Details

analyze2.1s (2.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

Compiler

Compiled 126 to 112 computations (11.1% saved)

sample1.6s (2%)

Algorithm

1×

intervals

Results

1.5s	133×	body	8192	exit
88.0ms	256×	body	128	valid
6.0ms	393×	pre	128	true
2.0ms	4×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify212.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

339×	`associate-+l+_binary64_9559`
290×	`associate-+r+_binary64_9558`
274×	`distribute-rgt-in_binary64_9576`
267×	`distribute-lft-in_binary64_9575`
231×	`sub-neg_binary64_9619`
220×	`associate-r_binary64_9566`
208×	`associate-l_binary64_9567`
204×	`associate-/r/_binary64_9572`
187×	`exp-sum_binary64_9672`
170×	`distribute-rgt-out_binary64_9579`
142×	`+-commutative_binary64_9556`
115×	`exp-diff_binary64_9674`
107×	`distribute-lft-out_binary64_9577`
90×	`distribute-neg-in_binary64_9587`
81×	`div-sub_binary64_9631`
77×	`cancel-sign-sub-inv_binary64_9592`
68×	`associate-+l-_binary64_9561`
66×	`*-commutative_binary64_9557`
62×	`unsub-neg_binary64_9620`
60×	`associate--r+_binary64_9562`
59×	`associate-+r-_binary64_9560`
56×	`associate-*r/_binary64_9568`
52×	`neg-mul-1_binary64_9622` `neg-sub0_binary64_9621`
51×	`associate--l+_binary64_9563`
49×	`associate-*l/_binary64_9569`
40×	`associate-/l/_binary64_9573`
31×	`distribute-lft-neg-out_binary64_9585`
27×	`*-rgt-identity_binary64_9616` `associate--r-_binary64_9565`
26×	`associate--l-_binary64_9564`
22×	`*-lft-identity_binary64_9615`
20×	`exp-prod_binary64_9678` `associate-/r*_binary64_9570`
14×	`distribute-rgt-neg-out_binary64_9586` `distribute-lft-neg-in_binary64_9583`
12×	`times-frac_binary64_9632` `remove-double-neg_binary64_9614` `+-rgt-identity_binary64_9611` `sqr-pow_binary64_9598` `associate-/l*_binary64_9571`
10×	`distribute-neg-out_binary64_9588`
9×	`unswap-sqr_binary64_9594`
8×	`distribute-lft-out--_binary64_9578`
6×	`pow-sqr_binary64_9599`
4×	`distribute-rgt-neg-in_binary64_9584` `distribute-rgt1-in_binary64_9582`
3×	`div-exp_binary64_9677` `sub0-neg_binary64_9613`
2×	`--rgt-identity_binary64_9612` `distribute-neg-frac_binary64_9590` `distribute-rgt-out--_binary64_9580` `count-2_binary64_9574`
1×	`unpow1/2_binary64_9690` `exp-neg_binary64_9673` `1-exp_binary64_9670` `exp-1-e_binary64_9669` `cube-unmult_binary64_9663` `sqr-neg_binary64_9640` `/-rgt-identity_binary64_9617` `+-inverses_binary64_9605` `distribute-lft1-in_binary64_9581`
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_9889` `erf-erfc_binary64_9888` `erf-odd_binary64_9887` `if-if-and-not_binary64_9886` `if-if-and_binary64_9885` `if-if-or-not_binary64_9884` `if-if-or_binary64_9883` `if-not_binary64_9882` `if-same_binary64_9881` `if-false_binary64_9880` `if-true_binary64_9879` `not-gte_binary64_9878` `not-lte_binary64_9877` `not-gt_binary64_9876` `not-lt_binary64_9875` `gte-same_binary64_9874` `lte-same_binary64_9873` `gt-same_binary64_9872` `lt-same_binary64_9871` `sinh---cosh_binary64_9818` `sinh-+-cosh_binary64_9817` `sinh-cosh_binary64_9816` `tanh-def-c_binary64_9815` `tanh-def-b_binary64_9814` `tanh-def-a_binary64_9813` `cosh-def_binary64_9812` `sinh-def_binary64_9811` `tan-neg_binary64_9758` `cos-neg_binary64_9757` `sin-neg_binary64_9756` `tan-0_binary64_9755` `cos-0_binary64_9754` `sin-0_binary64_9753` `hang-m-tan_binary64_9752` `hang-p-tan_binary64_9751` `hang-m0-tan_binary64_9750` `hang-p0-tan_binary64_9749` `hang-0m-tan_binary64_9748` `hang-0p-tan_binary64_9747` `tan-+PI/2_binary64_9746` `tan-+PI_binary64_9745` `tan-PI_binary64_9744` `tan-PI/3_binary64_9743` `tan-PI/4_binary64_9742` `tan-PI/6_binary64_9741` `cos-+PI/2_binary64_9740` `cos-+PI_binary64_9739` `cos-PI_binary64_9738` `cos-PI/2_binary64_9737` `cos-PI/3_binary64_9736` `cos-PI/4_binary64_9735` `cos-PI/6_binary64_9734` `sin-+PI/2_binary64_9733` `sin-+PI_binary64_9732` `sin-PI_binary64_9731` `sin-PI/2_binary64_9730` `sin-PI/3_binary64_9729` `sin-PI/4_binary64_9728` `sin-PI/6_binary64_9727` `sub-1-sin_binary64_9726` `sub-1-cos_binary64_9725` `-1-add-sin_binary64_9724` `-1-add-cos_binary64_9723` `1-sub-sin_binary64_9722` `1-sub-cos_binary64_9721` `cos-sin-sum_binary64_9720` `log-E_binary64_9716` `log-pow_binary64_9715` `log-rec_binary64_9714` `log-div_binary64_9713` `log-prod_binary64_9712` `pow-base-0_binary64_9710` `unpow1/3_binary64_9693` `unpow3_binary64_9692` `unpow2_binary64_9691` `pow-plus_binary64_9689` `exp-to-pow_binary64_9688` `pow-base-1_binary64_9686` `unpow0_binary64_9685` `unpow1_binary64_9684` `unpow-1_binary64_9683` `exp-lft-cube_binary64_9682` `exp-lft-sqr_binary64_9681` `exp-cbrt_binary64_9680` `exp-sqrt_binary64_9679` `rec-exp_binary64_9676` `prod-exp_binary64_9675` `e-exp-1_binary64_9671` `exp-0_binary64_9668` `rem-log-exp_binary64_9667` `rem-exp-log_binary64_9666` `cube-mult_binary64_9656` `cube-div_binary64_9655` `cube-prod_binary64_9654` `cube-neg_binary64_9653` `rem-3cbrt-rft_binary64_9652` `rem-3cbrt-lft_binary64_9651` `rem-cbrt-cube_binary64_9650` `rem-cube-cbrt_binary64_9649` `sqr-abs_binary64_9641` `rem-sqrt-square_binary64_9639` `rem-square-sqrt_binary64_9638` `mul-1-neg_binary64_9618` `+-lft-identity_binary64_9610` `mul0-rgt_binary64_9609` `mul0-lft_binary64_9608` `div0_binary64_9607` `*-inverses_binary64_9606` `lft-mult-inverse_binary64_9604` `rgt-mult-inverse_binary64_9603` `remove-double-div_binary64_9602` `difference-of-sqr--1_binary64_9597` `difference-of-sqr-1_binary64_9596` `difference-of-squares_binary64_9595` `swap-sqr_binary64_9593` `cancel-sign-sub_binary64_9591` `distribute-frac-neg_binary64_9589`

Counts

1 → 4

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	189
1	152	186
2	624	141
3	3545	121

prune22.0ms (0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	0	4	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	4	5

Error

0.2b

Counts

5 → 4

Compiler

Compiled 820 to 683 computations (16.7% saved)

localize49.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)
4.9b	(-.f64 (-.f64 1 z) 1)

rewrite458.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

36×	`*-un-lft-identity_binary64_9626`
28×	`add-sqr-sqrt_binary64_9648`
24×	`add-log-exp_binary64_9665` `cancel-sign-sub-inv_binary64_9592`
16×	`associate--l+_binary64_9563`
12×	`diff-log_binary64_9718` `add-cube-cbrt_binary64_9661` `distribute-lft-out--_binary64_9578`
8×	`sub-neg_binary64_9619` `difference-of-squares_binary64_9595`
4×	`pow1_binary64_9687` `add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662` `flip3--_binary64_9630` `flip--_binary64_9601` `difference-of-sqr-1_binary64_9596` `associate--l-_binary64_9564`

Counts

4 → 100

Calls

4 calls:

7.0ms	(-.f64 (-.f64 1 z) 1)
7.0ms	(-.f64 (-.f64 1 z) 1)
6.0ms	(-.f64 (-.f64 1 z) 1)
6.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 12896 to 10998 computations (14.7% saved)

series110.0ms (0.1%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

19.0ms	(-.f64 (-.f64 1 z) 1)
19.0ms	(-.f64 (-.f64 1 z) 1)
19.0ms	(-.f64 (-.f64 1 z) 1)
19.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4356 to 3833 computations (12% saved)

simplify1.2s (1.6%)

Algorithm

1×	egg-herbie

Rules

334×	`sub-neg_binary64_9619`
289×	`associate-+l+_binary64_9559`
278×	`exp-prod_binary64_9678`
255×	`distribute-neg-in_binary64_9587`
241×	`associate-+r+_binary64_9558`
186×	`sqr-pow_binary64_9598`
157×	`neg-sub0_binary64_9621`
150×	`cube-prod_binary64_9654`
147×	`log-prod_binary64_9712`
140×	`neg-mul-1_binary64_9622`
133×	`cancel-sign-sub-inv_binary64_9592`
117×	`exp-sum_binary64_9672`
115×	`div-sub_binary64_9631`
107×	`associate-+l-_binary64_9561`
97×	`associate--r+_binary64_9562`
96×	`*-commutative_binary64_9557`
95×	`unsub-neg_binary64_9620`
94×	`distribute-rgt-out_binary64_9579`
85×	`pow-sqr_binary64_9599`
83×	`associate-l_binary64_9567`
82×	`distribute-lft-out_binary64_9577`
81×	`associate-r_binary64_9566`
80×	`distribute-rgt-neg-out_binary64_9586`
74×	`unswap-sqr_binary64_9594`
69×	`distribute-rgt-in_binary64_9576`
67×	`distribute-lft-neg-out_binary64_9585`
65×	`associate--l+_binary64_9563`
62×	`associate-+r-_binary64_9560`
61×	`exp-diff_binary64_9674`
60×	`swap-sqr_binary64_9593` `distribute-lft-in_binary64_9575`
54×	`distribute-neg-frac_binary64_9590`
50×	`+-commutative_binary64_9556`
48×	`remove-double-neg_binary64_9614`
45×	`log-pow_binary64_9715`
44×	`pow-plus_binary64_9689` `difference-of-squares_binary64_9595`
36×	`associate-*l/_binary64_9569`
35×	`distribute-rgt-out--_binary64_9580` `associate-*r/_binary64_9568`
30×	`cube-div_binary64_9655` `distribute-frac-neg_binary64_9589`
28×	`+-rgt-identity_binary64_9611`
27×	`log-div_binary64_9713`
25×	`exp-neg_binary64_9673` `distribute-rgt-neg-in_binary64_9584` `associate-/l*_binary64_9571`
23×	`distribute-lft-out--_binary64_9578` `associate--l-_binary64_9564`
22×	`distribute-neg-out_binary64_9588`
21×	`difference-of-sqr--1_binary64_9597`
20×	`unpow3_binary64_9692` `exp-to-pow_binary64_9688` `*-rgt-identity_binary64_9616`
18×	`distribute-lft-neg-in_binary64_9583`
17×	`sqr-neg_binary64_9640` `rem-sqrt-square_binary64_9639` `sub0-neg_binary64_9613`
16×	`times-frac_binary64_9632` `+-lft-identity_binary64_9610`
15×	`pow-base-1_binary64_9686` `cube-mult_binary64_9656` `mul0-rgt_binary64_9609`
14×	`cube-neg_binary64_9653` `distribute-rgt1-in_binary64_9582` `associate--r-_binary64_9565`
12×	`*-lft-identity_binary64_9615` `mul0-lft_binary64_9608`
11×	`cancel-sign-sub_binary64_9591`
8×	`div-exp_binary64_9677` `prod-exp_binary64_9675` `cube-unmult_binary64_9663` `mul-1-neg_binary64_9618` `distribute-lft1-in_binary64_9581` `associate-/r*_binary64_9570`
7×	`associate-/l/_binary64_9573`
6×	`--rgt-identity_binary64_9612` `difference-of-sqr-1_binary64_9596`
3×	`*-inverses_binary64_9606` `count-2_binary64_9574` `associate-/r/_binary64_9572`
2×	`rem-3cbrt-lft_binary64_9651` `rem-square-sqrt_binary64_9638` `/-rgt-identity_binary64_9617` `+-inverses_binary64_9605`
1×	`log-E_binary64_9716` `exp-lft-sqr_binary64_9681` `rec-exp_binary64_9676` `1-exp_binary64_9670` `exp-1-e_binary64_9669` `rem-log-exp_binary64_9667` `rem-cbrt-cube_binary64_9650` `div0_binary64_9607` `rgt-mult-inverse_binary64_9603`
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_9889` `erf-erfc_binary64_9888` `erf-odd_binary64_9887` `if-if-and-not_binary64_9886` `if-if-and_binary64_9885` `if-if-or-not_binary64_9884` `if-if-or_binary64_9883` `if-not_binary64_9882` `if-same_binary64_9881` `if-false_binary64_9880` `if-true_binary64_9879` `not-gte_binary64_9878` `not-lte_binary64_9877` `not-gt_binary64_9876` `not-lt_binary64_9875` `gte-same_binary64_9874` `lte-same_binary64_9873` `gt-same_binary64_9872` `lt-same_binary64_9871` `sinh---cosh_binary64_9818` `sinh-+-cosh_binary64_9817` `sinh-cosh_binary64_9816` `tanh-def-c_binary64_9815` `tanh-def-b_binary64_9814` `tanh-def-a_binary64_9813` `cosh-def_binary64_9812` `sinh-def_binary64_9811` `tan-neg_binary64_9758` `cos-neg_binary64_9757` `sin-neg_binary64_9756` `tan-0_binary64_9755` `cos-0_binary64_9754` `sin-0_binary64_9753` `hang-m-tan_binary64_9752` `hang-p-tan_binary64_9751` `hang-m0-tan_binary64_9750` `hang-p0-tan_binary64_9749` `hang-0m-tan_binary64_9748` `hang-0p-tan_binary64_9747` `tan-+PI/2_binary64_9746` `tan-+PI_binary64_9745` `tan-PI_binary64_9744` `tan-PI/3_binary64_9743` `tan-PI/4_binary64_9742` `tan-PI/6_binary64_9741` `cos-+PI/2_binary64_9740` `cos-+PI_binary64_9739` `cos-PI_binary64_9738` `cos-PI/2_binary64_9737` `cos-PI/3_binary64_9736` `cos-PI/4_binary64_9735` `cos-PI/6_binary64_9734` `sin-+PI/2_binary64_9733` `sin-+PI_binary64_9732` `sin-PI_binary64_9731` `sin-PI/2_binary64_9730` `sin-PI/3_binary64_9729` `sin-PI/4_binary64_9728` `sin-PI/6_binary64_9727` `sub-1-sin_binary64_9726` `sub-1-cos_binary64_9725` `-1-add-sin_binary64_9724` `-1-add-cos_binary64_9723` `1-sub-sin_binary64_9722` `1-sub-cos_binary64_9721` `cos-sin-sum_binary64_9720` `log-rec_binary64_9714` `pow-base-0_binary64_9710` `unpow1/3_binary64_9693` `unpow2_binary64_9691` `unpow1/2_binary64_9690` `unpow0_binary64_9685` `unpow1_binary64_9684` `unpow-1_binary64_9683` `exp-lft-cube_binary64_9682` `exp-cbrt_binary64_9680` `exp-sqrt_binary64_9679` `e-exp-1_binary64_9671` `exp-0_binary64_9668` `rem-exp-log_binary64_9666` `rem-3cbrt-rft_binary64_9652` `rem-cube-cbrt_binary64_9649` `sqr-abs_binary64_9641` `lft-mult-inverse_binary64_9604` `remove-double-div_binary64_9602`

Counts

112 → 468

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	1080
1	128	988
2	233	780
3	861	744
4	3064	736

prune4.4s (5.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	468	0	468
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	468	4	472

Error

0.2b

Counts

472 → 4

Compiler

Compiled 61163 to 51814 computations (15.3% saved)

localize55.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(-.f64 1 (+.f64 z 1))
4.9b	(-.f64 1 (+.f64 z 1))
4.9b	(-.f64 1 (+.f64 z 1))
4.9b	(-.f64 1 (+.f64 z 1))

rewrite376.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

40×	`*-un-lft-identity_binary64_9626`
24×	`add-log-exp_binary64_9665`
20×	`add-sqr-sqrt_binary64_9648`
16×	`cancel-sign-sub-inv_binary64_9592`
8×	`diff-log_binary64_9718` `add-cube-cbrt_binary64_9661` `difference-of-squares_binary64_9595` `distribute-lft-out_binary64_9577` `distribute-lft-out--_binary64_9578`
4×	`sum-log_binary64_9717` `pow1_binary64_9687` `add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662` `flip3--_binary64_9630` `sub-neg_binary64_9619` `flip--_binary64_9601` `associate--r+_binary64_9562`

Counts

4 → 84

Calls

4 calls:

6.0ms	(-.f64 1 (+.f64 z 1))
6.0ms	(-.f64 1 (+.f64 z 1))
6.0ms	(-.f64 1 (+.f64 z 1))
6.0ms	(-.f64 1 (+.f64 z 1))

Compiler

Compiled 10696 to 9126 computations (14.7% saved)

series107.0ms (0.1%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

19.0ms	(-.f64 1 (+.f64 z 1))
18.0ms	(-.f64 1 (+.f64 z 1))
18.0ms	(-.f64 1 (+.f64 z 1))
18.0ms	(-.f64 1 (+.f64 z 1))

Compiler

Compiled 4284 to 3761 computations (12.2% saved)

simplify675.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

455×	`sub-neg_binary64_9619`
280×	`associate-/l*_binary64_9571`
269×	`unsub-neg_binary64_9620`
214×	`cancel-sign-sub-inv_binary64_9592`
188×	`distribute-rgt-neg-in_binary64_9584`
173×	`distribute-neg-out_binary64_9588`
162×	`distribute-neg-in_binary64_9587`
158×	`associate--r+_binary64_9562`
155×	`associate-/l/_binary64_9573`
154×	`distribute-rgt-neg-out_binary64_9586`
148×	`distribute-lft-neg-in_binary64_9583`
139×	`sqr-pow_binary64_9598`
129×	`distribute-lft-neg-out_binary64_9585` `distribute-rgt-out_binary64_9579`
116×	`associate-+l-_binary64_9561`
107×	`associate-/r/_binary64_9572`
104×	`associate-l_binary64_9567`
102×	`exp-prod_binary64_9678`
100×	`neg-sub0_binary64_9621` `distribute-rgt-in_binary64_9576`
97×	`associate-r_binary64_9566`
95×	`associate--l+_binary64_9563`
93×	`neg-mul-1_binary64_9622`
83×	`+-commutative_binary64_9556`
81×	`pow-sqr_binary64_9599`
78×	`distribute-lft-in_binary64_9575`
77×	`div-sub_binary64_9631`
75×	`exp-sum_binary64_9672` `*-commutative_binary64_9557`
71×	`associate-+r-_binary64_9560`
70×	`distribute-lft-out_binary64_9577`
69×	`distribute-rgt1-in_binary64_9582`
62×	`associate-+l+_binary64_9559`
59×	`distribute-neg-frac_binary64_9590`
57×	`associate--l-_binary64_9564`
52×	`exp-diff_binary64_9674`
47×	`pow-plus_binary64_9689`
40×	`associate-*l/_binary64_9569`
38×	`associate-*r/_binary64_9568`
37×	`log-pow_binary64_9715` `associate-+r+_binary64_9558`
36×	`difference-of-squares_binary64_9595`
34×	`cube-prod_binary64_9654`
33×	`distribute-rgt-out--_binary64_9580`
29×	`log-prod_binary64_9712`
27×	`swap-sqr_binary64_9593` `distribute-lft1-in_binary64_9581`
25×	`sub0-neg_binary64_9613` `unswap-sqr_binary64_9594`
19×	`cube-div_binary64_9655`
18×	`*-rgt-identity_binary64_9616` `distribute-lft-out--_binary64_9578`
15×	`pow-base-1_binary64_9686`
14×	`exp-to-pow_binary64_9688` `remove-double-neg_binary64_9614`
13×	`+-rgt-identity_binary64_9611`
12×	`times-frac_binary64_9632`
11×	`log-div_binary64_9713` `*-lft-identity_binary64_9615` `mul0-rgt_binary64_9609` `difference-of-sqr-1_binary64_9596` `cancel-sign-sub_binary64_9591`
10×	`mul0-lft_binary64_9608`
9×	`unpow3_binary64_9692` `prod-exp_binary64_9675` `associate-/r*_binary64_9570` `associate--r-_binary64_9565`
8×	`div-exp_binary64_9677` `cube-unmult_binary64_9663` `sqr-neg_binary64_9640`
7×	`--rgt-identity_binary64_9612`
6×	`exp-neg_binary64_9673` `cube-mult_binary64_9656` `rem-sqrt-square_binary64_9639` `distribute-frac-neg_binary64_9589` `count-2_binary64_9574`
4×	`mul-1-neg_binary64_9618`
3×	`cube-neg_binary64_9653` `*-inverses_binary64_9606` `difference-of-sqr--1_binary64_9597`
1×	`log-E_binary64_9716` `exp-lft-sqr_binary64_9681` `1-exp_binary64_9670` `exp-1-e_binary64_9669` `rem-log-exp_binary64_9667` `rem-3cbrt-lft_binary64_9651` `rem-square-sqrt_binary64_9638` `/-rgt-identity_binary64_9617` `+-inverses_binary64_9605` `rgt-mult-inverse_binary64_9603`
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_9889` `erf-erfc_binary64_9888` `erf-odd_binary64_9887` `if-if-and-not_binary64_9886` `if-if-and_binary64_9885` `if-if-or-not_binary64_9884` `if-if-or_binary64_9883` `if-not_binary64_9882` `if-same_binary64_9881` `if-false_binary64_9880` `if-true_binary64_9879` `not-gte_binary64_9878` `not-lte_binary64_9877` `not-gt_binary64_9876` `not-lt_binary64_9875` `gte-same_binary64_9874` `lte-same_binary64_9873` `gt-same_binary64_9872` `lt-same_binary64_9871` `sinh---cosh_binary64_9818` `sinh-+-cosh_binary64_9817` `sinh-cosh_binary64_9816` `tanh-def-c_binary64_9815` `tanh-def-b_binary64_9814` `tanh-def-a_binary64_9813` `cosh-def_binary64_9812` `sinh-def_binary64_9811` `tan-neg_binary64_9758` `cos-neg_binary64_9757` `sin-neg_binary64_9756` `tan-0_binary64_9755` `cos-0_binary64_9754` `sin-0_binary64_9753` `hang-m-tan_binary64_9752` `hang-p-tan_binary64_9751` `hang-m0-tan_binary64_9750` `hang-p0-tan_binary64_9749` `hang-0m-tan_binary64_9748` `hang-0p-tan_binary64_9747` `tan-+PI/2_binary64_9746` `tan-+PI_binary64_9745` `tan-PI_binary64_9744` `tan-PI/3_binary64_9743` `tan-PI/4_binary64_9742` `tan-PI/6_binary64_9741` `cos-+PI/2_binary64_9740` `cos-+PI_binary64_9739` `cos-PI_binary64_9738` `cos-PI/2_binary64_9737` `cos-PI/3_binary64_9736` `cos-PI/4_binary64_9735` `cos-PI/6_binary64_9734` `sin-+PI/2_binary64_9733` `sin-+PI_binary64_9732` `sin-PI_binary64_9731` `sin-PI/2_binary64_9730` `sin-PI/3_binary64_9729` `sin-PI/4_binary64_9728` `sin-PI/6_binary64_9727` `sub-1-sin_binary64_9726` `sub-1-cos_binary64_9725` `-1-add-sin_binary64_9724` `-1-add-cos_binary64_9723` `1-sub-sin_binary64_9722` `1-sub-cos_binary64_9721` `cos-sin-sum_binary64_9720` `log-rec_binary64_9714` `pow-base-0_binary64_9710` `unpow1/3_binary64_9693` `unpow2_binary64_9691` `unpow1/2_binary64_9690` `unpow0_binary64_9685` `unpow1_binary64_9684` `unpow-1_binary64_9683` `exp-lft-cube_binary64_9682` `exp-cbrt_binary64_9680` `exp-sqrt_binary64_9679` `rec-exp_binary64_9676` `e-exp-1_binary64_9671` `exp-0_binary64_9668` `rem-exp-log_binary64_9666` `rem-3cbrt-rft_binary64_9652` `rem-cbrt-cube_binary64_9650` `rem-cube-cbrt_binary64_9649` `sqr-abs_binary64_9641` `+-lft-identity_binary64_9610` `div0_binary64_9607` `lft-mult-inverse_binary64_9604` `remove-double-div_binary64_9602`

Counts

96 → 256

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	972
1	118	872
2	255	708
3	1061	672
4	2640	672

prune1.4s (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	256	4	260

Error

0.2b

Counts

260 → 4

Compiler

Compiled 32678 to 27538 computations (15.7% saved)

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 848079078717083/1099511627776 (-.f64 3 z))))) (+.f64 (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)))) (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
1.0b	(+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)))
1.0b	(+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite925.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

193×	`*-un-lft-identity_binary64_9626`
173×	`add-log-exp_binary64_9665`
141×	`distribute-lft-out_binary64_9577`
137×	`sum-log_binary64_9717`
99×	`frac-add_binary64_9634`
44×	`flip3-+_binary64_9629` `flip-+_binary64_9600`
8×	`times-frac_binary64_9632`
7×	`pow1_binary64_9687`
4×	`add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662` `add-cube-cbrt_binary64_9661` `add-sqr-sqrt_binary64_9648` `distribute-lft-out--_binary64_9578`
3×	`+-commutative_binary64_9556`
2×	`sqrt-pow1_binary64_9644` `associate-+r+_binary64_9558`
1×	`pow1/2_binary64_9706` `pow-prod-down_binary64_9697` `sqrt-prod_binary64_9642` `associate-+l+_binary64_9559`

Counts

4 → 147

Calls

4 calls:

106.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 848079078717083/1099511627776 (-.f64 3 z))))) (+.f64 (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)))) (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
37.0ms	(+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))))
21.0ms	(+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 21276 to 17089 computations (19.7% saved)

series95.0ms (0.1%)

Error

0.1b

Counts

4 → 20

Calls

4 calls:

24.0ms	(+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))))
20.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 848079078717083/1099511627776 (-.f64 3 z))))) (+.f64 (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)))) (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z)))))
19.0ms	(+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2730 to 2177 computations (20.3% saved)

simplify2.2s (2.7%)

Algorithm

1×	egg-herbie

Rules

701×	`associate-r_binary64_9566`
649×	`associate-l_binary64_9567`
458×	`*-commutative_binary64_9557`
221×	`+-commutative_binary64_9556`
210×	`associate-+l+_binary64_9559`
193×	`associate-+r+_binary64_9558`
117×	`times-frac_binary64_9632`
86×	`associate-*l/_binary64_9569`
81×	`associate-*r/_binary64_9568`
74×	`distribute-rgt-in_binary64_9576` `distribute-lft-in_binary64_9575`
58×	`prod-exp_binary64_9675`
54×	`associate--r+_binary64_9562`
49×	`sub-neg_binary64_9619`
40×	`associate--l+_binary64_9563`
38×	`sqr-pow_binary64_9598`
33×	`distribute-neg-in_binary64_9587`
32×	`cancel-sign-sub-inv_binary64_9592`
27×	`neg-mul-1_binary64_9622` `neg-sub0_binary64_9621`
23×	`unpow3_binary64_9692` `cube-mult_binary64_9656`
20×	`exp-sum_binary64_9672` `distribute-rgt-neg-in_binary64_9584`
16×	`associate-/l*_binary64_9571`
15×	`distribute-neg-frac_binary64_9590`
14×	`pow-sqr_binary64_9599`
13×	`distribute-lft-neg-out_binary64_9585`
7×	`distribute-lft-neg-in_binary64_9583`
6×	`difference-of-squares_binary64_9595` `distribute-rgt-out--_binary64_9580` `associate-+l-_binary64_9561` `associate-+r-_binary64_9560`
5×	`cube-div_binary64_9655`
3×	`pow-plus_binary64_9689`
2×	`cube-unmult_binary64_9663`
1×	`unpow2_binary64_9691` `unpow1_binary64_9684` `1-exp_binary64_9670` `rem-sqrt-square_binary64_9639` `rem-square-sqrt_binary64_9638` `-rgt-identity_binary64_9616` `-inverses_binary64_9606`
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_9889` `erf-erfc_binary64_9888` `erf-odd_binary64_9887` `if-if-and-not_binary64_9886` `if-if-and_binary64_9885` `if-if-or-not_binary64_9884` `if-if-or_binary64_9883` `if-not_binary64_9882` `if-same_binary64_9881` `if-false_binary64_9880` `if-true_binary64_9879` `not-gte_binary64_9878` `not-lte_binary64_9877` `not-gt_binary64_9876` `not-lt_binary64_9875` `gte-same_binary64_9874` `lte-same_binary64_9873` `gt-same_binary64_9872` `lt-same_binary64_9871` `sinh---cosh_binary64_9818` `sinh-+-cosh_binary64_9817` `sinh-cosh_binary64_9816` `tanh-def-c_binary64_9815` `tanh-def-b_binary64_9814` `tanh-def-a_binary64_9813` `cosh-def_binary64_9812` `sinh-def_binary64_9811` `tan-neg_binary64_9758` `cos-neg_binary64_9757` `sin-neg_binary64_9756` `tan-0_binary64_9755` `cos-0_binary64_9754` `sin-0_binary64_9753` `hang-m-tan_binary64_9752` `hang-p-tan_binary64_9751` `hang-m0-tan_binary64_9750` `hang-p0-tan_binary64_9749` `hang-0m-tan_binary64_9748` `hang-0p-tan_binary64_9747` `tan-+PI/2_binary64_9746` `tan-+PI_binary64_9745` `tan-PI_binary64_9744` `tan-PI/3_binary64_9743` `tan-PI/4_binary64_9742` `tan-PI/6_binary64_9741` `cos-+PI/2_binary64_9740` `cos-+PI_binary64_9739` `cos-PI_binary64_9738` `cos-PI/2_binary64_9737` `cos-PI/3_binary64_9736` `cos-PI/4_binary64_9735` `cos-PI/6_binary64_9734` `sin-+PI/2_binary64_9733` `sin-+PI_binary64_9732` `sin-PI_binary64_9731` `sin-PI/2_binary64_9730` `sin-PI/3_binary64_9729` `sin-PI/4_binary64_9728` `sin-PI/6_binary64_9727` `sub-1-sin_binary64_9726` `sub-1-cos_binary64_9725` `-1-add-sin_binary64_9724` `-1-add-cos_binary64_9723` `1-sub-sin_binary64_9722` `1-sub-cos_binary64_9721` `cos-sin-sum_binary64_9720` `log-E_binary64_9716` `log-pow_binary64_9715` `log-rec_binary64_9714` `log-div_binary64_9713` `log-prod_binary64_9712` `pow-base-0_binary64_9710` `unpow1/3_binary64_9693` `unpow1/2_binary64_9690` `exp-to-pow_binary64_9688` `pow-base-1_binary64_9686` `unpow0_binary64_9685` `unpow-1_binary64_9683` `exp-lft-cube_binary64_9682` `exp-lft-sqr_binary64_9681` `exp-cbrt_binary64_9680` `exp-sqrt_binary64_9679` `exp-prod_binary64_9678` `div-exp_binary64_9677` `rec-exp_binary64_9676` `exp-diff_binary64_9674` `exp-neg_binary64_9673` `e-exp-1_binary64_9671` `exp-1-e_binary64_9669` `exp-0_binary64_9668` `rem-log-exp_binary64_9667` `rem-exp-log_binary64_9666` `cube-prod_binary64_9654` `cube-neg_binary64_9653` `rem-3cbrt-rft_binary64_9652` `rem-3cbrt-lft_binary64_9651` `rem-cbrt-cube_binary64_9650` `rem-cube-cbrt_binary64_9649` `sqr-abs_binary64_9641` `sqr-neg_binary64_9640` `div-sub_binary64_9631` `unsub-neg_binary64_9620` `mul-1-neg_binary64_9618` `/-rgt-identity_binary64_9617` `-lft-identity_binary64_9615` `remove-double-neg_binary64_9614` `sub0-neg_binary64_9613` `--rgt-identity_binary64_9612` `+-rgt-identity_binary64_9611` `+-lft-identity_binary64_9610` `mul0-rgt_binary64_9609` `mul0-lft_binary64_9608` `div0_binary64_9607` `+-inverses_binary64_9605` `lft-mult-inverse_binary64_9604` `rgt-mult-inverse_binary64_9603` `remove-double-div_binary64_9602` `difference-of-sqr--1_binary64_9597` `difference-of-sqr-1_binary64_9596` `unswap-sqr_binary64_9594` `swap-sqr_binary64_9593` `cancel-sign-sub_binary64_9591` `distribute-frac-neg_binary64_9589` `distribute-neg-out_binary64_9588` `distribute-rgt-neg-out_binary64_9586` `distribute-rgt1-in_binary64_9582` `distribute-lft1-in_binary64_9581` `distribute-rgt-out_binary64_9579` `distribute-lft-out--_binary64_9578` `distribute-lft-out_binary64_9577` `count-2_binary64_9574` `associate-/l/_binary64_9573` `associate-/r/_binary64_9572` `associate-/r_binary64_9570` `associate--r-_binary64_9565` `associate--l-_binary64_9564`

Counts

167 → 497

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	459	20278
1	1561	20121
2	4876	20121

prune8.5s (10.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	492	5	497
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	494	7	501

Error

0.1b

Counts

501 → 7

Compiler

Compiled 105003 to 85304 computations (18.8% saved)

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (.f64 PI.f64 2)) (.f64 (pow.f64 (+.f64 7 (-.f64 1/2 z)) (-.f64 1/2 z)) (.f64 (+.f64 562949953421205/562949953421312 (+.f64 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))))))) (.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (exp.f64 (-.f64 z (+.f64 7 1/2)))))))
1.0b	(+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)))
1.0b	(+.f64 (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite724.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

199×	`*-un-lft-identity_binary64_9626`
72×	`times-frac_binary64_9632`
61×	`distribute-lft-out_binary64_9577`
50×	`add-exp-log_binary64_9664`
46×	`associate-*r/_binary64_9568`
40×	`prod-exp_binary64_9675`
36×	`distribute-lft-out--_binary64_9578`
29×	`frac-times_binary64_9636`
24×	`add-cbrt-cube_binary64_9662`
18×	`add-log-exp_binary64_9665`
16×	`frac-add_binary64_9634` `flip3-+_binary64_9629` `flip-+_binary64_9600`
14×	`cbrt-unprod_binary64_9659`
12×	`exp-diff_binary64_9674` `pow-sub_binary64_9702`
11×	`associate-*l/_binary64_9569`
9×	`pow1_binary64_9687` `sum-log_binary64_9717`
5×	`add-cube-cbrt_binary64_9661` `add-sqr-sqrt_binary64_9648`
4×	`pow-to-exp_binary64_9695` `pow-exp_binary64_9694` `associate-l_binary64_9567`
3×	`div-exp_binary64_9677`
2×	`pow-prod-down_binary64_9697` `sqrt-pow1_binary64_9644` `sqrt-prod_binary64_9642` `+-commutative_binary64_9556`
1×	`pow1/2_binary64_9706` `associate-+l+_binary64_9559` `associate-+r+_binary64_9558` `cbrt-undiv_binary64_9660` `associate-r_binary64_9566` `*-commutative_binary64_9557`

Counts

4 → 128

Calls

4 calls:

169.0ms	(.f64 (sqrt.f64 (.f64 PI.f64 2)) (.f64 (pow.f64 (+.f64 7 (-.f64 1/2 z)) (-.f64 1/2 z)) (.f64 (+.f64 562949953421205/562949953421312 (+.f64 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))))))) (.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (exp.f64 (-.f64 z (+.f64 7 1/2)))))))
49.0ms	(+.f64 (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))))
22.0ms	(+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 14714 to 11599 computations (21.2% saved)

series175.0ms (0.2%)

Error

0.1b

Counts

4 → 18

Calls

4 calls:

101.0ms	(.f64 (sqrt.f64 (.f64 PI.f64 2)) (.f64 (pow.f64 (+.f64 7 (-.f64 1/2 z)) (-.f64 1/2 z)) (.f64 (+.f64 562949953421205/562949953421312 (+.f64 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))) (+.f64 (/.f64 -6214088902520669/35184372088832 (-.f64 4 z)) (+.f64 (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))))))) (.f64 (/.f64 PI.f64 (sin.f64 (.f64 PI.f64 z))) (exp.f64 (-.f64 z (+.f64 7 1/2)))))))
21.0ms	(+.f64 (+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (+.f64 (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)) (/.f64 5688119651184367/37778931862957161709568 (-.f64 8 z))))
19.0ms	(+.f64 (/.f64 7041008316161153/562949953421312 (-.f64 5 z)) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3122 to 2568 computations (17.7% saved)

simplify1.7s (2.1%)

Algorithm

1×	egg-herbie

Rules

739×	`associate-l_binary64_9567`
302×	`distribute-rgt-in_binary64_9576`
290×	`distribute-lft-in_binary64_9575`
191×	`*-commutative_binary64_9557`
174×	`associate-+r+_binary64_9558`
139×	`associate-+l+_binary64_9559`
133×	`associate-r_binary64_9566`
114×	`associate-*r/_binary64_9568`
101×	`associate-*l/_binary64_9569`
69×	`+-commutative_binary64_9556`
49×	`sub-neg_binary64_9619`
44×	`sqr-pow_binary64_9598`
40×	`associate-/l*_binary64_9571` `associate--r+_binary64_9562`
31×	`associate--l+_binary64_9563`
28×	`cancel-sign-sub-inv_binary64_9592`
22×	`neg-mul-1_binary64_9622` `neg-sub0_binary64_9621` `distribute-neg-in_binary64_9587`
19×	`unpow3_binary64_9692` `cube-mult_binary64_9656`
18×	`pow-sqr_binary64_9599`
16×	`associate-+r-_binary64_9560`
14×	`distribute-rgt-out_binary64_9579`
13×	`distribute-rgt-neg-in_binary64_9584`
12×	`times-frac_binary64_9632` `distribute-neg-frac_binary64_9590` `associate-+l-_binary64_9561`
11×	`cube-unmult_binary64_9663` `swap-sqr_binary64_9593`
10×	`associate-/r*_binary64_9570`
9×	`log-prod_binary64_9712`
8×	`prod-exp_binary64_9675` `distribute-lft-neg-out_binary64_9585`
5×	`distribute-lft-neg-in_binary64_9583` `distribute-rgt-out--_binary64_9580`
4×	`exp-sum_binary64_9672` `cube-div_binary64_9655` `difference-of-squares_binary64_9595`
3×	`log-div_binary64_9713` `exp-prod_binary64_9678` `exp-diff_binary64_9674` `rem-sqrt-square_binary64_9639` `unswap-sqr_binary64_9594` `associate-/r/_binary64_9572`
2×	`unpow2_binary64_9691` `pow-plus_binary64_9689` `associate--r-_binary64_9565`
1×	`log-pow_binary64_9715` `unpow1/2_binary64_9690` `1-exp_binary64_9670` `rem-log-exp_binary64_9667` `rem-square-sqrt_binary64_9638` `div-sub_binary64_9631` `*-inverses_binary64_9606` `count-2_binary64_9574` `associate-/l/_binary64_9573`
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_9889` `erf-erfc_binary64_9888` `erf-odd_binary64_9887` `if-if-and-not_binary64_9886` `if-if-and_binary64_9885` `if-if-or-not_binary64_9884` `if-if-or_binary64_9883` `if-not_binary64_9882` `if-same_binary64_9881` `if-false_binary64_9880` `if-true_binary64_9879` `not-gte_binary64_9878` `not-lte_binary64_9877` `not-gt_binary64_9876` `not-lt_binary64_9875` `gte-same_binary64_9874` `lte-same_binary64_9873` `gt-same_binary64_9872` `lt-same_binary64_9871` `sinh---cosh_binary64_9818` `sinh-+-cosh_binary64_9817` `sinh-cosh_binary64_9816` `tanh-def-c_binary64_9815` `tanh-def-b_binary64_9814` `tanh-def-a_binary64_9813` `cosh-def_binary64_9812` `sinh-def_binary64_9811` `tan-neg_binary64_9758` `cos-neg_binary64_9757` `sin-neg_binary64_9756` `tan-0_binary64_9755` `cos-0_binary64_9754` `sin-0_binary64_9753` `hang-m-tan_binary64_9752` `hang-p-tan_binary64_9751` `hang-m0-tan_binary64_9750` `hang-p0-tan_binary64_9749` `hang-0m-tan_binary64_9748` `hang-0p-tan_binary64_9747` `tan-+PI/2_binary64_9746` `tan-+PI_binary64_9745` `tan-PI_binary64_9744` `tan-PI/3_binary64_9743` `tan-PI/4_binary64_9742` `tan-PI/6_binary64_9741` `cos-+PI/2_binary64_9740` `cos-+PI_binary64_9739` `cos-PI_binary64_9738` `cos-PI/2_binary64_9737` `cos-PI/3_binary64_9736` `cos-PI/4_binary64_9735` `cos-PI/6_binary64_9734` `sin-+PI/2_binary64_9733` `sin-+PI_binary64_9732` `sin-PI_binary64_9731` `sin-PI/2_binary64_9730` `sin-PI/3_binary64_9729` `sin-PI/4_binary64_9728` `sin-PI/6_binary64_9727` `sub-1-sin_binary64_9726` `sub-1-cos_binary64_9725` `-1-add-sin_binary64_9724` `-1-add-cos_binary64_9723` `1-sub-sin_binary64_9722` `1-sub-cos_binary64_9721` `cos-sin-sum_binary64_9720` `log-E_binary64_9716` `log-rec_binary64_9714` `pow-base-0_binary64_9710` `unpow1/3_binary64_9693` `exp-to-pow_binary64_9688` `pow-base-1_binary64_9686` `unpow0_binary64_9685` `unpow1_binary64_9684` `unpow-1_binary64_9683` `exp-lft-cube_binary64_9682` `exp-lft-sqr_binary64_9681` `exp-cbrt_binary64_9680` `exp-sqrt_binary64_9679` `div-exp_binary64_9677` `rec-exp_binary64_9676` `exp-neg_binary64_9673` `e-exp-1_binary64_9671` `exp-1-e_binary64_9669` `exp-0_binary64_9668` `rem-exp-log_binary64_9666` `cube-prod_binary64_9654` `cube-neg_binary64_9653` `rem-3cbrt-rft_binary64_9652` `rem-3cbrt-lft_binary64_9651` `rem-cbrt-cube_binary64_9650` `rem-cube-cbrt_binary64_9649` `sqr-abs_binary64_9641` `sqr-neg_binary64_9640` `unsub-neg_binary64_9620` `mul-1-neg_binary64_9618` `/-rgt-identity_binary64_9617` `-rgt-identity_binary64_9616` `-lft-identity_binary64_9615` `remove-double-neg_binary64_9614` `sub0-neg_binary64_9613` `--rgt-identity_binary64_9612` `+-rgt-identity_binary64_9611` `+-lft-identity_binary64_9610` `mul0-rgt_binary64_9609` `mul0-lft_binary64_9608` `div0_binary64_9607` `+-inverses_binary64_9605` `lft-mult-inverse_binary64_9604` `rgt-mult-inverse_binary64_9603` `remove-double-div_binary64_9602` `difference-of-sqr--1_binary64_9597` `difference-of-sqr-1_binary64_9596` `cancel-sign-sub_binary64_9591` `distribute-frac-neg_binary64_9589` `distribute-neg-out_binary64_9588` `distribute-rgt-neg-out_binary64_9586` `distribute-rgt1-in_binary64_9582` `distribute-lft1-in_binary64_9581` `distribute-lft-out--_binary64_9578` `distribute-lft-out_binary64_9577` `associate--l-_binary64_9564`

Counts

146 → 284

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	460	12698
1	1416	11249

prune1.6s (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	277	7	284
Fresh	4	0	4
Picked	1	0	1
Done	2	0	2
Total	284	7	291

Error

Counts

291 → 7

Compiler

Compiled 35448 to 28086 computations (20.8% saved)

regimes917.0ms (1.1%)

Accuracy

Total 0.4b remaining (93.2%)

Threshold costs 0.4b (93.2%)

Compiler

Compiled 23874 to 19984 computations (16.3% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

21×	`+-commutative_binary64_9556`
11×	`sub-neg_binary64_9619`
9×	`*-commutative_binary64_9557`
1×	`1-exp_binary64_9670` `neg-mul-1_binary64_9622` `neg-sub0_binary64_9621`
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_9886` `if-if-and_binary64_9885` `if-if-or-not_binary64_9884` `if-if-or_binary64_9883` `if-not_binary64_9882` `if-same_binary64_9881` `if-false_binary64_9880` `if-true_binary64_9879` `tan-0_binary64_9755` `cos-0_binary64_9754` `sin-0_binary64_9753` `unpow1_binary64_9684` `e-exp-1_binary64_9671` `exp-1-e_binary64_9669` `exp-0_binary64_9668` `sqr-abs_binary64_9641` `sqr-neg_binary64_9640` `unsub-neg_binary64_9620` `mul-1-neg_binary64_9618` `/-rgt-identity_binary64_9617` `-rgt-identity_binary64_9616` `-lft-identity_binary64_9615` `remove-double-neg_binary64_9614` `sub0-neg_binary64_9613` `--rgt-identity_binary64_9612` `+-rgt-identity_binary64_9611` `+-lft-identity_binary64_9610` `cancel-sign-sub-inv_binary64_9592` `cancel-sign-sub_binary64_9591` `distribute-neg-frac_binary64_9590` `distribute-frac-neg_binary64_9589` `distribute-neg-out_binary64_9588` `distribute-neg-in_binary64_9587` `distribute-rgt-neg-out_binary64_9586` `distribute-lft-neg-out_binary64_9585` `distribute-rgt-neg-in_binary64_9584` `distribute-lft-neg-in_binary64_9583`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	131
1	95	131
2	108	131
3	110	131
4	111	131

Proof

(/ f64 (* f64 (* f64 (sqrt f64 (* f64 2 (PI f64))) (sqrt f64 (- f64 (+ f64 1/2 7) h0))) (* f64 (+ f64 562949953421205/562949953421312 (+ f64 (+ f64 (+ f64 (+ f64 (/ f64 5950736089418501/8796093022208 (- f64 1 h0)) (/ f64 -5537752839100187/4398046511104 (- f64 2 h0))) (/ f64 848079078717083/1099511627776 (- f64 3 h0))) (/ f64 -6214088902520669/35184372088832 (- f64 4 h0))) (+ f64 (/ f64 7041008316161153/562949953421312 (- f64 5 h0)) (+ f64 (/ f64 -4992549864024149/36028797018963968 (- f64 6 h0)) (+ f64 (/ f64 5893731530977871/590295810358705651712 (- f64 7 h0)) (/ f64 5688119651184367/37778931862957161709568 (- f64 8 h0))))))) (* f64 (PI f64) (exp f64 h0)))) (* f64 (pow f64 (+ f64 7 (- f64 1/2 h0)) h0) (* f64 (sin f64 (* f64 (PI f64) h0)) (exp f64 (+ f64 7 1/2)))))
<= +-commutative_binary64_9556
(/ f64 (* f64 (* f64 (sqrt f64 (* f64 2 (PI f64))) (sqrt f64 (- f64 (+ f64 1/2 7) h0))) (* f64 (+ f64 562949953421205/562949953421312 (+ f64 (+ f64 (+ f64 (+ f64 (/ f64 5950736089418501/8796093022208 (- f64 1 h0)) (/ f64 -5537752839100187/4398046511104 (- f64 2 h0))) (/ f64 848079078717083/1099511627776 (- f64 3 h0))) (/ f64 -6214088902520669/35184372088832 (- f64 4 h0))) (+ f64 (/ f64 7041008316161153/562949953421312 (- f64 5 h0)) (+ f64 (/ f64 -4992549864024149/36028797018963968 (- f64 6 h0)) (+ f64 (/ f64 5893731530977871/590295810358705651712 (- f64 7 h0)) (/ f64 5688119651184367/37778931862957161709568 (- f64 8 h0))))))) (* f64 (PI f64) (exp f64 h0)))) (* f64 (pow f64 (+ f64 7 (- f64 1/2 h0)) h0) (* f64 (sin f64 (* f64 (PI f64) h0)) (exp f64 (<= (+ f64 1/2 7))))))

end0.0ms (0%)

sample50.3s (62.9%)

Algorithm

1×

intervals

Results

41.8s	3859×	body	8192	exit
2.7s	8000×	body	128	valid
173.0ms	11965×	pre	128	true
38.0ms	106×	body	128	invalid

Compiler

Compiled 12023 to 10064 computations (16.3% saved)

Details

analyze2.1s (2.6%)

sample1.6s (2%)

simplify212.0ms (0.3%)

prune22.0ms (0%)

localize49.0ms (0.1%)

rewrite458.0ms (0.6%)

series110.0ms (0.1%)

simplify1.2s (1.6%)

prune4.4s (5.5%)

localize55.0ms (0.1%)

rewrite376.0ms (0.5%)

series107.0ms (0.1%)

simplify675.0ms (0.8%)

prune1.4s (1.8%)

localize46.0ms (0.1%)

rewrite925.0ms (1.2%)

series95.0ms (0.1%)

simplify2.2s (2.7%)

prune8.5s (10.7%)

localize46.0ms (0.1%)

rewrite724.0ms (0.9%)

series175.0ms (0.2%)

simplify1.7s (2.1%)

prune1.6s (1.9%)

regimes917.0ms (1.1%)

bsearch0.0ms (0%)

simplify9.0ms (0%)

end0.0ms (0%)

sample50.3s (62.9%)

Profiling