Details

analyze475.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample43.0ms (0%)

Algorithm

1×

intervals

Results

9.0ms	176×	body	128	valid
8.0ms	33×	body	2048	valid
5.0ms	24×	body	1024	valid
2.0ms	11×	body	512	valid
2.0ms	5×	body	4096	valid
1.0ms	25×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 38 to 38 computations (0% saved)

simplify406.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (314.0ms)

Iter	Nodes	Cost
0	1834	27
1	1834	27

prune4.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Kept	Total
New	4	4
Fresh	4	4
Picked	0	0
Done	0	0
Total	8	8

Error

27.3b

Counts

8 → 5

Compiler

Compiled 19 to 16 computations (15.8% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_441`
15×	`*-un-lft-identity_binary64_419`
14×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`pow1_binary64_480`
9×	`add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `difference-of-squares_binary64_388` `add-log-exp_binary64_458` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`
4×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`pow-prod-down_binary64_490` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `associate-l_binary64_360` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `pow1/2_binary64_499` `div-inv_binary64_416` `associate-r_binary64_359` `-commutative_binary64_350` `frac-2neg_binary64_430` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `associate-/r_binary64_363` `rem-sqrt-square_binary64_432` `div-sub_binary64_424`

Counts

4 → 80

Calls

8 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
6.0ms	(.f64 4 (.f64 a c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series590.0ms (0.4%)

Counts

4 → 60

Calls

4 calls:

222.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
163.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
156.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
50.0ms	(.f64 4 (.f64 a c))

Compiler

Compiled 1914 to 1589 computations (17% saved)

simplify52.0ms (0%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5123	2772

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
1.5b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
1.5b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_419`
14×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`pow1_binary64_480`
9×	`add-sqr-sqrt_binary64_441`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
6×	`distribute-lft-out_binary64_370`
5×	`times-frac_binary64_425` `associate-/l*_binary64_364`
4×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`pow-prod-down_binary64_490` `distribute-rgt-neg-in_binary64_377` `associate-l_binary64_360` `sqrt-prod_binary64_435`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `associate-+l-_binary64_354` `sum-log_binary64_510` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366` `neg-sub0_binary64_414`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `associate-r_binary64_359` `flip3--_binary64_423` `-commutative_binary64_350` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `flip--_binary64_394` `associate-/r_binary64_363` `rem-sqrt-square_binary64_432` `neg-log_binary64_512` `+-commutative_binary64_349` `div-sub_binary64_424`

Counts

4 → 76

Calls

8 calls:

13.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
9.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(.f64 4 (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series587.0ms (0.4%)

Counts

4 → 60

Calls

4 calls:

217.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
161.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
155.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
54.0ms	(.f64 4 (.f64 a c))

Compiler

Compiled 1954 to 1629 computations (16.6% saved)

simplify53.0ms (0%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5347	2605

prune1.6s (1.1%)

Pruning

104 alts after pruning (102 fresh and 2 done)

	Pruned	Kept	Total
New	177	99	276
Fresh	0	3	3
Picked	0	0	0
Done	0	2	2
Total	177	104	281

Error

6.0b

Counts

281 → 104

Compiler

Compiled 6095 to 3764 computations (38.2% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

3.3b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
0.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.3b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
10.4b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite65.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
34×	`times-frac_binary64_425` `add-sqr-sqrt_binary64_441`
33×	`*-un-lft-identity_binary64_419`
17×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
14×	`associate-/l*_binary64_364`
13×	`add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`sqrt-prod_binary64_435`
10×	`difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371`
8×	`add-log-exp_binary64_458` `associate-/r*_binary64_363`
6×	`associate-/r/_binary64_365` `cancel-sign-sub-inv_binary64_385`
5×	`distribute-rgt-neg-in_binary64_377` `flip3--_binary64_423` `flip--_binary64_394` `pow1_binary64_480`
4×	`div-inv_binary64_416`
2×	`sqrt-div_binary64_436` `clear-num_binary64_418` `frac-2neg_binary64_430` `diff-log_binary64_511`
1×	`sub-neg_binary64_412` `pow1/2_binary64_499` `associate--l-_binary64_357` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `neg-log_binary64_512` `associate-/l/_binary64_366` `neg-sub0_binary64_414`

Counts

4 → 125

Calls

8 calls:

21.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
15.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series915.0ms (0.6%)

Counts

4 → 74

Calls

4 calls:

315.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
271.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
168.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
161.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2965 to 2311 computations (22.1% saved)

simplify121.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4933	5526
1	4933	5526

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

12.8b	(sqrt.f64 (.f64 c (.f64 a -4)))
0.5b	(.f64 c (.f64 a -4))
0.2b	(/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a)
0.0b	(-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))
0.0b	(-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))
0.2b	(/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a)
0.5b	(.f64 c (.f64 a -4))
12.8b	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_441`
31×	`*-un-lft-identity_binary64_419` `times-frac_binary64_425`
23×	`add-cube-cbrt_binary64_454`
15×	`pow1_binary64_480`
13×	`cancel-sign-sub-inv_binary64_385`
11×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`pow-prod-down_binary64_490` `add-log-exp_binary64_458`
5×	`sqrt-prod_binary64_435`
4×	`difference-of-squares_binary64_388` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `associate-/l*_binary64_364`
3×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363`
1×	`clear-num_binary64_418` `distribute-rgt-out--_binary64_373` `sub-neg_binary64_412` `pow1/2_binary64_499` `associate-r_binary64_359` `flip3--_binary64_423` `*-commutative_binary64_350` `frac-2neg_binary64_430` `diff-log_binary64_511` `flip--_binary64_394` `sub-div_binary64_426` `div-exp_binary64_470` `frac-sub_binary64_428` `cbrt-undiv_binary64_453`

Counts

4 → 96

Calls

8 calls:

19.0ms	(-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))
6.0ms	(/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a)
5.0ms	(.f64 c (.f64 a -4))
4.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
0.0ms	(-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))

series280.0ms (0.2%)

Counts

4 → 30

Calls

4 calls:

140.0ms	(-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))
52.0ms	(.f64 c (.f64 a -4))
46.0ms	(/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a)
41.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

Compiler

Compiled 838 to 740 computations (11.7% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4900	1799
1	4900	1799

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

5.6b	(sqrt.f64 (-.f64 (.f64 b b) (exp.f64 (log.f64 (.f64 4 (*.f64 a c))))))
1.3b	(exp.f64 (log.f64 (.f64 4 (.f64 a c))))
1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (exp.f64 (log.f64 (.f64 4 (*.f64 a c)))))))
0.0b	(.f64 4 (.f64 a c))
1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (exp.f64 (log.f64 (.f64 4 (*.f64 a c)))))))
1.3b	(exp.f64 (log.f64 (.f64 4 (.f64 a c))))
5.6b	(sqrt.f64 (-.f64 (.f64 b b) (exp.f64 (log.f64 (.f64 4 (*.f64 a c))))))
6.5b	(log.f64 (.f64 4 (.f64 a c)))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`pow1_binary64_480`
10×	`*-un-lft-identity_binary64_419` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458` `add-sqr-sqrt_binary64_441`
6×	`pow-prod-down_binary64_490` `add-cube-cbrt_binary64_454` `exp-prod_binary64_471` `log-pow_binary64_508`
4×	`add-cbrt-cube_binary64_455` `sqrt-prod_binary64_435`
3×	`rem-log-exp_binary64_460` `prod-exp_binary64_468`
2×	`sqrt-div_binary64_436` `log-prod_binary64_505` `sum-log_binary64_510` `distribute-lft-out_binary64_370`
1×	`flip3-+_binary64_422` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `associate-+l-_binary64_354` `distribute-rgt-neg-in_binary64_377` `flip3--_binary64_423` `flip-+_binary64_393` `exp-sum_binary64_465` `sqrt-pow1_binary64_437` `flip--_binary64_394` `rem-exp-log_binary64_459` `rem-sqrt-square_binary64_432` `neg-log_binary64_512` `+-commutative_binary64_349` `neg-sub0_binary64_414`

Counts

4 → 60

Calls

8 calls:

14.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (exp.f64 (log.f64 (.f64 4 (*.f64 a c)))))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (exp.f64 (log.f64 (.f64 4 (*.f64 a c))))))
5.0ms	(exp.f64 (log.f64 (.f64 4 (.f64 a c))))
5.0ms	(log.f64 (.f64 4 (.f64 a c)))
0.0ms	(.f64 4 (.f64 a c))

series902.0ms (0.6%)

Counts

4 → 33

Calls

4 calls:

334.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (exp.f64 (log.f64 (.f64 4 (*.f64 a c)))))))
285.0ms	(sqrt.f64 (-.f64 (.f64 b b) (exp.f64 (log.f64 (.f64 4 (*.f64 a c))))))
152.0ms	(exp.f64 (log.f64 (.f64 4 (.f64 a c))))
131.0ms	(log.f64 (.f64 4 (.f64 a c)))

Compiler

Compiled 1334 to 1173 computations (12.1% saved)

simplify62.0ms (0%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4937	1341
1	4937	1341

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
0.1b	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_441`
12×	`*-un-lft-identity_binary64_419`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `sqrt-prod_binary64_435`
6×	`cancel-sign-sub-inv_binary64_385` `pow1_binary64_480`
4×	`sqrt-div_binary64_436` `difference-of-squares_binary64_388` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394`
2×	`sub-neg_binary64_412` `pow1/2_binary64_499` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 64

Calls

8 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series660.0ms (0.5%)

Counts

4 → 74

Calls

4 calls:

173.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
166.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
161.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
160.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4044 to 3024 computations (25.2% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4965	2744
1	4965	2744

prune9.4s (6.5%)

Pruning

297 alts after pruning (291 fresh and 6 done)

	Pruned	Kept	Total
New	355	201	556
Fresh	7	90	97
Picked	0	0	0
Done	1	6	7
Total	363	297	660

Error

3.9b

Counts

660 → 297

Compiler

Compiled 18158 to 11268 computations (37.9% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.1b	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.0b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
0.1b	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite55.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_441`
40×	`*-un-lft-identity_binary64_419`
21×	`times-frac_binary64_425`
20×	`add-cube-cbrt_binary64_454` `add-exp-log_binary64_457`
15×	`add-cbrt-cube_binary64_455`
11×	`sqrt-prod_binary64_435`
10×	`difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `pow1_binary64_480`
9×	`prod-exp_binary64_468`
8×	`add-log-exp_binary64_458`
7×	`associate-/r*_binary64_363`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`distribute-rgt-neg-in_binary64_377` `cbrt-unprod_binary64_452`
3×	`pow-prod-down_binary64_490` `flip3--_binary64_423` `associate-l_binary64_360` `flip--_binary64_394` `div-exp_binary64_470` `associate-/l*_binary64_364`
2×	`sqrt-div_binary64_436` `1-exp_binary64_463` `associate-*r/_binary64_361` `associate-/r/_binary64_365` `diff-log_binary64_511` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `pow1/2_binary64_499` `div-inv_binary64_416` `associate-r_binary64_359` `*-commutative_binary64_350` `frac-2neg_binary64_430` `associate--l-_binary64_357` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `neg-log_binary64_512` `neg-sub0_binary64_414`

Counts

4 → 106

Calls

8 calls:

15.0ms	(.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
15.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series862.0ms (0.6%)

Counts

4 → 74

Calls

4 calls:

281.0ms	(.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
264.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
165.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
152.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2637 to 2178 computations (17.4% saved)

simplify90.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5097	4527

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
1.5b	(-.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) b)
0.1b	(/.f64 (-.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) b) (.f64 a 2))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (-.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) b) (.f64 a 2))
1.5b	(-.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) b)
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_441`
15×	`*-un-lft-identity_binary64_419`
14×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`pow1_binary64_480`
9×	`add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458`
5×	`times-frac_binary64_425` `associate-/l*_binary64_364`
4×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`pow-prod-down_binary64_490` `difference-of-squares_binary64_388` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `associate-l_binary64_360` `flip--_binary64_394` `sqrt-prod_binary64_435` `cancel-sign-sub-inv_binary64_385`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `pow1/2_binary64_499` `div-inv_binary64_416` `associate-r_binary64_359` `-commutative_binary64_350` `frac-2neg_binary64_430` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `associate-/r_binary64_363` `rem-sqrt-square_binary64_432` `div-sub_binary64_424`

Counts

4 → 77

Calls

8 calls:

10.0ms	(/.f64 (-.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) b) (.f64 a 2))
5.0ms	(.f64 4 (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) b)
0.0ms	(.f64 4 (.f64 a c))

series455.0ms (0.3%)

Counts

4 → 46

Calls

4 calls:

211.0ms	(/.f64 (-.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) b) (.f64 a 2))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
78.0ms	(-.f64 (fabs.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) b)
52.0ms	(.f64 4 (.f64 a c))

Compiler

Compiled 1422 to 1222 computations (14.1% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5292	2352

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) a)
0.0b	(sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) a)))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) a)
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.8b	(log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) a))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite49.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64_441`
45×	`*-un-lft-identity_binary64_419`
36×	`times-frac_binary64_425`
29×	`add-cube-cbrt_binary64_454`
25×	`log-pow_binary64_508`
24×	`sqrt-pow1_binary64_437`
22×	`exp-prod_binary64_471`
16×	`difference-of-squares_binary64_388`
14×	`sqrt-prod_binary64_435`
8×	`distribute-lft-out--_binary64_371`
7×	`add-exp-log_binary64_457` `pow1_binary64_480`
6×	`add-log-exp_binary64_458` `log-prod_binary64_505` `add-cbrt-cube_binary64_455` `associate-/l*_binary64_364`
3×	`sqrt-div_binary64_436` `flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385` `associate-/r*_binary64_363`
2×	`pow1/2_binary64_499` `div-inv_binary64_416` `associate-/l/_binary64_366` `div-sub_binary64_424`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `exp-diff_binary64_467` `rem-log-exp_binary64_460` `frac-2neg_binary64_430` `diff-log_binary64_511` `rem-sqrt-square_binary64_432` `log-div_binary64_506` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 114

Calls

8 calls:

12.0ms	(log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) a))))
12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series642.0ms (0.4%)

Counts

4 → 44

Calls

4 calls:

356.0ms	(log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) a))))
128.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) a)
95.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 1484 to 1283 computations (13.5% saved)

simplify125.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4935	3770
1	4935	3770

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 a c) -4)
0.0b	(+.f64 b (+.f64 (sqrt.f64 (.f64 (.f64 a c) -4)) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 (.f64 a c) -4))))))
0.0b	(.f64 4 (.f64 a c))
0.0b	(+.f64 (sqrt.f64 (.f64 (.f64 a c) -4)) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 (.f64 a c) -4)))))
8.7b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 (.f64 a c) -4)) 3))) (+.f64 b (+.f64 (sqrt.f64 (.f64 (.f64 a c) -4)) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 (*.f64 a c) -4))))))))
12.8b	(sqrt.f64 (.f64 (.f64 a c) -4))
12.8b	(sqrt.f64 (.f64 (.f64 a c) -4))
12.8b	(sqrt.f64 (.f64 (.f64 a c) -4))

rewrite52.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64_480`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`pow-prod-down_binary64_490` `sqrt-pow1_binary64_437`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`add-log-exp_binary64_458` `associate-/r/_binary64_365`
3×	`times-frac_binary64_425` `pow1/2_binary64_499` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sqrt-prod_binary64_435` `associate-/r*_binary64_363` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`associate-*r/_binary64_361` `frac-sub_binary64_428`
1×	`flip3-+_binary64_422` `clear-num_binary64_418` `div-inv_binary64_416` `flip3--_binary64_423` `frac-2neg_binary64_430` `flip-+_binary64_393` `flip--_binary64_394` `associate-/l*_binary64_364`

Counts

4 → 63

Calls

8 calls:

27.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 (.f64 a c) -4)) 3))) (+.f64 b (+.f64 (sqrt.f64 (.f64 (.f64 a c) -4)) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 (*.f64 a c) -4))))))))
4.0ms	(sqrt.f64 (.f64 (.f64 a c) -4))
4.0ms	(sqrt.f64 (.f64 (.f64 a c) -4))
4.0ms	(sqrt.f64 (.f64 (.f64 a c) -4))
0.0ms	(+.f64 (sqrt.f64 (.f64 (.f64 a c) -4)) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 (.f64 a c) -4)))))

series766.0ms (0.5%)

Counts

4 → 30

Calls

4 calls:

623.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 (.f64 a c) -4)) 3))) (+.f64 b (+.f64 (sqrt.f64 (.f64 (.f64 a c) -4)) (.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 (*.f64 a c) -4))))))))
48.0ms	(sqrt.f64 (.f64 (.f64 a c) -4))
47.0ms	(sqrt.f64 (.f64 (.f64 a c) -4))
47.0ms	(sqrt.f64 (.f64 (.f64 a c) -4))

Compiler

Compiled 2768 to 2069 computations (25.3% saved)

simplify58.0ms (0%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5182	3044

prune16.3s (11.2%)

Pruning

475 alts after pruning (465 fresh and 10 done)

	Pruned	Kept	Total
New	353	201	554
Fresh	22	264	286
Picked	0	0	0
Done	1	10	11
Total	376	475	851

Error

3.9b

Counts

851 → 475

Compiler

Compiled 25522 to 16614 computations (34.9% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.0b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.6b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
9.4b	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite52.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_435`
59×	`add-sqr-sqrt_binary64_441`
34×	`sqrt-pow1_binary64_437`
29×	`pow1_binary64_480`
28×	`sqrt-div_binary64_436`
18×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `pow1/2_binary64_499`
15×	`swap-sqr_binary64_386`
10×	`rem-sqrt-square_binary64_432`
9×	`associate-r_binary64_359` `unswap-sqr_binary64_387` `flip3--_binary64_423` `associate-l_binary64_360` `flip--_binary64_394` `pow-prod-up_binary64_489`
8×	`add-log-exp_binary64_458`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`pow-prod-down_binary64_490` `pow-sqr_binary64_392`
4×	`sqr-abs_binary64_434` `frac-times_binary64_429`
2×	`associate-l/_binary64_362` `associate-r/_binary64_361` `diff-log_binary64_511`
1×	`sub-neg_binary64_412` `difference-of-squares_binary64_388` `sqrt-unprod_binary64_439` `rem-square-sqrt_binary64_431` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-plus_binary64_482` `*-commutative_binary64_350` `associate--l-_binary64_357` `cancel-sign-sub-inv_binary64_385` `neg-log_binary64_512` `pow2_binary64_500` `neg-sub0_binary64_414`

Counts

4 → 132

Calls

8 calls:

19.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
5.0ms	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series672.0ms (0.5%)

Counts

4 → 88

Calls

4 calls:

170.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
169.0ms	(-.f64 (neg.f64 b) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
168.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
165.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3635 to 2914 computations (19.8% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5520	4852

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 (/.f64 b a) -1/2)
0.0b	(*.f64 (/.f64 b a) -1/2)

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_441`
13×	`associate-l_binary64_360`
10×	`times-frac_binary64_425`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`associate-r_binary64_359` `pow1_binary64_480`
2×	`unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `add-log-exp_binary64_458` `div-inv_binary64_416` `-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

1 → 32

Calls

2 calls:

6.0ms	(*.f64 (/.f64 b a) -1/2)
0.0ms	(*.f64 (/.f64 b a) -1/2)

series64.0ms (0%)

Counts

1 → 6

Calls

1 calls:

64.0ms

(*.f64 (/.f64 b a) -1/2)

Compiler

Compiled 60 to 72 computations (-20% saved)

simplify117.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4899	357
1	4899	357

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b	(.f64 c (.f64 a -4))
0.2b	(/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a)
0.1b	(.f64 a (sqrt.f64 (.f64 c (*.f64 a -4))))
0.0b	(-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))
2.2b	(+.f64 (.f64 1/4 (/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 c (.f64 a -4)))))) (.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))))
9.3b	(/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 c (.f64 a -4)))))
12.8b	(sqrt.f64 (.f64 c (.f64 a -4)))
12.8b	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite53.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`associate-+r+_binary64_351`
26×	`cancel-sign-sub-inv_binary64_385`
19×	`times-frac_binary64_425`
18×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
16×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
14×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
8×	`associate-*r/_binary64_361`
6×	`pow-prod-down_binary64_490` `add-log-exp_binary64_458` `sqrt-pow1_binary64_437`
4×	`frac-add_binary64_427` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`div-inv_binary64_416`
2×	`sub-neg_binary64_412` `pow1/2_binary64_499` `sqrt-prod_binary64_435`
1×	`flip3-+_binary64_422` `clear-num_binary64_418` `sum-log_binary64_510` `flip3--_binary64_423` `frac-2neg_binary64_430` `flip-+_binary64_393` `flip--_binary64_394` `associate-/r_binary64_363` `sub-div_binary64_426` `+-commutative_binary64_349` `frac-sub_binary64_428` `associate-/l_binary64_364`

Counts

4 → 88

Calls

8 calls:

24.0ms	(+.f64 (.f64 1/4 (/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 c (.f64 a -4)))))) (.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))))
10.0ms	(/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 c (.f64 a -4)))))
4.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
4.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
0.0ms	(-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))

series654.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

398.0ms	(+.f64 (.f64 1/4 (/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 c (.f64 a -4)))))) (.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (/.f64 b a))))
171.0ms	(/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 c (.f64 a -4)))))
42.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
42.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

Compiler

Compiled 1964 to 1557 computations (20.7% saved)

simplify57.0ms (0%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5029	3294

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.1b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 a 2))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.3b	(.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.6b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
21.7b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
21.7b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_441`
11×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
10×	`cbrt-prod_binary64_450`
9×	`associate-r_binary64_359`
8×	`sqrt-prod_binary64_435`
6×	`add-log-exp_binary64_458` `cbrt-div_binary64_451` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394`
3×	`unswap-sqr_binary64_387` `associate-l_binary64_360` `cancel-sign-sub-inv_binary64_385`
2×	`sqrt-div_binary64_436` `pow1/3_binary64_501` `associate-*r/_binary64_361`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `diff-log_binary64_511`

Counts

4 → 68

Calls

8 calls:

13.0ms	(.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
10.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series1.4s (1%)

Counts

4 → 77

Calls

4 calls:

460.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
417.0ms	(.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
282.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
265.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 6396 to 5149 computations (19.5% saved)

simplify112.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4949	5689
1	4949	5689

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 2 (.f64 1 (/.f64 c (-.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
0.0b	(.f64 4 (.f64 a c))
10.6b	(-.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
21.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite31.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_441`
9×	`sqrt-prod_binary64_435`
8×	`add-log-exp_binary64_458`
7×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `pow1_binary64_480`
6×	`sqrt-div_binary64_436`
4×	`flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394`
3×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
2×	`diff-log_binary64_511`
1×	`sub-neg_binary64_412` `associate--l-_binary64_357` `cancel-sign-sub-inv_binary64_385` `neg-log_binary64_512` `neg-sub0_binary64_414`

Counts

4 → 59

Calls

8 calls:

5.0ms	(-.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series707.0ms (0.5%)

Counts

4 → 79

Calls

4 calls:

185.0ms	(-.f64 (neg.f64 b) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
180.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
171.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
171.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 5007 to 3654 computations (27% saved)

simplify73.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5191	2658

prune27.6s (19%)

Pruning

676 alts after pruning (662 fresh and 14 done)

	Pruned	Kept	Total
New	457	208	665
Fresh	6	454	460
Picked	0	0	0
Done	1	14	15
Total	464	676	1140

Error

3.9b

Counts

1140 → 676

Compiler

Compiled 15335 to 8692 computations (43.3% saved)

simplify1.1s (0.7%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5094	55845

regimes36.0s (24.8%)

Compiler: Compiled 136249 to 97452 computations (28.5% saved)

bsearch159.0ms (0.1%)

Steps

Iters

Range

Point

1.8590571521096164e+71

1.0900040514885267e+77

4.816931246986667e+76

-5.936746772193797e-279

-2.9479252491687336e-292

-6.613044434627782e-283

-7.587833005939957e+152

-4.0151733111361164e+152

-4.89437030841433e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.8s (1.2%)

Compiler: Compiled 6726 to 5808 computations (13.6% saved)

bsearch108.0ms (0.1%)

Steps

Iters

Range

Point

1.8590571521096164e+71

1.0900040514885267e+77

4.816931246986667e+76

-5.936746772193797e-279

-2.9479252491687336e-292

-2.8094746472583994e-281

-7.587833005939957e+152

-4.0151733111361164e+152

-4.0737268480388477e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.3s (0.9%)

Compiler: Compiled 4242 to 3693 computations (12.9% saved)

bsearch109.0ms (0.1%)

Steps

Iters

Range

Point

1.8590571521096164e+71

1.0900040514885267e+77

9.7059850177998e+76

-5.936746772193797e-279

-2.9479252491687336e-292

-9.078145301820259e-283

-7.587833005939957e+152

-4.0151733111361164e+152

-4.191727865581558e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.3s (0.9%)

Compiler: Compiled 4089 to 3567 computations (12.8% saved)

bsearch37.0ms (0%)

Steps

Iters	Range		Point
5	6.186315751188359e-20	1.8978217974980654e-19	1.0684527239595751e-19
4	-7.587833005939957e+152	-4.0151733111361164e+152	-6.065441046468951e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes912.0ms (0.6%)

Compiler: Compiled 3081 to 2724 computations (11.6% saved)

bsearch38.0ms (0%)

Steps

Iters	Range		Point
5	6.186315751188359e-20	1.8978217974980654e-19	6.595244068316303e-20
4	-8.425887895792173e-25	-6.008291599166684e-25	-6.666572808649524e-25

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes987.0ms (0.7%)

Compiler: Compiled 2733 to 2427 computations (11.2% saved)

bsearch132.0ms (0.1%)

Steps

Iters	Range		Point
5	6.186315751188359e-20	1.8978217974980654e-19	6.322625190231006e-20
9	5.909365780477668e-57	4.9117095738258094e-52	2.1306939922765858e-52
9	2.4727976163752376e-71	2.4289174126669396e-66	1.624296268777243e-68
9	-3.65908399407251e-36	-3.443997492976351e-43	-1.0036134703492082e-42

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes799.0ms (0.5%)

Compiler: Compiled 2373 to 2100 computations (11.5% saved)

bsearch52.0ms (0%)

Steps

Iters	Range		Point
5	6.186315751188359e-20	1.8978217974980654e-19	6.322625190231006e-20
9	-3.65908399407251e-36	-3.443997492976351e-43	-5.614797585418129e-41

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes683.0ms (0.5%)

Compiler: Compiled 2109 to 1845 computations (12.5% saved)

bsearch54.0ms (0%)

Steps

Iters	Range		Point
5	6.186315751188359e-20	1.8978217974980654e-19	6.322625190231006e-20
9	-3.65908399407251e-36	-3.443997492976351e-43	-1.036257904214663e-42

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes499.0ms (0.3%)

Compiler: Compiled 2049 to 1785 computations (12.9% saved)

bsearch38.0ms (0%)

Steps

Iters	Range		Point
9	4.1710930405996304e-169	8.683647907175649e-162	4.2341774179204834e-169

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes507.0ms (0.3%)

Compiler: Compiled 1998 to 1734 computations (13.2% saved)

bsearch33.0ms (0%)

Steps

Iters	Range		Point
8	8.338938791839915e-226	1.879920592135896e-221	8.529742819354031e-226

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes29.0ms (0%)

Compiler: Compiled 27 to 69 computations (-155.6% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Accuracy

Total 3.7b remaining (56.4%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch16.0ms (0%)

Compiler: Compiled 394 to 281 computations (28.7% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	237	584
1	237	584

end0.0ms (0%)

sample30.4s (20.9%)

Algorithm

1×

intervals

Results

286.0ms	1091×	body	2048	valid
282.0ms	5180×	body	128	valid
157.0ms	768×	body	1024	valid
136.0ms	421×	body	4096	valid
55.0ms	354×	body	512	valid
35.0ms	695×	body	128	nan
22.0ms	371×	body	128	invalid
19.0ms	186×	body	256	valid

Compiler

Compiled 34878 to 24937 computations (28.5% saved)

Pareto

0.4194013805960902