Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample25.0ms (0%)

Algorithm

1×

intervals

Results

6.0ms	187×	body	128	valid
5.0ms	40×	body	1024	valid
4.0ms	256×	pre	128	true
1.0ms	13×	body	512	valid
1.0ms	7×	body	2048	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify350.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (249.0ms)

Iter	Nodes	Cost
0	5018	19

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.6b

Counts

2 → 1

Compiler

Compiled 13 to 11 computations (15.4% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

2.2b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.2b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_760`
26×	`add-sqr-sqrt_binary64_782`
25×	`times-frac_binary64_766`
19×	`distribute-lft-out_binary64_711`
14×	`add-cube-cbrt_binary64_795`
6×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712`
5×	`associate-/r_binary64_704` `associate-/l_binary64_705`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
2×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `div-sub_binary64_765` `pow1_binary64_821`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-+l-_binary64_695` `div-exp_binary64_811` `clear-num_binary64_759` `flip--_binary64_735` `flip3--_binary64_764`

Counts

2 → 65

Calls

4 calls:

19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
0.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
0.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series363.0ms (0.2%)

Counts

2 → 40

Calls

2 calls:

220.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
143.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 1856 to 1558 computations (16.1% saved)

simplify73.0ms (0%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4970	2918
1	4970	2918

prune658.0ms (0.3%)

Pruning

59 alts after pruning (58 fresh and 1 done)

	Pruned	Kept	Total
New	47	58	105
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	47	59	106

Error

0.0b

Counts

106 → 59

Compiler

Compiled 3259 to 2102 computations (35.5% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
2.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite82.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64_760`
54×	`add-sqr-sqrt_binary64_782`
37×	`times-frac_binary64_766`
27×	`add-cube-cbrt_binary64_795`
24×	`distribute-lft-out_binary64_711`
16×	`cancel-sign-sub-inv_binary64_726`
11×	`add-log-exp_binary64_799`
10×	`associate-/r*_binary64_704` `difference-of-squares_binary64_729`
8×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
6×	`associate-/l*_binary64_705`
5×	`distribute-lft-out--_binary64_712`
4×	`diff-log_binary64_852` `associate-/r/_binary64_706` `difference-of-sqr-1_binary64_730` `associate--r+_binary64_696` `pow1_binary64_821`
3×	`sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`
2×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734` `frac-sub_binary64_769` `div-exp_binary64_811` `clear-num_binary64_759`
1×	`associate--r-_binary64_699`

Counts

4 → 128

Calls

8 calls:

34.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
7.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)

series543.0ms (0.3%)

Counts

4 → 66

Calls

4 calls:

222.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
121.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
101.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
99.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 3251 to 2628 computations (19.2% saved)

simplify76.0ms (0%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5060	4846

localize2.0ms (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

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

26.2b	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)))
2.2b	(+.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))) 1)
1.4b	(-.f64 (.f64 beta beta) (.f64 alpha alpha))
0.0b	(*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
0.0b	(*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
1.4b	(-.f64 (.f64 beta beta) (.f64 alpha alpha))
2.2b	(+.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))) 1)
26.2b	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)))

rewrite58.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_760`
13×	`flip3-+_binary64_763` `flip-+_binary64_734`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`add-sqr-sqrt_binary64_782`
8×	`associate-/r/_binary64_706` `add-cube-cbrt_binary64_795` `add-log-exp_binary64_799` `frac-times_binary64_770`
6×	`pow1_binary64_821`
5×	`distribute-lft-out_binary64_711` `associate-r_binary64_700`
4×	`associate-l/_binary64_703` `associate-/l_binary64_705` `associate-l_binary64_701` `associate-*r/_binary64_702` `times-frac_binary64_766`
3×	`difference-of-squares_binary64_729`
2×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `associate-/l/_binary64_707` `div-sub_binary64_765` `cbrt-unprod_binary64_793` `div-exp_binary64_811` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `unswap-sqr_binary64_728` `frac-2neg_binary64_771` `cancel-sign-sub-inv_binary64_726` `distribute-lft-in_binary64_709` `associate-/r_binary64_704` `div-inv_binary64_757` `distribute-rgt-in_binary64_710` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-+l-_binary64_695` `clear-num_binary64_759` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

4 → 91

Calls

8 calls:

19.0ms	(+.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))) 1)
15.0ms	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)))
11.0ms	(*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
4.0ms	(-.f64 (.f64 beta beta) (.f64 alpha alpha))
0.0ms	(*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))

series700.0ms (0.4%)

Counts

4 → 66

Calls

4 calls:

267.0ms	(+.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))) 1)
187.0ms	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)))
141.0ms	(*.f64 (+.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
105.0ms	(-.f64 (.f64 beta beta) (.f64 alpha alpha))

Compiler

Compiled 2914 to 2378 computations (18.4% saved)

simplify97.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4953	3507
1	4953	3507

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

2.2b	(log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
2.2b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
0.0b	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
0.0b	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
2.2b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
2.2b	(log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))

rewrite82.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_760`
31×	`add-sqr-sqrt_binary64_782`
25×	`times-frac_binary64_766`
21×	`distribute-lft-out_binary64_711`
19×	`add-cube-cbrt_binary64_795`
9×	`add-log-exp_binary64_799`
8×	`exp-prod_binary64_812`
6×	`add-exp-log_binary64_798` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796` `distribute-lft-out--_binary64_712`
5×	`associate-/r_binary64_704` `associate-/l_binary64_705` `log-pow_binary64_849` `pow1_binary64_821`
4×	`div-sub_binary64_765` `log-prod_binary64_846`
3×	`associate-+l-_binary64_695`
2×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `associate-/l/_binary64_707` `exp-diff_binary64_808` `rem-exp-log_binary64_800` `flip-+_binary64_734` `exp-sum_binary64_806` `sum-log_binary64_851`
1×	`log-div_binary64_847` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `+-commutative_binary64_690` `rem-log-exp_binary64_801` `div-exp_binary64_811` `clear-num_binary64_759` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 98

Calls

8 calls:

23.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
20.0ms	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))

series955.0ms (0.5%)

Counts

4 → 80

Calls

4 calls:

348.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
289.0ms	(exp.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))
177.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
140.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 3998 to 3380 computations (15.5% saved)

simplify114.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4946	5801
1	4946	5801

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b	(/.f64 1 (*.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2))))
0.3b	(*.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))
0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2))))
0.3b	(/.f64 (-.f64 beta alpha) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))
0.7b	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
12.6b	(+.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) 1)

rewrite61.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_760`
15×	`cbrt-prod_binary64_791`
9×	`distribute-lft-out_binary64_711`
7×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
6×	`add-log-exp_binary64_799` `cbrt-div_binary64_792`
4×	`flip3-+_binary64_763` `add-exp-log_binary64_798` `flip-+_binary64_734` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`pow1/3_binary64_842`
1×	`+-commutative_binary64_690` `sum-log_binary64_851`

Counts

4 → 56

Calls

8 calls:

37.0ms	(+.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) 1)
6.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
0.0ms	(/.f64 (-.f64 beta alpha) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))

series784.0ms (0.4%)

Counts

4 → 62

Calls

4 calls:

239.0ms	(+.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (+.f64 (+.f64 beta alpha) 2)))) 1)
183.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
181.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))
180.0ms	(cbrt.f64 (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 4406 to 3652 computations (17.1% saved)

simplify80.0ms (0%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4992	3273
1	4992	3273

prune10.9s (5.6%)

Pruning

295 alts after pruning (290 fresh and 5 done)

	Pruned	Kept	Total
New	398	249	647
Fresh	12	41	53
Picked	0	0	0
Done	1	5	6
Total	411	295	706

Error

0.0b

Counts

706 → 295

Compiler

Compiled 23715 to 15047 computations (36.6% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
0.0b	(exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) 2)
0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
2.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
2.2b	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite60.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64_760`
50×	`add-sqr-sqrt_binary64_782`
36×	`times-frac_binary64_766`
28×	`add-cube-cbrt_binary64_795`
24×	`distribute-lft-out_binary64_711`
11×	`log-pow_binary64_849`
10×	`exp-prod_binary64_812` `associate-/r*_binary64_704`
8×	`add-exp-log_binary64_798` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796`
7×	`log-prod_binary64_846`
6×	`cancel-sign-sub-inv_binary64_726` `add-log-exp_binary64_799` `associate-/l*_binary64_705`
5×	`pow1_binary64_821`
4×	`associate-/r/_binary64_706` `difference-of-sqr-1_binary64_730` `exp-sum_binary64_806`
2×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734` `distribute-lft-out--_binary64_712` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`
1×	`diff-log_binary64_852` `log-div_binary64_847` `exp-diff_binary64_808` `rem-log-exp_binary64_801` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 122

Calls

8 calls:

18.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
8.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
7.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) 2)

series474.0ms (0.2%)

Counts

4 → 58

Calls

4 calls:

196.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
105.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
88.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
84.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 2827 to 2287 computations (19.1% saved)

simplify78.0ms (0%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4947	3258
1	4947	3258

localize3.0ms (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

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

4.1b	(+.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2))) 1)
1.4b	(-.f64 (.f64 beta beta) (.f64 alpha alpha))
0.1b	(*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))
0.0b	(pow.f64 (+.f64 beta alpha) 2)
1.4b	(-.f64 (.f64 beta beta) (.f64 alpha alpha))
4.1b	(+.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2))) 1)
5.3b	(/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2))
26.2b	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2)))

rewrite113.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_766`
66×	`*-un-lft-identity_binary64_760`
43×	`add-sqr-sqrt_binary64_782`
29×	`add-cube-cbrt_binary64_795`
21×	`difference-of-squares_binary64_729`
18×	`add-exp-log_binary64_798` `associate-/r*_binary64_704` `add-cbrt-cube_binary64_796`
14×	`distribute-lft-out--_binary64_712`
13×	`associate-/r/_binary64_706`
11×	`flip--_binary64_735` `flip3--_binary64_764`
10×	`associate-/l/_binary64_707`
8×	`distribute-lft-out_binary64_711` `add-log-exp_binary64_799`
7×	`cbrt-undiv_binary64_794` `div-inv_binary64_757` `div-exp_binary64_811`
5×	`associate-/l*_binary64_705`
4×	`flip3-+_binary64_763` `flip-+_binary64_734` `frac-times_binary64_770` `pow1_binary64_821`
2×	`frac-2neg_binary64_771` `associate-l/_binary64_703` `prod-exp_binary64_809` `div-sub_binary64_765` `associate-r/_binary64_702` `cbrt-unprod_binary64_793` `clear-num_binary64_759`
1×	`diff-log_binary64_852` `cancel-sign-sub-inv_binary64_726` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-+l-_binary64_695` `sub-neg_binary64_753`

Counts

4 → 147

Calls

8 calls:

37.0ms	(+.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2))) 1)
25.0ms	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2)))
22.0ms	(/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2))
4.0ms	(-.f64 (.f64 beta beta) (.f64 alpha alpha))
0.0ms	(pow.f64 (+.f64 beta alpha) 2)

series1.9s (1%)

Counts

4 → 66

Calls

4 calls:

866.0ms	(+.f64 (/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2))) 1)
472.0ms	(/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2))
439.0ms	(/.f64 (-.f64 (.f64 beta beta) (.f64 alpha alpha)) (/.f64 (*.f64 (+.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)) (-.f64 (+.f64 beta alpha) 2)))
104.0ms	(-.f64 (.f64 beta beta) (.f64 alpha alpha))

Compiler

Compiled 4658 to 3768 computations (19.1% saved)

simplify109.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4973	8212
1	4973	8212

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

2.2b	(log.f64 (exp.f64 (+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1)))
2.2b	(+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1)
0.0b	(exp.f64 (+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1))
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
0.0b	(exp.f64 (+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1))
2.2b	(+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1)
2.2b	(log.f64 (exp.f64 (+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1)))

rewrite96.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_760`
31×	`add-sqr-sqrt_binary64_782`
25×	`times-frac_binary64_766`
21×	`distribute-lft-out_binary64_711`
19×	`add-cube-cbrt_binary64_795`
9×	`add-log-exp_binary64_799`
8×	`exp-prod_binary64_812`
6×	`add-exp-log_binary64_798` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796` `distribute-lft-out--_binary64_712`
5×	`associate-/r_binary64_704` `associate-/l_binary64_705` `log-pow_binary64_849` `pow1_binary64_821`
4×	`log-prod_binary64_846`
2×	`associate-/r/_binary64_706` `flip3-+_binary64_763` `associate-/l/_binary64_707` `rem-exp-log_binary64_800` `flip-+_binary64_734` `exp-sum_binary64_806` `sum-log_binary64_851`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `+-commutative_binary64_690` `div-sub_binary64_765` `rem-log-exp_binary64_801` `div-exp_binary64_811` `clear-num_binary64_759` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 95

Calls

8 calls:

26.0ms	(+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1)
25.0ms	(log.f64 (exp.f64 (+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1)))
25.0ms	(exp.f64 (+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1))
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))

series935.0ms (0.5%)

Counts

4 → 80

Calls

4 calls:

348.0ms	(log.f64 (exp.f64 (+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1)))
278.0ms	(exp.f64 (+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1))
170.0ms	(+.f64 (pow.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1) 1)
139.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))

Compiler

Compiled 4044 to 3426 computations (15.3% saved)

simplify113.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4946	5714
1	4946	5714

localize31.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 2 (/.f64 beta alpha))
0.0b	(.f64 2 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))
0.0b	(+.f64 (*.f64 2 (/.f64 beta alpha)) (+.f64 (/.f64 2 alpha) (+.f64 1 (/.f64 4/3 (pow.f64 alpha 3)))))
0.0b	(+.f64 (/.f64 2 alpha) (+.f64 1 (/.f64 4/3 (pow.f64 alpha 3))))
8.7b	(/.f64 beta (*.f64 alpha alpha))
15.2b	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
16.3b	(log.f64 (-.f64 (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (/.f64 2 alpha) (+.f64 1 (/.f64 4/3 (pow.f64 alpha 3))))) (+.f64 (.f64 2 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (+.f64 (.f64 (pow.f64 (/.f64 beta alpha) 3) 2/3) (.f64 2 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3))))))))
17.0b	(-.f64 (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (/.f64 2 alpha) (+.f64 1 (/.f64 4/3 (pow.f64 alpha 3))))) (+.f64 (.f64 2 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (+.f64 (.f64 (pow.f64 (/.f64 beta alpha) 3) 2/3) (.f64 2 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))

rewrite217.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`frac-add_binary64_768`
128×	`associate-*r/_binary64_702`
84×	`add-log-exp_binary64_799` `frac-sub_binary64_769`
78×	`flip3-+_binary64_763` `flip-+_binary64_734`
48×	`sum-log_binary64_851`
44×	`log-div_binary64_847`
23×	`add-exp-log_binary64_798`
18×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
16×	`diff-log_binary64_852`
15×	`times-frac_binary64_766`
14×	`add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796`
13×	`associate-/r*_binary64_704`
12×	`associate-*l/_binary64_703` `cube-div_binary64_789`
8×	`div-exp_binary64_811`
6×	`cube-prod_binary64_788` `unpow-prod-down_binary64_839`
5×	`pow1_binary64_821` `log-prod_binary64_846`
4×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `associate-/l*_binary64_705`
3×	`cancel-sign-sub-inv_binary64_726`
2×	`cube-mult_binary64_790` `frac-2neg_binary64_771` `unpow3_binary64_826` `pow-exp_binary64_828` `div-inv_binary64_757` `difference-of-squares_binary64_729` `pow-to-exp_binary64_829` `distribute-lft-out--_binary64_712` `sqr-pow_binary64_732` `cbrt-unprod_binary64_793` `clear-num_binary64_759` `flip--_binary64_735` `flip3--_binary64_764`
1×	`log-pow_binary64_849` `associate--r+_binary64_696` `rem-log-exp_binary64_801` `associate--l+_binary64_697` `sub-neg_binary64_753`

Counts

4 → 197

Calls

8 calls:

62.0ms	(log.f64 (-.f64 (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (/.f64 2 alpha) (+.f64 1 (/.f64 4/3 (pow.f64 alpha 3))))) (+.f64 (.f64 2 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (+.f64 (.f64 (pow.f64 (/.f64 beta alpha) 3) 2/3) (.f64 2 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3))))))))
59.0ms	(-.f64 (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (/.f64 2 alpha) (+.f64 1 (/.f64 4/3 (pow.f64 alpha 3))))) (+.f64 (.f64 2 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (+.f64 (.f64 (pow.f64 (/.f64 beta alpha) 3) 2/3) (.f64 2 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))
7.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
5.0ms	(/.f64 beta (*.f64 alpha alpha))
0.0ms	(+.f64 (/.f64 2 alpha) (+.f64 1 (/.f64 4/3 (pow.f64 alpha 3))))

series709.0ms (0.4%)

Counts

4 → 44

Calls

4 calls:

310.0ms	(log.f64 (-.f64 (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (/.f64 2 alpha) (+.f64 1 (/.f64 4/3 (pow.f64 alpha 3))))) (+.f64 (.f64 2 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (+.f64 (.f64 (pow.f64 (/.f64 beta alpha) 3) 2/3) (.f64 2 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3))))))))
202.0ms	(-.f64 (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (/.f64 2 alpha) (+.f64 1 (/.f64 4/3 (pow.f64 alpha 3))))) (+.f64 (.f64 2 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (+.f64 (.f64 (pow.f64 (/.f64 beta alpha) 3) 2/3) (.f64 2 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)))))))
112.0ms	(/.f64 (*.f64 beta beta) (pow.f64 alpha 3))
84.0ms	(/.f64 beta (*.f64 alpha alpha))

Compiler

Compiled 3016 to 2487 computations (17.5% saved)

simplify297.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5048	35123

prune35.7s (18.3%)

Pruning

625 alts after pruning (616 fresh and 9 done)

	Pruned	Kept	Total
New	450	359	809
Fresh	28	257	285
Picked	0	0	0
Done	1	9	10
Total	479	625	1104

Error

0.0b

Counts

1104 → 625

Compiler

Compiled 77757 to 51019 computations (34.4% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
0.0b	(-.f64 (*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))))
0.0b	(exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.0b	(/.f64 (-.f64 (*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) 2)
0.0b	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.1b	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
2.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
2.2b	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))

rewrite72.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_760`
57×	`add-sqr-sqrt_binary64_782`
38×	`times-frac_binary64_766`
28×	`add-cube-cbrt_binary64_795`
21×	`distribute-lft-out_binary64_711` `associate-r_binary64_700`
17×	`add-exp-log_binary64_798`
11×	`add-cbrt-cube_binary64_796` `log-pow_binary64_849`
10×	`exp-prod_binary64_812`
8×	`difference-of-squares_binary64_729` `pow1_binary64_821`
7×	`log-prod_binary64_846`
6×	`cancel-sign-sub-inv_binary64_726` `add-log-exp_binary64_799`
5×	`associate-/r*_binary64_704`
4×	`prod-exp_binary64_809` `associate-/r/_binary64_706` `difference-of-sqr-1_binary64_730` `exp-sum_binary64_806` `div-exp_binary64_811`
3×	`unswap-sqr_binary64_728` `associate-/l_binary64_705` `associate-l*_binary64_701`
2×	`cbrt-undiv_binary64_794` `flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734` `distribute-lft-out--_binary64_712` `rec-exp_binary64_810` `cbrt-unprod_binary64_793` `sub-neg_binary64_753` `1-exp_binary64_804`
1×	`diff-log_binary64_852` `log-div_binary64_847` `frac-2neg_binary64_771` `exp-diff_binary64_808` `inv-pow_binary64_845` `associate-r/_binary64_702` `rem-log-exp_binary64_801` `clear-num_binary64_759` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `-commutative_binary64_691` `flip--_binary64_735` `pow-flip_binary64_834` `flip3--_binary64_764`

Counts

4 → 133

Calls

8 calls:

16.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)
15.0ms	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
8.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
0.0ms	(/.f64 (-.f64 (*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) (log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))) 2)

series492.0ms (0.3%)

Counts

4 → 63

Calls

4 calls:

199.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)))
110.0ms	(*.f64 beta (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
97.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))
86.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1)

Compiler

Compiled 3083 to 2508 computations (18.7% saved)

simplify103.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4960	3531
1	4960	3531

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.0b	(sqrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.0b	(-.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 (-.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.3b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
0.4b	(/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
0.5b	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
2.2b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite103.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`*-un-lft-identity_binary64_760`
126×	`add-sqr-sqrt_binary64_782`
121×	`times-frac_binary64_766`
81×	`sqrt-prod_binary64_776`
69×	`add-cube-cbrt_binary64_795`
42×	`distribute-lft-out_binary64_711`
32×	`add-exp-log_binary64_798`
30×	`associate-r_binary64_700` `associate-l_binary64_701`
20×	`add-cbrt-cube_binary64_796`
16×	`associate-/r*_binary64_704`
15×	`unswap-sqr_binary64_728`
11×	`div-exp_binary64_811`
8×	`prod-exp_binary64_809` `associate-/r/_binary64_706` `sqrt-div_binary64_777` `pow1_binary64_821`
6×	`cbrt-undiv_binary64_794` `add-log-exp_binary64_799` `associate-/l*_binary64_705`
4×	`flip3-+_binary64_763` `div-inv_binary64_757` `difference-of-squares_binary64_729` `flip-+_binary64_734` `cbrt-unprod_binary64_793`
3×	`cancel-sign-sub-inv_binary64_726` `rec-exp_binary64_810` `1-exp_binary64_804` `pow-flip_binary64_834`
2×	`frac-2neg_binary64_771` `difference-of-sqr-1_binary64_730` `clear-num_binary64_759`
1×	`diff-log_binary64_852` `associate-l/_binary64_703` `sqrt-pow1_binary64_778` `inv-pow_binary64_845` `distribute-lft-out--_binary64_712` `frac-times_binary64_770` `associate-r/_binary64_702` `pow1/2_binary64_840` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 224

Calls

8 calls:

37.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
12.0ms	(/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
0.0ms	(/.f64 (-.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)

series431.0ms (0.2%)

Counts

4 → 50

Calls

4 calls:

134.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
110.0ms	(/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
110.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (/.f64 beta (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
77.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))

Compiler

Compiled 2918 to 2305 computations (21% saved)

simplify105.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4978	6104
1	4978	6104

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(exp.f64 (+.f64 (pow.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2)))) 1) 1))
0.0b	(pow.f64 (+.f64 beta alpha) 3)
0.0b	(+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (*.f64 (+.f64 beta alpha) 2)))
0.0b	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))
5.5b	(/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8))
5.8b	(+.f64 (pow.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2)))) 1) 1)
5.8b	(log.f64 (exp.f64 (+.f64 (pow.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2)))) 1) 1)))
20.8b	(.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2))))

rewrite104.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_760`
51×	`add-sqr-sqrt_binary64_782`
41×	`times-frac_binary64_766`
34×	`frac-times_binary64_770`
32×	`frac-add_binary64_768`
29×	`flip3-+_binary64_763` `flip-+_binary64_734`
28×	`add-cube-cbrt_binary64_795`
26×	`associate-l_binary64_701` `associate-*r/_binary64_702`
17×	`flip--_binary64_735` `flip3--_binary64_764`
13×	`distribute-lft-out_binary64_711`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
9×	`associate-*l/_binary64_703` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712`
7×	`pow1_binary64_821`
6×	`add-log-exp_binary64_799`
5×	`associate-/l*_binary64_705` `log-pow_binary64_849`
4×	`associate-/r/_binary64_706` `exp-prod_binary64_812` `associate-/r*_binary64_704` `log-prod_binary64_846`
3×	`associate-r_binary64_700`
2×	`unswap-sqr_binary64_728` `cbrt-undiv_binary64_794` `prod-exp_binary64_809` `associate-/l/_binary64_707` `div-inv_binary64_757` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
1×	`frac-2neg_binary64_771` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `+-commutative_binary64_690` `exp-sum_binary64_806` `sum-log_binary64_851` `div-sub_binary64_765` `rem-log-exp_binary64_801` `clear-num_binary64_759` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 158

Calls

8 calls:

35.0ms	(.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2))))
15.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8))
14.0ms	(+.f64 (pow.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2)))) 1) 1)
7.0ms	(log.f64 (exp.f64 (+.f64 (pow.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2)))) 1) 1)))
0.0ms	(*.f64 (+.f64 beta alpha) (+.f64 beta alpha))

series3.1s (1.6%)

Counts

4 → 66

Calls

4 calls:

1.6s	(log.f64 (exp.f64 (+.f64 (pow.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2)))) 1) 1)))
950.0ms	(+.f64 (pow.f64 (.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2)))) 1) 1)
493.0ms	(.f64 (/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8)) (+.f64 (.f64 (+.f64 beta alpha) (+.f64 beta alpha)) (-.f64 (.f64 2 2) (.f64 (+.f64 beta alpha) 2))))
99.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (pow.f64 (+.f64 beta alpha) 3) 8))

Compiler

Compiled 5919 to 4960 computations (16.2% saved)

simplify137.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	6245	13959

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (-.f64 (+.f64 beta alpha) 2) (.f64 1 (/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)))) 1)) (cbrt.f64 (+.f64 (.f64 (-.f64 (+.f64 beta alpha) 2) (.f64 1 (/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)))) 1))) (cbrt.f64 (+.f64 (.f64 (-.f64 (+.f64 beta alpha) 2) (.f64 1 (/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)))) 1)))
0.0b	(pow.f64 (+.f64 beta alpha) 2)
0.0b	(pow.f64 (+.f64 beta alpha) 2)
0.0b	(pow.f64 (+.f64 beta alpha) 2)
5.4b	(+.f64 (.f64 (-.f64 (+.f64 beta alpha) 2) (.f64 1 (/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)))) 1)
19.6b	(/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))
19.6b	(/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))
19.6b	(/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))

rewrite119.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

211×	`add-sqr-sqrt_binary64_782`
139×	`*-un-lft-identity_binary64_760`
120×	`times-frac_binary64_766`
99×	`difference-of-squares_binary64_729`
49×	`add-cube-cbrt_binary64_795`
45×	`distribute-lft-out--_binary64_712`
24×	`associate-/r*_binary64_704`
18×	`unpow2_binary64_825` `sqr-pow_binary64_732` `unpow-prod-down_binary64_839`
15×	`associate-/l*_binary64_705`
10×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
6×	`associate-/r/_binary64_706` `associate-/l/_binary64_707` `add-log-exp_binary64_799` `flip--_binary64_735` `flip3--_binary64_764`
4×	`pow1_binary64_821`
3×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `div-sub_binary64_765` `div-exp_binary64_811` `clear-num_binary64_759`
1×	`flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `sum-log_binary64_851`

Counts

4 → 221

Calls

8 calls:

28.0ms	(+.f64 (.f64 (-.f64 (+.f64 beta alpha) 2) (.f64 1 (/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)))) 1)
15.0ms	(/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))
15.0ms	(/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))
15.0ms	(/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))
0.0ms	(pow.f64 (+.f64 beta alpha) 2)

series1.2s (0.6%)

Counts

4 → 69

Calls

4 calls:

572.0ms	(+.f64 (.f64 (-.f64 (+.f64 beta alpha) 2) (.f64 1 (/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4)))) 1)
229.0ms	(/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))
224.0ms	(/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))
223.0ms	(/.f64 (-.f64 beta alpha) (-.f64 (pow.f64 (+.f64 beta alpha) 2) 4))

Compiler

Compiled 8236 to 6117 computations (25.7% saved)

simplify155.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4943	8494
1	4943	8494

prune1.3min (39.7%)

Pruning

956 alts after pruning (942 fresh and 14 done)

	Pruned	Kept	Total
New	622	362	984
Fresh	31	580	611
Picked	0	0	0
Done	0	14	14
Total	653	956	1609

Error

0.0b

Counts

1609 → 956

Compiler

Compiled 35044 to 21222 computations (39.4% saved)

simplify1.7s (0.9%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	7689	126079

regimes27.1s (13.9%)

Compiler: Compiled 412489 to 285450 computations (30.8% saved)

bsearch123.0ms (0.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes8.8s (4.5%)

Compiler: Compiled 111744 to 81135 computations (27.4% saved)

bsearch41.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes3.1s (1.6%)

Compiler: Compiled 40709 to 30455 computations (25.2% saved)

bsearch16.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes2.7s (1.4%)

Compiler: Compiled 32269 to 24010 computations (25.6% saved)

bsearch13.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes2.4s (1.2%)

Compiler: Compiled 31639 to 23520 computations (25.7% saved)

bsearch12.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes2.1s (1.1%)

Compiler: Compiled 28379 to 20725 computations (27% saved)

bsearch14.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes953.0ms (0.5%)

Compiler: Compiled 11592 to 8911 computations (23.1% saved)

bsearch5.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes543.0ms (0.3%)

Compiler: Compiled 5617 to 4631 computations (17.6% saved)

bsearch3.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes392.0ms (0.2%)

Compiler: Compiled 3622 to 3136 computations (13.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes197.0ms (0.1%)

Compiler: Compiled 1322 to 1237 computations (6.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

regimes46.0ms (0%)

Compiler: Compiled 184 to 196 computations (-6.5% saved)

bsearch15.0ms (0%)

Steps

Iters	Range		Point
8	4746723128106.877	4.081681975463958e+16	4858852822362.639

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes21.0ms (0%)

Compiler: Compiled 28 to 44 computations (-57.1% saved)

bsearch0.0ms (0%)

regimes16.0ms (0%)

Compiler: Compiled 10 to 26 computations (-160% saved)

bsearch25.0ms (0%)

Compiler: Compiled 599 to 419 computations (30.1% saved)

simplify47.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	1051	890
1	1051	890

end0.0ms (0%)

sample3.7s (1.9%)

Algorithm

1×

intervals

Results

205.0ms	5927×	body	128	valid
146.0ms	8000×	pre	128	true
137.0ms	1083×	body	1024	valid
61.0ms	616×	body	512	valid
18.0ms	277×	body	256	valid
16.0ms	97×	body	2048	valid

Compiler

Compiled 83650 to 57867 computations (30.8% saved)