-+_binary64` `frac-times_binary64` `flip-+_binary64` `associate-l/_binary64`
1×	`log-div_binary64` `log-prod_binary64` `cbrt-undiv_binary64` `div-inv_binary64`

Counts

4 → 95

Calls

4 calls:

23.0ms	(.f64 (+.f64 (neg.f64 (log.f64 f)) (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) PI.f64)))) (/.f64 -4 PI.f64))
8.0ms	(log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))
4.0ms	(*.f64 PI.f64 f)
4.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 3012 to 1740 computations (42.2% saved)

series95.0ms (0.7%)

Error

1.3b

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 (+.f64 (neg.f64 (log.f64 f)) (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (*.f64 PI.f64 f))) PI.f64)))) (/.f64 -4 PI.f64))
26.0ms	(log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) PI.f64)))
11.0ms	(*.f64 PI.f64 f)
8.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 790 to 616 computations (22% saved)

simplify132.0ms (1%)

Algorithm

1×	egg-herbie

Rules

761×	`div-sub_binary64`
559×	`distribute-rgt-in_binary64`
540×	`distribute-lft-in_binary64`
273×	`associate-/l*_binary64`
222×	`times-frac_binary64`
129×	`associate-l_binary64`
102×	`associate-r_binary64`
89×	`*-commutative_binary64`
79×	`associate-/l/_binary64`
74×	`exp-sum_binary64`
70×	`distribute-rgt-neg-out_binary64`
68×	`exp-prod_binary64`
66×	`log-div_binary64`
64×	`distribute-lft-neg-out_binary64`
60×	`sub-neg_binary64`
58×	`associate-/r*_binary64`
52×	`log-prod_binary64`
48×	`associate-*r/_binary64`
38×	`sqr-pow_binary64`
37×	`cube-prod_binary64`
32×	`/-rgt-identity_binary64`
31×	`associate-/r/_binary64`
30×	`cube-div_binary64`
29×	`exp-diff_binary64`
28×	`associate-*l/_binary64`
27×	`*-lft-identity_binary64`
26×	`*-rgt-identity_binary64`
24×	`unsub-neg_binary64`
23×	`neg-sub0_binary64` `cancel-sign-sub-inv_binary64`
20×	`neg-mul-1_binary64` `+-commutative_binary64`
13×	`distribute-rgt-neg-in_binary64`
12×	`log-rec_binary64` `swap-sqr_binary64` `distribute-neg-in_binary64`
10×	`associate-+l-_binary64`
9×	`rem-exp-log_binary64` `distribute-lft-neg-in_binary64` `associate-+r-_binary64`
8×	`distribute-neg-out_binary64`
7×	`unpow3_binary64` `exp-to-pow_binary64` `cube-mult_binary64` `pow-sqr_binary64` `distribute-rgt-out_binary64` `distribute-lft-out_binary64` `associate-+l+_binary64`
6×	`cube-unmult_binary64`
5×	`distribute-frac-neg_binary64`
4×	`cube-neg_binary64` `distribute-neg-frac_binary64` `associate--l-_binary64`
3×	`sqr-neg_binary64` `sub0-neg_binary64` `difference-of-squares_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64` `associate-+r+_binary64`
2×	`log-pow_binary64` `unpow1/2_binary64` `exp-neg_binary64` `remove-double-neg_binary64` `+-rgt-identity_binary64` `associate--r-_binary64`
1×	`rec-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `--rgt-identity_binary64` `cancel-sign-sub_binary64` `associate--r+_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `pow-plus_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` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64`

Counts

107 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	3597
1	395	3186
2	1470	3183
3	4502	3180
4	6161	3180

prune76.0ms (0.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	4	9	13
Picked	0	1	1
Done	0	1	1
Total	64	13	77

Error

1.2b

Counts

77 → 13

Compiler

Compiled 1604 to 972 computations (39.4% saved)

regimes2.4s (17.6%)

Accuracy

Total 1.0b remaining (69.8%)

Threshold costs 1.0b (69.8%)

Compiler

Compiled 47118 to 35276 computations (25.1% saved)

bsearch16.0ms (0.1%)

Compiler: Compiled 29 to 23 computations (20.7% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
8×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
1×	`cancel-sign-sub-inv_binary64` `distribute-neg-frac_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `unpow1_binary64` `e-exp-1_binary64` `1-exp_binary64` `exp-1-e_binary64` `exp-0_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	97
1	48	97
2	61	97
3	70	97
4	75	97
5	76	97
6	76	97

end2.0ms (0%)

Compiler: Compiled 57 to 42 computations (26.3% saved)

sample7.1s (51.5%)

Algorithm

1×

intervals

Results

2.0s	3892×	body	1024	valid
1.8s	3874×	body	1024	nan
707.0ms	1999×	body	512	valid
632.0ms	1896×	body	512	nan
483.0ms	468×	body	2048	valid
249.0ms	1008×	body	256	valid
221.0ms	980×	body	256	nan
80.0ms	633×	body	128	valid
3.0ms	5×	body	2048	nan
0.0ms	2×	body	128	overflowed
0.0ms	1×	body	128	nan

Compiler

Compiled 662 to 484 computations (26.9% saved)

Details

analyze1.2s (8.8%)

sample218.0ms (1.6%)

simplify84.0ms (0.6%)

prune12.0ms (0.1%)

localize19.0ms (0.1%)

rewrite413.0ms (3%)

series84.0ms (0.6%)

simplify235.0ms (1.7%)

prune147.0ms (1.1%)

localize18.0ms (0.1%)

rewrite237.0ms (1.7%)

series96.0ms (0.7%)

simplify190.0ms (1.4%)

prune156.0ms (1.1%)

localize17.0ms (0.1%)

rewrite189.0ms (1.4%)

series96.0ms (0.7%)

simplify179.0ms (1.3%)

prune100.0ms (0.7%)

localize19.0ms (0.1%)

rewrite207.0ms (1.5%)

series95.0ms (0.7%)

simplify132.0ms (1%)

prune76.0ms (0.6%)

regimes2.4s (17.6%)

bsearch16.0ms (0.1%)

simplify7.0ms (0%)

end2.0ms (0%)

sample7.1s (51.5%)

Profiling