Details

analyze449.0ms (2.6%)

Algorithm

1×	search
2×	egg-herbie

Rules

729×	`div-sub_binary64_4175`
432×	`cancel-sign-sub-inv_binary64_4136`
372×	`unsub-neg_binary64_4164`
310×	`associate-l_binary64_4111`
297×	`associate-r_binary64_4110`
290×	`unswap-sqr_binary64_4138`
213×	`sub-neg_binary64_4163`
192×	`neg-mul-1_binary64_4166`
158×	`distribute-rgt-in_binary64_4120`
157×	`distribute-lft-in_binary64_4119`
118×	`*-commutative_binary64_4101`
105×	`neg-sub0_binary64_4165`
96×	`associate-+l+_binary64_4103`
93×	`associate-*l/_binary64_4113`
91×	`associate-+r+_binary64_4102`
74×	`times-frac_binary64_4176`
72×	`associate-/l*_binary64_4115`
65×	`*-lft-identity_binary64_4159`
64×	`*-rgt-identity_binary64_4160`
63×	`associate-*r/_binary64_4112`
61×	`associate-/r*_binary64_4114`
56×	`+-commutative_binary64_4100`
49×	`sqr-pow_binary64_4142`
46×	`associate-+l-_binary64_4105`
40×	`swap-sqr_binary64_4137`
35×	`pow-plus_binary64_4233` `sub0-neg_binary64_4157` `distribute-rgt-neg-out_binary64_4130` `distribute-lft-neg-out_binary64_4129`
30×	`associate-+r-_binary64_4104`
28×	`difference-of-squares_binary64_4139`
24×	`cube-prod_binary64_4198` `associate--r+_binary64_4106`
21×	`cube-unmult_binary64_4207`
18×	`distribute-rgt-neg-in_binary64_4128`
17×	`unpow3_binary64_4236` `mul0-rgt_binary64_4153` `mul0-lft_binary64_4152`
16×	`associate--r-_binary64_4109` `associate--l+_binary64_4107`
12×	`cube-div_binary64_4199` `distribute-lft-neg-in_binary64_4127`
11×	`sqr-neg_binary64_4184` `+-rgt-identity_binary64_4155`
10×	`rem-sqrt-square_binary64_4183` `+-lft-identity_binary64_4154`
9×	`/-rgt-identity_binary64_4161`
8×	`--rgt-identity_binary64_4156` `distribute-neg-in_binary64_4131` `distribute-rgt-out_binary64_4123` `distribute-lft-out_binary64_4121` `associate-/r/_binary64_4116` `associate--l-_binary64_4108`
7×	`unpow2_binary64_4235` `unpow1/2_binary64_4234` `unpow1_binary64_4228`
6×	`div0_binary64_4151`
4×	`remove-double-neg_binary64_4158` `distribute-frac-neg_binary64_4133` `distribute-neg-out_binary64_4132` `associate-/l/_binary64_4117`
3×	`cube-mult_binary64_4200` `mul-1-neg_binary64_4162`
1×	`1-exp_binary64_4214`
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_4433` `erf-erfc_binary64_4432` `erf-odd_binary64_4431` `if-if-and-not_binary64_4430` `if-if-and_binary64_4429` `if-if-or-not_binary64_4428` `if-if-or_binary64_4427` `if-not_binary64_4426` `if-same_binary64_4425` `if-false_binary64_4424` `if-true_binary64_4423` `not-gte_binary64_4422` `not-lte_binary64_4421` `not-gt_binary64_4420` `not-lt_binary64_4419` `gte-same_binary64_4418` `lte-same_binary64_4417` `gt-same_binary64_4416` `lt-same_binary64_4415` `sinh---cosh_binary64_4362` `sinh-+-cosh_binary64_4361` `sinh-cosh_binary64_4360` `tanh-def-c_binary64_4359` `tanh-def-b_binary64_4358` `tanh-def-a_binary64_4357` `cosh-def_binary64_4356` `sinh-def_binary64_4355` `tan-neg_binary64_4302` `cos-neg_binary64_4301` `sin-neg_binary64_4300` `tan-0_binary64_4299` `cos-0_binary64_4298` `sin-0_binary64_4297` `hang-m-tan_binary64_4296` `hang-p-tan_binary64_4295` `hang-m0-tan_binary64_4294` `hang-p0-tan_binary64_4293` `hang-0m-tan_binary64_4292` `hang-0p-tan_binary64_4291` `tan-+PI/2_binary64_4290` `tan-+PI_binary64_4289` `tan-PI_binary64_4288` `tan-PI/3_binary64_4287` `tan-PI/4_binary64_4286` `tan-PI/6_binary64_4285` `cos-+PI/2_binary64_4284` `cos-+PI_binary64_4283` `cos-PI_binary64_4282` `cos-PI/2_binary64_4281` `cos-PI/3_binary64_4280` `cos-PI/4_binary64_4279` `cos-PI/6_binary64_4278` `sin-+PI/2_binary64_4277` `sin-+PI_binary64_4276` `sin-PI_binary64_4275` `sin-PI/2_binary64_4274` `sin-PI/3_binary64_4273` `sin-PI/4_binary64_4272` `sin-PI/6_binary64_4271` `sub-1-sin_binary64_4270` `sub-1-cos_binary64_4269` `-1-add-sin_binary64_4268` `-1-add-cos_binary64_4267` `1-sub-sin_binary64_4266` `1-sub-cos_binary64_4265` `cos-sin-sum_binary64_4264` `log-E_binary64_4260` `log-pow_binary64_4259` `log-rec_binary64_4258` `log-div_binary64_4257` `log-prod_binary64_4256` `pow-base-0_binary64_4254` `unpow1/3_binary64_4237` `exp-to-pow_binary64_4232` `pow-base-1_binary64_4230` `unpow0_binary64_4229` `unpow-1_binary64_4227` `exp-lft-cube_binary64_4226` `exp-lft-sqr_binary64_4225` `exp-cbrt_binary64_4224` `exp-sqrt_binary64_4223` `exp-prod_binary64_4222` `div-exp_binary64_4221` `rec-exp_binary64_4220` `prod-exp_binary64_4219` `exp-diff_binary64_4218` `exp-neg_binary64_4217` `exp-sum_binary64_4216` `e-exp-1_binary64_4215` `exp-1-e_binary64_4213` `exp-0_binary64_4212` `rem-log-exp_binary64_4211` `rem-exp-log_binary64_4210` `cube-neg_binary64_4197` `rem-3cbrt-rft_binary64_4196` `rem-3cbrt-lft_binary64_4195` `rem-cbrt-cube_binary64_4194` `rem-cube-cbrt_binary64_4193` `sqr-abs_binary64_4185` `rem-square-sqrt_binary64_4182` `*-inverses_binary64_4150` `+-inverses_binary64_4149` `lft-mult-inverse_binary64_4148` `rgt-mult-inverse_binary64_4147` `remove-double-div_binary64_4146` `pow-sqr_binary64_4143` `difference-of-sqr--1_binary64_4141` `difference-of-sqr-1_binary64_4140` `cancel-sign-sub_binary64_4135` `distribute-neg-frac_binary64_4134` `distribute-rgt1-in_binary64_4126` `distribute-lft1-in_binary64_4125` `distribute-rgt-out--_binary64_4124` `distribute-lft-out--_binary64_4122` `count-2_binary64_4118`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	144
1	129	132
2	296	132
3	938	132
4	2843	132
5	4501	132
6	4959	132
7	4999	132
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 24 to 21 computations (12.5% saved)

sample76.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	177×	body	128	valid
19.0ms	26×	body	4096	valid
15.0ms	28×	body	2048	valid
4.0ms	13×	body	512	valid
4.0ms	9×	body	1024	valid
1.0ms	3×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

763×	`div-sub_binary64_4175`
378×	`cancel-sign-sub-inv_binary64_4136`
353×	`associate-/r/_binary64_4116`
331×	`distribute-rgt-in_binary64_4120`
294×	`associate-/l/_binary64_4117`
282×	`neg-mul-1_binary64_4166`
257×	`neg-sub0_binary64_4165`
255×	`distribute-lft-in_binary64_4119`
231×	`unsub-neg_binary64_4164`
179×	`associate-l_binary64_4111`
163×	`times-frac_binary64_4176`
153×	`distribute-rgt-neg-out_binary64_4130`
148×	`unswap-sqr_binary64_4138`
138×	`associate-r_binary64_4110`
132×	`distribute-lft-neg-out_binary64_4129`
109×	`sub-neg_binary64_4163` `distribute-rgt-out_binary64_4123`
107×	`distribute-rgt-neg-in_binary64_4128`
103×	`associate-/r*_binary64_4114`
98×	`associate-*l/_binary64_4113`
80×	`distribute-lft-neg-in_binary64_4127`
76×	`associate-/l*_binary64_4115`
73×	`distribute-neg-frac_binary64_4134`
71×	`associate-*r/_binary64_4112`
68×	`associate-+r+_binary64_4102`
65×	`distribute-frac-neg_binary64_4133` `associate-+l+_binary64_4103`
59×	`distribute-rgt-out--_binary64_4124`
51×	`*-commutative_binary64_4101`
44×	`distribute-neg-out_binary64_4132`
32×	`+-commutative_binary64_4100`
27×	`sqr-pow_binary64_4142` `associate--r+_binary64_4106`
24×	`pow-plus_binary64_4233` `*-rgt-identity_binary64_4160`
23×	`associate-+l-_binary64_4105`
22×	`*-lft-identity_binary64_4159`
21×	`distribute-lft-out_binary64_4121`
19×	`unpow3_binary64_4236` `cube-prod_binary64_4198` `associate--r-_binary64_4109`
18×	`cube-div_binary64_4199` `sub0-neg_binary64_4157`
16×	`swap-sqr_binary64_4137` `cancel-sign-sub_binary64_4135`
13×	`mul0-rgt_binary64_4153`
12×	`+-rgt-identity_binary64_4155` `mul0-lft_binary64_4152` `associate--l+_binary64_4107`
11×	`distribute-neg-in_binary64_4131`
10×	`cube-unmult_binary64_4207` `cube-mult_binary64_4200` `associate-+r-_binary64_4104`
8×	`associate--l-_binary64_4108`
7×	`rem-sqrt-square_binary64_4183`
6×	`remove-double-neg_binary64_4158`
5×	`sqr-neg_binary64_4184` `/-rgt-identity_binary64_4161` `div0_binary64_4151`
4×	`unpow2_binary64_4235`
3×	`--rgt-identity_binary64_4156`
2×	`unpow1/2_binary64_4234` `unpow1_binary64_4228` `mul-1-neg_binary64_4162` `+-lft-identity_binary64_4154` `pow-sqr_binary64_4143`
1×	`1-exp_binary64_4214` `distribute-rgt1-in_binary64_4126` `distribute-lft-out--_binary64_4122`
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_4433` `erf-erfc_binary64_4432` `erf-odd_binary64_4431` `if-if-and-not_binary64_4430` `if-if-and_binary64_4429` `if-if-or-not_binary64_4428` `if-if-or_binary64_4427` `if-not_binary64_4426` `if-same_binary64_4425` `if-false_binary64_4424` `if-true_binary64_4423` `not-gte_binary64_4422` `not-lte_binary64_4421` `not-gt_binary64_4420` `not-lt_binary64_4419` `gte-same_binary64_4418` `lte-same_binary64_4417` `gt-same_binary64_4416` `lt-same_binary64_4415` `sinh---cosh_binary64_4362` `sinh-+-cosh_binary64_4361` `sinh-cosh_binary64_4360` `tanh-def-c_binary64_4359` `tanh-def-b_binary64_4358` `tanh-def-a_binary64_4357` `cosh-def_binary64_4356` `sinh-def_binary64_4355` `tan-neg_binary64_4302` `cos-neg_binary64_4301` `sin-neg_binary64_4300` `tan-0_binary64_4299` `cos-0_binary64_4298` `sin-0_binary64_4297` `hang-m-tan_binary64_4296` `hang-p-tan_binary64_4295` `hang-m0-tan_binary64_4294` `hang-p0-tan_binary64_4293` `hang-0m-tan_binary64_4292` `hang-0p-tan_binary64_4291` `tan-+PI/2_binary64_4290` `tan-+PI_binary64_4289` `tan-PI_binary64_4288` `tan-PI/3_binary64_4287` `tan-PI/4_binary64_4286` `tan-PI/6_binary64_4285` `cos-+PI/2_binary64_4284` `cos-+PI_binary64_4283` `cos-PI_binary64_4282` `cos-PI/2_binary64_4281` `cos-PI/3_binary64_4280` `cos-PI/4_binary64_4279` `cos-PI/6_binary64_4278` `sin-+PI/2_binary64_4277` `sin-+PI_binary64_4276` `sin-PI_binary64_4275` `sin-PI/2_binary64_4274` `sin-PI/3_binary64_4273` `sin-PI/4_binary64_4272` `sin-PI/6_binary64_4271` `sub-1-sin_binary64_4270` `sub-1-cos_binary64_4269` `-1-add-sin_binary64_4268` `-1-add-cos_binary64_4267` `1-sub-sin_binary64_4266` `1-sub-cos_binary64_4265` `cos-sin-sum_binary64_4264` `log-E_binary64_4260` `log-pow_binary64_4259` `log-rec_binary64_4258` `log-div_binary64_4257` `log-prod_binary64_4256` `pow-base-0_binary64_4254` `unpow1/3_binary64_4237` `exp-to-pow_binary64_4232` `pow-base-1_binary64_4230` `unpow0_binary64_4229` `unpow-1_binary64_4227` `exp-lft-cube_binary64_4226` `exp-lft-sqr_binary64_4225` `exp-cbrt_binary64_4224` `exp-sqrt_binary64_4223` `exp-prod_binary64_4222` `div-exp_binary64_4221` `rec-exp_binary64_4220` `prod-exp_binary64_4219` `exp-diff_binary64_4218` `exp-neg_binary64_4217` `exp-sum_binary64_4216` `e-exp-1_binary64_4215` `exp-1-e_binary64_4213` `exp-0_binary64_4212` `rem-log-exp_binary64_4211` `rem-exp-log_binary64_4210` `cube-neg_binary64_4197` `rem-3cbrt-rft_binary64_4196` `rem-3cbrt-lft_binary64_4195` `rem-cbrt-cube_binary64_4194` `rem-cube-cbrt_binary64_4193` `sqr-abs_binary64_4185` `rem-square-sqrt_binary64_4182` `*-inverses_binary64_4150` `+-inverses_binary64_4149` `lft-mult-inverse_binary64_4148` `rgt-mult-inverse_binary64_4147` `remove-double-div_binary64_4146` `difference-of-sqr--1_binary64_4141` `difference-of-sqr-1_binary64_4140` `difference-of-squares_binary64_4139` `distribute-lft1-in_binary64_4125` `count-2_binary64_4118`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	36
1	44	33
2	92	33
3	250	33
4	624	33
5	1837	33
6	4068	33
7	4861	33
8	4970	33

prune5.0ms (0%)

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

27.7b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 A C) 2)
0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
0.8b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
34.8b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite216.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

27.5b

Rules

25×	`add-sqr-sqrt_binary64_4192` `*-un-lft-identity_binary64_4170`
18×	`add-cube-cbrt_binary64_4205`
9×	`add-log-exp_binary64_4209` `cancel-sign-sub-inv_binary64_4136` `times-frac_binary64_4176`
7×	`add-exp-log_binary64_4208` `sqrt-prod_binary64_4186`
6×	`pow1_binary64_4231` `add-cbrt-cube_binary64_4206` `sqrt-div_binary64_4187`
5×	`unpow-prod-down_binary64_4249`
4×	`frac-sub_binary64_4179` `distribute-lft-out--_binary64_4122` `associate--l+_binary64_4107`
3×	`flip3-+_binary64_4173` `flip-+_binary64_4144` `diff-log_binary64_4262` `flip3--_binary64_4174` `flip--_binary64_4145` `difference-of-squares_binary64_4139` `associate-/l_binary64_4115` `associate-/r_binary64_4114` `pow-unpow_binary64_4247`
2×	`sub-neg_binary64_4163`
1×	`pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `rem-sqrt-square_binary64_4183` `associate--l-_binary64_4108` `div-exp_binary64_4221` `cbrt-undiv_binary64_4204` `frac-2neg_binary64_4181` `clear-num_binary64_4169` `div-inv_binary64_4167` `pow-pow_binary64_4242` `pow-to-exp_binary64_4239` `pow-exp_binary64_4238` `unpow2_binary64_4235` `sqr-pow_binary64_4142`

Counts

4 → 93

Calls

4 calls:

18.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
6.0ms	(pow.f64 (-.f64 A C) 2)
6.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)

Compiler

Compiled 3294 to 1614 computations (51% saved)

series1.4s (8.3%)

Error

6.6b

Counts

4 → 73

Calls

4 calls:

476.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
468.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
286.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
42.0ms	(pow.f64 (-.f64 A C) 2)

Compiler

Compiled 5767 to 4402 computations (23.7% saved)

simplify178.0ms (1%)

Algorithm

1×	egg-herbie

Rules

560×	`cancel-sign-sub-inv_binary64_4136`
393×	`sub-neg_binary64_4163`
186×	`+-commutative_binary64_4100`
135×	`neg-sub0_binary64_4165`
133×	`neg-mul-1_binary64_4166`
130×	`*-commutative_binary64_4101`
125×	`times-frac_binary64_4176`
118×	`associate--l+_binary64_4107`
114×	`unswap-sqr_binary64_4138`
105×	`associate-r_binary64_4110` `associate--r+_binary64_4106` `associate-+l+_binary64_4103`
98×	`associate-+r+_binary64_4102`
96×	`associate-/l*_binary64_4115`
91×	`unsub-neg_binary64_4164` `distribute-neg-frac_binary64_4134`
89×	`associate-/r*_binary64_4114`
77×	`exp-prod_binary64_4222` `associate-l_binary64_4111`
71×	`sqr-pow_binary64_4142`
62×	`distribute-neg-in_binary64_4131`
52×	`distribute-rgt-in_binary64_4120`
51×	`distribute-lft-in_binary64_4119`
50×	`distribute-rgt-neg-in_binary64_4128`
40×	`associate-*l/_binary64_4113`
37×	`associate-*r/_binary64_4112`
34×	`distribute-lft-neg-in_binary64_4127`
28×	`log-prod_binary64_4256`
23×	`difference-of-squares_binary64_4139`
18×	`unpow3_binary64_4236`
17×	`associate-/r/_binary64_4116`
16×	`distribute-lft-neg-out_binary64_4129` `associate-/l/_binary64_4117`
15×	`div-sub_binary64_4175`
13×	`pow-plus_binary64_4233` `cube-prod_binary64_4198`
12×	`log-pow_binary64_4259`
11×	`exp-sum_binary64_4216` `distribute-rgt-out_binary64_4123`
10×	`cube-unmult_binary64_4207` `distribute-lft-out_binary64_4121`
9×	`unpow2_binary64_4235` `unpow1/2_binary64_4234` `unpow1_binary64_4228` `cube-mult_binary64_4200` `pow-sqr_binary64_4143` `associate-+r-_binary64_4104`
7×	`exp-diff_binary64_4218` `rem-sqrt-square_binary64_4183` `mul-1-neg_binary64_4162` `+-rgt-identity_binary64_4155`
6×	`swap-sqr_binary64_4137` `associate-+l-_binary64_4105`
4×	`rem-square-sqrt_binary64_4182` `/-rgt-identity_binary64_4161` `*-rgt-identity_binary64_4160`
3×	`log-div_binary64_4257` `div-exp_binary64_4221` `distribute-rgt-neg-out_binary64_4130`
2×	`rem-3cbrt-lft_binary64_4195` `sub0-neg_binary64_4157` `distribute-rgt-out--_binary64_4124` `associate--l-_binary64_4108`
1×	`prod-exp_binary64_4219` `1-exp_binary64_4214` `cube-div_binary64_4199` `rem-3cbrt-rft_binary64_4196` `*-lft-identity_binary64_4159` `cancel-sign-sub_binary64_4135` `distribute-neg-out_binary64_4132` `distribute-rgt1-in_binary64_4126` `distribute-lft-out--_binary64_4122`
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_4433` `erf-erfc_binary64_4432` `erf-odd_binary64_4431` `if-if-and-not_binary64_4430` `if-if-and_binary64_4429` `if-if-or-not_binary64_4428` `if-if-or_binary64_4427` `if-not_binary64_4426` `if-same_binary64_4425` `if-false_binary64_4424` `if-true_binary64_4423` `not-gte_binary64_4422` `not-lte_binary64_4421` `not-gt_binary64_4420` `not-lt_binary64_4419` `gte-same_binary64_4418` `lte-same_binary64_4417` `gt-same_binary64_4416` `lt-same_binary64_4415` `sinh---cosh_binary64_4362` `sinh-+-cosh_binary64_4361` `sinh-cosh_binary64_4360` `tanh-def-c_binary64_4359` `tanh-def-b_binary64_4358` `tanh-def-a_binary64_4357` `cosh-def_binary64_4356` `sinh-def_binary64_4355` `tan-neg_binary64_4302` `cos-neg_binary64_4301` `sin-neg_binary64_4300` `tan-0_binary64_4299` `cos-0_binary64_4298` `sin-0_binary64_4297` `hang-m-tan_binary64_4296` `hang-p-tan_binary64_4295` `hang-m0-tan_binary64_4294` `hang-p0-tan_binary64_4293` `hang-0m-tan_binary64_4292` `hang-0p-tan_binary64_4291` `tan-+PI/2_binary64_4290` `tan-+PI_binary64_4289` `tan-PI_binary64_4288` `tan-PI/3_binary64_4287` `tan-PI/4_binary64_4286` `tan-PI/6_binary64_4285` `cos-+PI/2_binary64_4284` `cos-+PI_binary64_4283` `cos-PI_binary64_4282` `cos-PI/2_binary64_4281` `cos-PI/3_binary64_4280` `cos-PI/4_binary64_4279` `cos-PI/6_binary64_4278` `sin-+PI/2_binary64_4277` `sin-+PI_binary64_4276` `sin-PI_binary64_4275` `sin-PI/2_binary64_4274` `sin-PI/3_binary64_4273` `sin-PI/4_binary64_4272` `sin-PI/6_binary64_4271` `sub-1-sin_binary64_4270` `sub-1-cos_binary64_4269` `-1-add-sin_binary64_4268` `-1-add-cos_binary64_4267` `1-sub-sin_binary64_4266` `1-sub-cos_binary64_4265` `cos-sin-sum_binary64_4264` `log-E_binary64_4260` `log-rec_binary64_4258` `pow-base-0_binary64_4254` `unpow1/3_binary64_4237` `exp-to-pow_binary64_4232` `pow-base-1_binary64_4230` `unpow0_binary64_4229` `unpow-1_binary64_4227` `exp-lft-cube_binary64_4226` `exp-lft-sqr_binary64_4225` `exp-cbrt_binary64_4224` `exp-sqrt_binary64_4223` `rec-exp_binary64_4220` `exp-neg_binary64_4217` `e-exp-1_binary64_4215` `exp-1-e_binary64_4213` `exp-0_binary64_4212` `rem-log-exp_binary64_4211` `rem-exp-log_binary64_4210` `cube-neg_binary64_4197` `rem-cbrt-cube_binary64_4194` `rem-cube-cbrt_binary64_4193` `sqr-abs_binary64_4185` `sqr-neg_binary64_4184` `remove-double-neg_binary64_4158` `--rgt-identity_binary64_4156` `+-lft-identity_binary64_4154` `mul0-rgt_binary64_4153` `mul0-lft_binary64_4152` `div0_binary64_4151` `*-inverses_binary64_4150` `+-inverses_binary64_4149` `lft-mult-inverse_binary64_4148` `rgt-mult-inverse_binary64_4147` `remove-double-div_binary64_4146` `difference-of-sqr--1_binary64_4141` `difference-of-sqr-1_binary64_4140` `distribute-frac-neg_binary64_4133` `distribute-lft1-in_binary64_4125` `count-2_binary64_4118` `associate--r-_binary64_4109`

Counts

166 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	404	5205
1	1047	4978
2	3370	4966
3	4950	4966
4	5016	4966

prune240.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	130	10	140
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	10	141

Error

6.6b

Counts

141 → 10

Compiler

Compiled 4663 to 2201 computations (52.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
34.8b	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))

rewrite171.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

17×	`add-sqr-sqrt_binary64_4192`
15×	`*-un-lft-identity_binary64_4170`
13×	`sqrt-prod_binary64_4186`
10×	`add-cube-cbrt_binary64_4205`
9×	`add-log-exp_binary64_4209` `cancel-sign-sub-inv_binary64_4136`
7×	`pow1_binary64_4231`
6×	`sqrt-div_binary64_4187`
4×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206` `frac-sub_binary64_4179` `associate--l+_binary64_4107`
3×	`pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173` `flip-+_binary64_4144` `rem-sqrt-square_binary64_4183` `diff-log_binary64_4262` `flip3--_binary64_4174` `flip--_binary64_4145` `distribute-lft-out--_binary64_4122`
2×	`sub-neg_binary64_4163` `difference-of-squares_binary64_4139`
1×	`associate--l-_binary64_4108`

Counts

4 → 72

Calls

4 calls:

21.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2))))
9.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2811 to 1359 computations (51.7% saved)

series1.0s (6%)

Error

6.6b

Counts

4 → 58

Calls

4 calls:

470.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2))))
442.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 5356 to 3963 computations (26% saved)

simplify138.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

534×	`cancel-sign-sub-inv_binary64_4136`
374×	`neg-mul-1_binary64_4166`
368×	`sub-neg_binary64_4163`
216×	`distribute-rgt-neg-in_binary64_4128`
210×	`distribute-neg-in_binary64_4131`
174×	`+-commutative_binary64_4100`
122×	`neg-sub0_binary64_4165` `*-commutative_binary64_4101`
117×	`times-frac_binary64_4176`
108×	`associate--l+_binary64_4107`
104×	`unswap-sqr_binary64_4138`
103×	`associate--r+_binary64_4106`
101×	`associate-r_binary64_4110`
100×	`associate-+l+_binary64_4103`
96×	`associate-+r+_binary64_4102`
87×	`unsub-neg_binary64_4164` `distribute-neg-frac_binary64_4134`
81×	`associate-/r*_binary64_4114`
78×	`associate-/l*_binary64_4115`
73×	`associate-l_binary64_4111`
48×	`exp-prod_binary64_4222`
47×	`distribute-rgt-in_binary64_4120`
46×	`distribute-lft-neg-out_binary64_4129` `distribute-lft-in_binary64_4119`
45×	`sqr-pow_binary64_4142`
33×	`distribute-lft-neg-in_binary64_4127`
31×	`exp-sum_binary64_4216`
28×	`associate-*r/_binary64_4112`
27×	`associate-*l/_binary64_4113`
25×	`div-sub_binary64_4175`
23×	`difference-of-squares_binary64_4139`
18×	`unpow3_binary64_4236`
17×	`cube-prod_binary64_4198`
16×	`exp-diff_binary64_4218` `distribute-rgt-neg-out_binary64_4130`
12×	`cube-unmult_binary64_4207`
11×	`distribute-rgt-out_binary64_4123`
10×	`distribute-lft-out_binary64_4121` `associate-/r/_binary64_4116`
9×	`cube-mult_binary64_4200` `rem-sqrt-square_binary64_4183` `associate-+r-_binary64_4104`
7×	`pow-plus_binary64_4233` `+-rgt-identity_binary64_4155`
6×	`associate-+l-_binary64_4105`
4×	`log-prod_binary64_4256` `unpow2_binary64_4235` `unpow1/2_binary64_4234` `unpow1_binary64_4228` `rem-square-sqrt_binary64_4182` `mul-1-neg_binary64_4162` `swap-sqr_binary64_4137`
3×	`div-exp_binary64_4221` `pow-sqr_binary64_4143`
2×	`rem-3cbrt-lft_binary64_4195` `sub0-neg_binary64_4157` `associate--l-_binary64_4108`
1×	`log-pow_binary64_4259` `prod-exp_binary64_4219` `1-exp_binary64_4214` `sqr-neg_binary64_4184` `cancel-sign-sub_binary64_4135` `distribute-neg-out_binary64_4132` `distribute-rgt1-in_binary64_4126` `distribute-rgt-out--_binary64_4124` `distribute-lft-out--_binary64_4122` `associate-/l/_binary64_4117`
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_4433` `erf-erfc_binary64_4432` `erf-odd_binary64_4431` `if-if-and-not_binary64_4430` `if-if-and_binary64_4429` `if-if-or-not_binary64_4428` `if-if-or_binary64_4427` `if-not_binary64_4426` `if-same_binary64_4425` `if-false_binary64_4424` `if-true_binary64_4423` `not-gte_binary64_4422` `not-lte_binary64_4421` `not-gt_binary64_4420` `not-lt_binary64_4419` `gte-same_binary64_4418` `lte-same_binary64_4417` `gt-same_binary64_4416` `lt-same_binary64_4415` `sinh---cosh_binary64_4362` `sinh-+-cosh_binary64_4361` `sinh-cosh_binary64_4360` `tanh-def-c_binary64_4359` `tanh-def-b_binary64_4358` `tanh-def-a_binary64_4357` `cosh-def_binary64_4356` `sinh-def_binary64_4355` `tan-neg_binary64_4302` `cos-neg_binary64_4301` `sin-neg_binary64_4300` `tan-0_binary64_4299` `cos-0_binary64_4298` `sin-0_binary64_4297` `hang-m-tan_binary64_4296` `hang-p-tan_binary64_4295` `hang-m0-tan_binary64_4294` `hang-p0-tan_binary64_4293` `hang-0m-tan_binary64_4292` `hang-0p-tan_binary64_4291` `tan-+PI/2_binary64_4290` `tan-+PI_binary64_4289` `tan-PI_binary64_4288` `tan-PI/3_binary64_4287` `tan-PI/4_binary64_4286` `tan-PI/6_binary64_4285` `cos-+PI/2_binary64_4284` `cos-+PI_binary64_4283` `cos-PI_binary64_4282` `cos-PI/2_binary64_4281` `cos-PI/3_binary64_4280` `cos-PI/4_binary64_4279` `cos-PI/6_binary64_4278` `sin-+PI/2_binary64_4277` `sin-+PI_binary64_4276` `sin-PI_binary64_4275` `sin-PI/2_binary64_4274` `sin-PI/3_binary64_4273` `sin-PI/4_binary64_4272` `sin-PI/6_binary64_4271` `sub-1-sin_binary64_4270` `sub-1-cos_binary64_4269` `-1-add-sin_binary64_4268` `-1-add-cos_binary64_4267` `1-sub-sin_binary64_4266` `1-sub-cos_binary64_4265` `cos-sin-sum_binary64_4264` `log-E_binary64_4260` `log-rec_binary64_4258` `log-div_binary64_4257` `pow-base-0_binary64_4254` `unpow1/3_binary64_4237` `exp-to-pow_binary64_4232` `pow-base-1_binary64_4230` `unpow0_binary64_4229` `unpow-1_binary64_4227` `exp-lft-cube_binary64_4226` `exp-lft-sqr_binary64_4225` `exp-cbrt_binary64_4224` `exp-sqrt_binary64_4223` `rec-exp_binary64_4220` `exp-neg_binary64_4217` `e-exp-1_binary64_4215` `exp-1-e_binary64_4213` `exp-0_binary64_4212` `rem-log-exp_binary64_4211` `rem-exp-log_binary64_4210` `cube-div_binary64_4199` `cube-neg_binary64_4197` `rem-3cbrt-rft_binary64_4196` `rem-cbrt-cube_binary64_4194` `rem-cube-cbrt_binary64_4193` `sqr-abs_binary64_4185` `/-rgt-identity_binary64_4161` `-rgt-identity_binary64_4160` `-lft-identity_binary64_4159` `remove-double-neg_binary64_4158` `--rgt-identity_binary64_4156` `+-lft-identity_binary64_4154` `mul0-rgt_binary64_4153` `mul0-lft_binary64_4152` `div0_binary64_4151` `*-inverses_binary64_4150` `+-inverses_binary64_4149` `lft-mult-inverse_binary64_4148` `rgt-mult-inverse_binary64_4147` `remove-double-div_binary64_4146` `difference-of-sqr--1_binary64_4141` `difference-of-sqr-1_binary64_4140` `distribute-frac-neg_binary64_4133` `distribute-lft1-in_binary64_4125` `count-2_binary64_4118` `associate--r-_binary64_4109`

Counts

130 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	3457
1	886	3359
2	3009	3350
3	4861	3350
4	5194	3350

prune160.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	81	11	92

Error

6.6b

Counts

92 → 11

Compiler

Compiled 3401 to 1667 computations (51% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 A C) 2)
0.0b	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))) B))))
0.8b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2))))
34.8b	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))

rewrite337.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

75×	`times-frac_binary64_4176`
59×	`add-sqr-sqrt_binary64_4192` `*-un-lft-identity_binary64_4170`
52×	`add-cube-cbrt_binary64_4205`
16×	`add-exp-log_binary64_4208`
13×	`associate-/r*_binary64_4114`
9×	`add-log-exp_binary64_4209` `add-cbrt-cube_binary64_4206` `cancel-sign-sub-inv_binary64_4136`
7×	`pow1_binary64_4231` `sqrt-prod_binary64_4186` `div-exp_binary64_4221`
6×	`sqrt-div_binary64_4187`
5×	`div-inv_binary64_4167` `unpow-prod-down_binary64_4249`
4×	`frac-sub_binary64_4179` `distribute-lft-out--_binary64_4122` `associate--l+_binary64_4107`
3×	`flip3-+_binary64_4173` `flip-+_binary64_4144` `diff-log_binary64_4262` `flip3--_binary64_4174` `flip--_binary64_4145` `difference-of-squares_binary64_4139` `cbrt-undiv_binary64_4204` `associate-/l*_binary64_4115` `pow-unpow_binary64_4247`
2×	`sub-neg_binary64_4163` `1-exp_binary64_4214` `rec-exp_binary64_4220`
1×	`pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `rem-sqrt-square_binary64_4183` `associate--l-_binary64_4108` `inv-pow_binary64_4255` `pow-flip_binary64_4244` `frac-2neg_binary64_4181` `clear-num_binary64_4169` `associate-/r/_binary64_4116` `pow-pow_binary64_4242` `pow-to-exp_binary64_4239` `pow-exp_binary64_4238` `unpow2_binary64_4235` `sqr-pow_binary64_4142`

Counts

4 → 142

Calls

4 calls:

19.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2))))
9.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
7.0ms	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))) B))))
5.0ms	(pow.f64 (-.f64 A C) 2)

Compiler

Compiled 5729 to 3042 computations (46.9% saved)

series1.4s (8%)

Error

6.6b

Counts

4 → 73

Calls

4 calls:

459.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
450.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2))))
277.0ms	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))) B))))
39.0ms	(pow.f64 (-.f64 A C) 2)

Compiler

Compiled 6055 to 4690 computations (22.5% saved)

simplify202.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

559×	`cancel-sign-sub-inv_binary64_4136`
399×	`sub-neg_binary64_4163`
190×	`+-commutative_binary64_4100`
165×	`*-commutative_binary64_4101`
136×	`neg-mul-1_binary64_4166`
135×	`neg-sub0_binary64_4165`
132×	`times-frac_binary64_4176`
126×	`associate-r_binary64_4110`
118×	`associate--l+_binary64_4107`
117×	`unswap-sqr_binary64_4138` `associate-/l*_binary64_4115`
110×	`associate-/r*_binary64_4114`
107×	`associate--r+_binary64_4106`
105×	`associate-+l+_binary64_4103` `associate-+r+_binary64_4102`
104×	`associate-/r/_binary64_4116`
93×	`unsub-neg_binary64_4164`
86×	`associate-l_binary64_4111`
83×	`associate-*l/_binary64_4113`
73×	`sqr-pow_binary64_4142`
64×	`associate-*r/_binary64_4112`
63×	`distribute-neg-in_binary64_4131`
56×	`associate-/l/_binary64_4117`
53×	`distribute-rgt-in_binary64_4120`
52×	`distribute-lft-in_binary64_4119`
48×	`distribute-rgt-neg-in_binary64_4128`
35×	`exp-prod_binary64_4222`
33×	`distribute-lft-neg-in_binary64_4127`
23×	`difference-of-squares_binary64_4139`
22×	`*-rgt-identity_binary64_4160`
20×	`cube-prod_binary64_4198`
17×	`div-sub_binary64_4175`
16×	`log-prod_binary64_4256`
15×	`distribute-lft-neg-out_binary64_4129`
12×	`associate-+r-_binary64_4104`
11×	`exp-sum_binary64_4216` `cube-unmult_binary64_4207` `distribute-rgt-out_binary64_4123`
10×	`log-div_binary64_4257` `unpow3_binary64_4236` `swap-sqr_binary64_4137` `distribute-lft-out_binary64_4121`
9×	`unpow2_binary64_4235` `unpow1/2_binary64_4234` `unpow1_binary64_4228` `cube-mult_binary64_4200` `/-rgt-identity_binary64_4161` `pow-sqr_binary64_4143`
8×	`+-rgt-identity_binary64_4155`
7×	`exp-diff_binary64_4218` `rem-sqrt-square_binary64_4183` `mul-1-neg_binary64_4162` `distribute-neg-frac_binary64_4134`
6×	`pow-plus_binary64_4233` `associate-+l-_binary64_4105`
5×	`log-pow_binary64_4259` `*-lft-identity_binary64_4159`
4×	`log-rec_binary64_4258` `rem-square-sqrt_binary64_4182` `remove-double-div_binary64_4146`
3×	`div-exp_binary64_4221` `cube-div_binary64_4199` `sub0-neg_binary64_4157` `distribute-rgt-neg-out_binary64_4130`
2×	`rem-3cbrt-lft_binary64_4195` `+-lft-identity_binary64_4154` `associate--r-_binary64_4109` `associate--l-_binary64_4108`
1×	`prod-exp_binary64_4219` `1-exp_binary64_4214` `rem-3cbrt-rft_binary64_4196` `distribute-neg-out_binary64_4132` `distribute-rgt1-in_binary64_4126` `distribute-rgt-out--_binary64_4124` `distribute-lft-out--_binary64_4122`
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_4433` `erf-erfc_binary64_4432` `erf-odd_binary64_4431` `if-if-and-not_binary64_4430` `if-if-and_binary64_4429` `if-if-or-not_binary64_4428` `if-if-or_binary64_4427` `if-not_binary64_4426` `if-same_binary64_4425` `if-false_binary64_4424` `if-true_binary64_4423` `not-gte_binary64_4422` `not-lte_binary64_4421` `not-gt_binary64_4420` `not-lt_binary64_4419` `gte-same_binary64_4418` `lte-same_binary64_4417` `gt-same_binary64_4416` `lt-same_binary64_4415` `sinh---cosh_binary64_4362` `sinh-+-cosh_binary64_4361` `sinh-cosh_binary64_4360` `tanh-def-c_binary64_4359` `tanh-def-b_binary64_4358` `tanh-def-a_binary64_4357` `cosh-def_binary64_4356` `sinh-def_binary64_4355` `tan-neg_binary64_4302` `cos-neg_binary64_4301` `sin-neg_binary64_4300` `tan-0_binary64_4299` `cos-0_binary64_4298` `sin-0_binary64_4297` `hang-m-tan_binary64_4296` `hang-p-tan_binary64_4295` `hang-m0-tan_binary64_4294` `hang-p0-tan_binary64_4293` `hang-0m-tan_binary64_4292` `hang-0p-tan_binary64_4291` `tan-+PI/2_binary64_4290` `tan-+PI_binary64_4289` `tan-PI_binary64_4288` `tan-PI/3_binary64_4287` `tan-PI/4_binary64_4286` `tan-PI/6_binary64_4285` `cos-+PI/2_binary64_4284` `cos-+PI_binary64_4283` `cos-PI_binary64_4282` `cos-PI/2_binary64_4281` `cos-PI/3_binary64_4280` `cos-PI/4_binary64_4279` `cos-PI/6_binary64_4278` `sin-+PI/2_binary64_4277` `sin-+PI_binary64_4276` `sin-PI_binary64_4275` `sin-PI/2_binary64_4274` `sin-PI/3_binary64_4273` `sin-PI/4_binary64_4272` `sin-PI/6_binary64_4271` `sub-1-sin_binary64_4270` `sub-1-cos_binary64_4269` `-1-add-sin_binary64_4268` `-1-add-cos_binary64_4267` `1-sub-sin_binary64_4266` `1-sub-cos_binary64_4265` `cos-sin-sum_binary64_4264` `log-E_binary64_4260` `pow-base-0_binary64_4254` `unpow1/3_binary64_4237` `exp-to-pow_binary64_4232` `pow-base-1_binary64_4230` `unpow0_binary64_4229` `unpow-1_binary64_4227` `exp-lft-cube_binary64_4226` `exp-lft-sqr_binary64_4225` `exp-cbrt_binary64_4224` `exp-sqrt_binary64_4223` `rec-exp_binary64_4220` `exp-neg_binary64_4217` `e-exp-1_binary64_4215` `exp-1-e_binary64_4213` `exp-0_binary64_4212` `rem-log-exp_binary64_4211` `rem-exp-log_binary64_4210` `cube-neg_binary64_4197` `rem-cbrt-cube_binary64_4194` `rem-cube-cbrt_binary64_4193` `sqr-abs_binary64_4185` `sqr-neg_binary64_4184` `remove-double-neg_binary64_4158` `--rgt-identity_binary64_4156` `mul0-rgt_binary64_4153` `mul0-lft_binary64_4152` `div0_binary64_4151` `*-inverses_binary64_4150` `+-inverses_binary64_4149` `lft-mult-inverse_binary64_4148` `rgt-mult-inverse_binary64_4147` `difference-of-sqr--1_binary64_4141` `difference-of-sqr-1_binary64_4140` `cancel-sign-sub_binary64_4135` `distribute-frac-neg_binary64_4133` `distribute-lft1-in_binary64_4125` `count-2_binary64_4118`

Counts

215 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	463	8076
1	1185	7645
2	3843	7615
3	5227	7615

prune289.0ms (1.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	162	11	173

Error

6.6b

Counts

173 → 11

Compiler

Compiled 5789 to 2867 computations (50.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2))))
34.8b	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
34.8b	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
34.8b	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))

rewrite302.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

17×	`add-sqr-sqrt_binary64_4192`
15×	`*-un-lft-identity_binary64_4170`
13×	`sqrt-prod_binary64_4186`
10×	`add-cube-cbrt_binary64_4205` `sqrt-div_binary64_4187`
9×	`add-log-exp_binary64_4209` `cancel-sign-sub-inv_binary64_4136`
7×	`pow1_binary64_4231`
5×	`flip3-+_binary64_4173` `flip-+_binary64_4144`
4×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206` `frac-sub_binary64_4179` `associate--l+_binary64_4107`
3×	`pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `rem-sqrt-square_binary64_4183` `diff-log_binary64_4262` `flip3--_binary64_4174` `flip--_binary64_4145` `distribute-lft-out--_binary64_4122`
2×	`sub-neg_binary64_4163` `difference-of-squares_binary64_4139`
1×	`associate--l-_binary64_4108`

Counts

4 → 76

Calls

4 calls:

19.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2))))
9.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
9.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
9.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))

Compiler

Compiled 5667 to 2762 computations (51.3% saved)

series2.1s (12.4%)

Error

6.6b

Counts

4 → 111

Calls

4 calls:

474.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2))))
428.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
427.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))
415.0ms	(sqrt.f64 (+.f64 (*.f64 B B) (pow.f64 (-.f64 A C) 2)))

Compiler

Compiled 17758 to 11044 computations (37.8% saved)

simplify216.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

399×	`cancel-sign-sub-inv_binary64_4136`
366×	`distribute-rgt-in_binary64_4120`
323×	`sub-neg_binary64_4163`
198×	`distribute-neg-in_binary64_4131`
169×	`distribute-rgt-neg-in_binary64_4128`
160×	`+-commutative_binary64_4100`
142×	`distribute-lft-neg-in_binary64_4127`
117×	`times-frac_binary64_4176`
110×	`neg-mul-1_binary64_4166` `neg-sub0_binary64_4165`
105×	`*-commutative_binary64_4101`
96×	`unswap-sqr_binary64_4138`
92×	`associate--l+_binary64_4107` `associate-+r+_binary64_4102`
91×	`associate-+l+_binary64_4103`
87×	`distribute-neg-frac_binary64_4134` `associate--r+_binary64_4106`
83×	`associate-r_binary64_4110`
78×	`associate-/l*_binary64_4115`
76×	`unsub-neg_binary64_4164`
75×	`associate-/r*_binary64_4114`
61×	`exp-prod_binary64_4222`
52×	`associate-l_binary64_4111`
44×	`distribute-rgt-out_binary64_4123`
40×	`distribute-lft-neg-out_binary64_4129`
39×	`distribute-lft-out_binary64_4121`
38×	`sqr-pow_binary64_4142` `distribute-lft-in_binary64_4119`
35×	`exp-sum_binary64_4216`
28×	`associate-*r/_binary64_4112`
27×	`associate-*l/_binary64_4113`
25×	`unpow3_binary64_4236`
24×	`div-sub_binary64_4175`
23×	`difference-of-squares_binary64_4139`
17×	`cube-prod_binary64_4198`
16×	`exp-diff_binary64_4218` `distribute-rgt-neg-out_binary64_4130`
11×	`pow-plus_binary64_4233` `cube-unmult_binary64_4207`
10×	`associate-/r/_binary64_4116`
9×	`associate-+r-_binary64_4104`
8×	`distribute-rgt-out--_binary64_4124`
7×	`cube-mult_binary64_4200` `rem-sqrt-square_binary64_4183` `+-rgt-identity_binary64_4155`
6×	`distribute-rgt1-in_binary64_4126` `associate-+l-_binary64_4105`
5×	`log-prod_binary64_4256`
4×	`unpow2_binary64_4235` `unpow1/2_binary64_4234` `unpow1_binary64_4228` `sqr-neg_binary64_4184` `mul-1-neg_binary64_4162` `swap-sqr_binary64_4137` `distribute-lft-out--_binary64_4122`
3×	`div-exp_binary64_4221` `rem-square-sqrt_binary64_4182` `pow-sqr_binary64_4143`
2×	`unpow-1_binary64_4227` `rem-3cbrt-lft_binary64_4195` `sub0-neg_binary64_4157` `associate--l-_binary64_4108`
1×	`log-pow_binary64_4259` `prod-exp_binary64_4219` `1-exp_binary64_4214` `cancel-sign-sub_binary64_4135` `distribute-neg-out_binary64_4132` `associate-/l/_binary64_4117`
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_4433` `erf-erfc_binary64_4432` `erf-odd_binary64_4431` `if-if-and-not_binary64_4430` `if-if-and_binary64_4429` `if-if-or-not_binary64_4428` `if-if-or_binary64_4427` `if-not_binary64_4426` `if-same_binary64_4425` `if-false_binary64_4424` `if-true_binary64_4423` `not-gte_binary64_4422` `not-lte_binary64_4421` `not-gt_binary64_4420` `not-lt_binary64_4419` `gte-same_binary64_4418` `lte-same_binary64_4417` `gt-same_binary64_4416` `lt-same_binary64_4415` `sinh---cosh_binary64_4362` `sinh-+-cosh_binary64_4361` `sinh-cosh_binary64_4360` `tanh-def-c_binary64_4359` `tanh-def-b_binary64_4358` `tanh-def-a_binary64_4357` `cosh-def_binary64_4356` `sinh-def_binary64_4355` `tan-neg_binary64_4302` `cos-neg_binary64_4301` `sin-neg_binary64_4300` `tan-0_binary64_4299` `cos-0_binary64_4298` `sin-0_binary64_4297` `hang-m-tan_binary64_4296` `hang-p-tan_binary64_4295` `hang-m0-tan_binary64_4294` `hang-p0-tan_binary64_4293` `hang-0m-tan_binary64_4292` `hang-0p-tan_binary64_4291` `tan-+PI/2_binary64_4290` `tan-+PI_binary64_4289` `tan-PI_binary64_4288` `tan-PI/3_binary64_4287` `tan-PI/4_binary64_4286` `tan-PI/6_binary64_4285` `cos-+PI/2_binary64_4284` `cos-+PI_binary64_4283` `cos-PI_binary64_4282` `cos-PI/2_binary64_4281` `cos-PI/3_binary64_4280` `cos-PI/4_binary64_4279` `cos-PI/6_binary64_4278` `sin-+PI/2_binary64_4277` `sin-+PI_binary64_4276` `sin-PI_binary64_4275` `sin-PI/2_binary64_4274` `sin-PI/3_binary64_4273` `sin-PI/4_binary64_4272` `sin-PI/6_binary64_4271` `sub-1-sin_binary64_4270` `sub-1-cos_binary64_4269` `-1-add-sin_binary64_4268` `-1-add-cos_binary64_4267` `1-sub-sin_binary64_4266` `1-sub-cos_binary64_4265` `cos-sin-sum_binary64_4264` `log-E_binary64_4260` `log-rec_binary64_4258` `log-div_binary64_4257` `pow-base-0_binary64_4254` `unpow1/3_binary64_4237` `exp-to-pow_binary64_4232` `pow-base-1_binary64_4230` `unpow0_binary64_4229` `exp-lft-cube_binary64_4226` `exp-lft-sqr_binary64_4225` `exp-cbrt_binary64_4224` `exp-sqrt_binary64_4223` `rec-exp_binary64_4220` `exp-neg_binary64_4217` `e-exp-1_binary64_4215` `exp-1-e_binary64_4213` `exp-0_binary64_4212` `rem-log-exp_binary64_4211` `rem-exp-log_binary64_4210` `cube-div_binary64_4199` `cube-neg_binary64_4197` `rem-3cbrt-rft_binary64_4196` `rem-cbrt-cube_binary64_4194` `rem-cube-cbrt_binary64_4193` `sqr-abs_binary64_4185` `/-rgt-identity_binary64_4161` `-rgt-identity_binary64_4160` `-lft-identity_binary64_4159` `remove-double-neg_binary64_4158` `--rgt-identity_binary64_4156` `+-lft-identity_binary64_4154` `mul0-rgt_binary64_4153` `mul0-lft_binary64_4152` `div0_binary64_4151` `*-inverses_binary64_4150` `+-inverses_binary64_4149` `lft-mult-inverse_binary64_4148` `rgt-mult-inverse_binary64_4147` `remove-double-div_binary64_4146` `difference-of-sqr--1_binary64_4141` `difference-of-sqr-1_binary64_4140` `distribute-frac-neg_binary64_4133` `distribute-lft1-in_binary64_4125` `count-2_binary64_4118` `associate--r-_binary64_4109`

Counts

187 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	282	5015
1	794	4877
2	2696	4646
3	4872	4643
4	4979	4643
5	4978	4643

prune421.0ms (2.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	125	11	136

Error

6.6b

Counts

136 → 11

Compiler

Compiled 8731 to 4199 computations (51.9% saved)

regimes2.5s (14.8%)

Accuracy

Total 11.7b remaining (65.1%)

Threshold costs 0b (0%)

Compiler

Compiled 24423 to 18181 computations (25.6% saved)

bsearch11.0ms (0.1%)

Compiler: Compiled 18 to 15 computations (16.7% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64_4100`
9×	`sub-neg_binary64_4163` `*-commutative_binary64_4101`
4×	`neg-mul-1_binary64_4166` `neg-sub0_binary64_4165`
1×	`1-exp_binary64_4214`
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_4430` `if-if-and_binary64_4429` `if-if-or-not_binary64_4428` `if-if-or_binary64_4427` `if-not_binary64_4426` `if-same_binary64_4425` `if-false_binary64_4424` `if-true_binary64_4423` `tan-0_binary64_4299` `cos-0_binary64_4298` `sin-0_binary64_4297` `unpow1_binary64_4228` `e-exp-1_binary64_4215` `exp-1-e_binary64_4213` `exp-0_binary64_4212` `sqr-abs_binary64_4185` `sqr-neg_binary64_4184` `unsub-neg_binary64_4164` `mul-1-neg_binary64_4162` `/-rgt-identity_binary64_4161` `-rgt-identity_binary64_4160` `-lft-identity_binary64_4159` `remove-double-neg_binary64_4158` `sub0-neg_binary64_4157` `--rgt-identity_binary64_4156` `+-rgt-identity_binary64_4155` `+-lft-identity_binary64_4154` `cancel-sign-sub-inv_binary64_4136` `cancel-sign-sub_binary64_4135` `distribute-neg-frac_binary64_4134` `distribute-frac-neg_binary64_4133` `distribute-neg-out_binary64_4132` `distribute-neg-in_binary64_4131` `distribute-rgt-neg-out_binary64_4130` `distribute-lft-neg-out_binary64_4129` `distribute-rgt-neg-in_binary64_4128` `distribute-lft-neg-in_binary64_4127`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	124
1	59	124
2	73	124
3	81	124
4	85	124
5	84	124

end0.0ms (0%)

sample5.0s (29.6%)

Algorithm

1×

intervals

Results

670.0ms	855×	body	4096	valid
531.0ms	5457×	body	128	valid
493.0ms	851×	body	2048	valid
198.0ms	465×	body	1024	valid
82.0ms	242×	body	512	valid
26.0ms	130×	body	256	valid

Compiler

Compiled 3569 to 2654 computations (25.6% saved)

Details

analyze449.0ms (2.6%)

sample76.0ms (0.4%)

simplify74.0ms (0.4%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite216.0ms (1.3%)

series1.4s (8.3%)

simplify178.0ms (1%)

prune240.0ms (1.4%)

localize18.0ms (0.1%)

rewrite171.0ms (1%)

series1.0s (6%)

simplify138.0ms (0.8%)

prune160.0ms (0.9%)

localize18.0ms (0.1%)

rewrite337.0ms (2%)

series1.4s (8%)

simplify202.0ms (1.2%)

prune289.0ms (1.7%)

localize23.0ms (0.1%)

rewrite302.0ms (1.8%)

series2.1s (12.4%)

simplify216.0ms (1.3%)

prune421.0ms (2.5%)

regimes2.5s (14.8%)

bsearch11.0ms (0.1%)

simplify7.0ms (0%)

end0.0ms (0%)

sample5.0s (29.6%)

Profiling