Details

analyze275.0ms (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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
31.2%	68.6%	0.1%	7
40.6%	59.3%	0.1%	8
43.7%	56.2%	0.1%	9
56.6%	43.3%	0.1%	10
61%	37.3%	1.7%	11
62.1%	34.8%	3.1%	12
68.6%	25.6%	5.8%	13
70.6%	22.1%	7.4%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample22.0ms (0%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
1.0ms	42×	body	128	invalid

Compiler

Compiled 18 to 22 computations (-22.2% saved)

simplify114.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	357	13
1	357	13

prune2.0ms (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

0.0b

Counts

8 → 4

Compiler

Compiled 10 to 9 computations (10% saved)

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 y x) z)
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.0b	(/.f64 (-.f64 y x) z)
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_78`
20×	`add-sqr-sqrt_binary64_100`
15×	`times-frac_binary64_84`
12×	`add-cube-cbrt_binary64_113`
5×	`associate-/l*_binary64_23`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `distribute-lft-out--_binary64_30` `add-exp-log_binary64_116` `difference-of-squares_binary64_47`
3×	`associate-/r*_binary64_22`
2×	`div-sub_binary64_83` `associate-/l/_binary64_25` `pow1_binary64_139`
1×	`+-commutative_binary64_8` `associate-+r-_binary64_12` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `flip3--_binary64_82` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

2 → 51

Calls

4 calls:

10.0ms	(+.f64 x (/.f64 (-.f64 y x) z))
6.0ms	(/.f64 (-.f64 y x) z)
0.0ms	(+.f64 x (/.f64 (-.f64 y x) z))
0.0ms	(/.f64 (-.f64 y x) z)

series260.0ms (0.3%)

Counts

2 → 33

Calls

2 calls:

149.0ms	(+.f64 x (/.f64 (-.f64 y x) z))
111.0ms	(/.f64 (-.f64 y x) z)

Compiler

Compiled 389 to 332 computations (14.7% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5014	953

prune240.0ms (0.2%)

Pruning

45 alts after pruning (44 fresh and 1 done)

	Pruned	Kept	Total
New	43	41	84
Fresh	0	3	3
Picked	0	0	0
Done	0	1	1
Total	43	45	88

Error

0.0b

Counts

88 → 45

Compiler

Compiled 1177 to 522 computations (55.6% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 y z) (/.f64 x z))
0.0b	(+.f64 x (-.f64 (/.f64 y z) (/.f64 x z)))
0.0b	(+.f64 x (-.f64 (/.f64 y z) (/.f64 x z)))
0.0b	(-.f64 (/.f64 y z) (/.f64 x z))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_78`
30×	`add-sqr-sqrt_binary64_100`
28×	`times-frac_binary64_84`
26×	`cancel-sign-sub-inv_binary64_44`
18×	`add-cube-cbrt_binary64_113`
14×	`associate-+r+_binary64_10`
9×	`add-log-exp_binary64_117`
5×	`distribute-lft-out--_binary64_30`
4×	`div-inv_binary64_75` `difference-of-squares_binary64_47`
2×	`add-cbrt-cube_binary64_114` `diff-log_binary64_170` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29` `sub-neg_binary64_71` `pow1_binary64_139` `sum-log_binary64_169`
1×	`+-commutative_binary64_8` `associate-+r-_binary64_12` `flip-+_binary64_52` `frac-sub_binary64_87` `flip3--_binary64_82` `flip--_binary64_53` `sub-div_binary64_85` `distribute-rgt-out--_binary64_32` `flip3-+_binary64_81`

Counts

2 → 64

Calls

4 calls:

20.0ms	(+.f64 x (-.f64 (/.f64 y z) (/.f64 x z)))
18.0ms	(-.f64 (/.f64 y z) (/.f64 x z))
0.0ms	(+.f64 x (-.f64 (/.f64 y z) (/.f64 x z)))
0.0ms	(-.f64 (/.f64 y z) (/.f64 x z))

series295.0ms (0.3%)

Counts

2 → 33

Calls

2 calls:

157.0ms	(+.f64 x (-.f64 (/.f64 y z) (/.f64 x z)))
138.0ms	(-.f64 (/.f64 y z) (/.f64 x z))

Compiler

Compiled 389 to 332 computations (14.7% saved)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4875	975
1	4875	975

localize2.0ms (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

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 y x) z)
0.0b	(+.f64 x (pow.f64 (/.f64 (-.f64 y x) z) 1))
0.0b	(/.f64 (-.f64 y x) z)
0.0b	(+.f64 x (pow.f64 (/.f64 (-.f64 y x) z) 1))

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_78`
20×	`add-sqr-sqrt_binary64_100`
15×	`times-frac_binary64_84`
12×	`add-cube-cbrt_binary64_113`
5×	`associate-/l*_binary64_23`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `distribute-lft-out--_binary64_30` `add-exp-log_binary64_116` `difference-of-squares_binary64_47`
3×	`associate-/r*_binary64_22`
2×	`associate-/l/_binary64_25` `pow1_binary64_139`
1×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `flip3--_binary64_82` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `div-sub_binary64_83` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

2 → 50

Calls

4 calls:

15.0ms	(+.f64 x (pow.f64 (/.f64 (-.f64 y x) z) 1))
6.0ms	(/.f64 (-.f64 y x) z)
0.0ms	(+.f64 x (pow.f64 (/.f64 (-.f64 y x) z) 1))
0.0ms	(/.f64 (-.f64 y x) z)

series275.0ms (0.3%)

Counts

2 → 33

Calls

2 calls:

161.0ms	(+.f64 x (pow.f64 (/.f64 (-.f64 y x) z) 1))
113.0ms	(/.f64 (-.f64 y x) z)

Compiler

Compiled 437 to 380 computations (13% saved)

simplify64.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4940	940
1	4940	940

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.1b	(*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z))
0.1b	(*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z))
0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-sqr-sqrt_binary64_100`
52×	`times-frac_binary64_84` `*-un-lft-identity_binary64_78`
45×	`sqrt-prod_binary64_94`
36×	`add-cube-cbrt_binary64_113`
28×	`associate-r_binary64_18`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`associate-l_binary64_19` `distribute-lft-out--_binary64_30` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
6×	`unswap-sqr_binary64_46` `sqrt-div_binary64_95`
4×	`pow1_binary64_139`
3×	`flip3--_binary64_82` `flip--_binary64_53` `associate-/r*_binary64_22`
2×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75` `frac-times_binary64_88` `associate-*l/_binary64_21` `associate-/l/_binary64_25`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77`

Counts

2 → 109

Calls

4 calls:

20.0ms	(*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z))
7.0ms	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.0ms	(*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z))
0.0ms	(/.f64 (sqrt.f64 (-.f64 y x)) z)

series216.0ms (0.2%)

Counts

2 → 25

Calls

2 calls:

109.0ms	(/.f64 (sqrt.f64 (-.f64 y x)) z)
107.0ms	(*.f64 (sqrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 y x)) z))

Compiler

Compiled 583 to 445 computations (23.7% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5547	2047

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (-.f64 y x) z)
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.5b	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))) (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))

rewrite69.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_109`
35×	`*-un-lft-identity_binary64_78`
23×	`add-sqr-sqrt_binary64_100`
18×	`cbrt-div_binary64_110`
15×	`add-cube-cbrt_binary64_113`
11×	`pow1_binary64_139`
9×	`flip-+_binary64_52` `swap-sqr_binary64_45` `pow1/3_binary64_160` `distribute-lft-out_binary64_29` `flip3-+_binary64_81`
7×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `frac-times_binary64_88` `unswap-sqr_binary64_46`
2×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-r/_binary64_20`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-plus_binary64_141`

Counts

4 → 95

Calls

8 calls:

25.0ms	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))) (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
13.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
10.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
10.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
0.0ms	(+.f64 x (/.f64 (-.f64 y x) z))

series2.6s (2.6%)

Counts

4 → 90

Calls

4 calls:

1.2s	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))) (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
462.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
459.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
459.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))

Compiler

Compiled 10590 to 7712 computations (27.2% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5381	8731

prune6.0s (6%)

Pruning

251 alts after pruning (245 fresh and 6 done)

	Pruned	Kept	Total
New	289	210	499
Fresh	4	35	39
Picked	0	0	0
Done	0	6	6
Total	293	251	544

Error

0.0b

Counts

544 → 251

Compiler

Compiled 18712 to 8180 computations (56.3% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))
0.0b	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64_117`
3×	`sum-log_binary64_169`
2×	`frac-add_binary64_86` `flip-+_binary64_52` `associate-*r/_binary64_20` `flip3-+_binary64_81`
1×	`add-cbrt-cube_binary64_114` `+-commutative_binary64_8` `add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `associate-+l+_binary64_11` `distribute-lft-neg-out_binary64_37` `add-exp-log_binary64_116` `unsub-neg_binary64_72` `*-un-lft-identity_binary64_78` `pow1_binary64_139`

Counts

1 → 16

Calls

2 calls:

10.0ms	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))
0.0ms	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))

series154.0ms (0.2%)

Counts

1 → 18

Calls

1 calls:

154.0ms

(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))

Compiler

Compiled 199 to 172 computations (13.6% saved)

simplify61.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5942	447

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 x (/.f64 x z))
0.0b	(-.f64 x (/.f64 x z))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100` `cancel-sign-sub-inv_binary64_44`
10×	`times-frac_binary64_84` `*-un-lft-identity_binary64_78`
8×	`add-cube-cbrt_binary64_113`
3×	`add-log-exp_binary64_117`
2×	`difference-of-squares_binary64_47`
1×	`add-cbrt-cube_binary64_114` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `div-inv_binary64_75` `flip--_binary64_53` `add-exp-log_binary64_116` `sub-neg_binary64_71` `pow1_binary64_139`

Counts

1 → 27

Calls

2 calls:

9.0ms	(-.f64 x (/.f64 x z))
0.0ms	(-.f64 x (/.f64 x z))

series59.0ms (0.1%)

Counts

1 → 9

Calls

1 calls:

59.0ms

(-.f64 x (/.f64 x z))

Compiler

Compiled 83 to 94 computations (-13.3% saved)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4903	325
1	4903	325

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(pow.f64 (-.f64 x (/.f64 x z)) 2)
0.0b	(-.f64 x (/.f64 x z))
0.0b	(/.f64 (-.f64 y x) z)
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.1b	(pow.f64 (-.f64 x (/.f64 x z)) 2)
0.3b	(*.f64 (cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2)) (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
27.5b	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))

rewrite63.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_100`
43×	`cbrt-prod_binary64_109`
24×	`*-un-lft-identity_binary64_78`
20×	`unpow-prod-down_binary64_157`
14×	`associate-l_binary64_19` `add-cube-cbrt_binary64_113`
10×	`unswap-sqr_binary64_46`
7×	`associate-r_binary64_18` `add-exp-log_binary64_116` `pow1_binary64_139`
6×	`difference-of-squares_binary64_47`
5×	`unpow2_binary64_143` `sqr-pow_binary64_50`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `add-log-exp_binary64_117` `pow1/3_binary64_160`
3×	`distribute-lft-out--_binary64_30` `times-frac_binary64_84` `pow-unpow_binary64_155`
2×	`flip-+_binary64_52` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29` `flip3-+_binary64_81`
1×	`*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-pow_binary64_150`

Counts

4 → 99

Calls

8 calls:

25.0ms	(*.f64 (cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2)) (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
12.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
8.0ms	(pow.f64 (-.f64 x (/.f64 x z)) 2)
8.0ms	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))
0.0ms	(+.f64 x (/.f64 (-.f64 y x) z))

series2.1s (2%)

Counts

4 → 60

Calls

4 calls:

1.4s	(*.f64 (cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2)) (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
312.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
245.0ms	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))
116.0ms	(pow.f64 (-.f64 x (/.f64 x z)) 2)

Compiler

Compiled 6059 to 4627 computations (23.6% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5006	4910

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.1b	(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)))
0.1b	(.f64 (sqrt.f64 (-.f64 y x)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))))
0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.3b	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
0.3b	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))

rewrite51.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`sqrt-prod_binary64_94`
106×	`add-sqr-sqrt_binary64_100`
100×	`times-frac_binary64_84`
96×	`*-un-lft-identity_binary64_78`
68×	`add-cube-cbrt_binary64_113`
16×	`associate-/l*_binary64_23`
14×	`distribute-lft-out--_binary64_30` `difference-of-squares_binary64_47`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`rem-sqrt-square_binary64_91` `associate-/r*_binary64_22` `sqrt-div_binary64_95` `pow1_binary64_139`
4×	`add-log-exp_binary64_117` `div-inv_binary64_75` `associate-/l/_binary64_25`
2×	`sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `frac-2neg_binary64_89` `flip--_binary64_53` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 180

Calls

8 calls:

8.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
8.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
7.0ms	(/.f64 (sqrt.f64 (-.f64 y x)) z)
7.0ms	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.0ms	(.f64 (sqrt.f64 (-.f64 y x)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))))

series453.0ms (0.5%)

Counts

4 → 40

Calls

4 calls:

123.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
123.0ms	(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
105.0ms	(/.f64 (sqrt.f64 (-.f64 y x)) z)
101.0ms	(/.f64 (sqrt.f64 (-.f64 y x)) z)

Compiler

Compiled 2300 to 1534 computations (33.3% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4877	3806
1	4877	3806

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.1b	(/.f64 (sqrt.f64 (-.f64 y x)) z)
0.1b	(.f64 (sqrt.f64 (-.f64 y x)) (.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))))
0.2b	(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)))
0.7b	(cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
0.7b	(cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
0.7b	(cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))

rewrite104.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

244×	`cbrt-prod_binary64_109`
223×	`add-sqr-sqrt_binary64_100`
208×	`times-frac_binary64_84`
181×	`*-un-lft-identity_binary64_78`
131×	`sqrt-prod_binary64_94`
121×	`add-cube-cbrt_binary64_113`
43×	`swap-sqr_binary64_45`
31×	`associate-l_binary64_19` `associate-r_binary64_18`
27×	`distribute-lft-out--_binary64_30`
21×	`difference-of-squares_binary64_47`
16×	`unswap-sqr_binary64_46`
11×	`pow1_binary64_139`
9×	`pow1/3_binary64_160`
7×	`cbrt-div_binary64_110` `div-inv_binary64_75`
6×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
2×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149`
1×	`pow2_binary64_159` `-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-times_binary64_88` `associate-l/_binary64_21` `associate-*r/_binary64_20` `pow-plus_binary64_141`

Counts

4 → 253

Calls

8 calls:

38.0ms	(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)))
7.0ms	(cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
7.0ms	(cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
7.0ms	(cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
0.0ms	(.f64 (sqrt.f64 (-.f64 y x)) (.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))))

series1.1s (1.1%)

Counts

4 → 38

Calls

4 calls:

280.0ms	(cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
274.0ms	(cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))
271.0ms	(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z)))
263.0ms	(cbrt.f64 (/.f64 (sqrt.f64 (-.f64 y x)) z))

Compiler

Compiled 2958 to 1909 computations (35.5% saved)

simplify215.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	4907	7819
1	4907	7819

prune23.6s (23.5%)

Pruning

512 alts after pruning (501 fresh and 11 done)

	Pruned	Kept	Total
New	473	267	740
Fresh	6	234	240
Picked	0	0	0
Done	0	11	11
Total	479	512	991

Error

0.0b

Counts

991 → 512

Compiler

Compiled 32415 to 13050 computations (59.7% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))
0.0b	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64_117`
3×	`sum-log_binary64_169`
2×	`frac-add_binary64_86` `flip-+_binary64_52` `associate-*r/_binary64_20` `flip3-+_binary64_81`
1×	`add-cbrt-cube_binary64_114` `+-commutative_binary64_8` `add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `associate-+l+_binary64_11` `distribute-lft-neg-out_binary64_37` `add-exp-log_binary64_116` `unsub-neg_binary64_72` `*-un-lft-identity_binary64_78` `pow1_binary64_139`

Counts

1 → 16

Calls

2 calls:

10.0ms	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))
0.0ms	(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))

series169.0ms (0.2%)

Counts

1 → 18

Calls

1 calls:

169.0ms

(+.f64 (+.f64 (/.f64 y z) x) (*.f64 (neg.f64 1) (/.f64 x z)))

Compiler

Compiled 253 to 226 computations (10.7% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5942	447

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

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(pow.f64 (-.f64 x (/.f64 x z)) 2)
0.0b	(-.f64 x (/.f64 x z))
0.0b	(/.f64 (-.f64 y x) z)
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.1b	(pow.f64 (-.f64 x (/.f64 x z)) 2)
0.3b	(*.f64 (cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2)) (pow.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))) 1))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
27.5b	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))

rewrite74.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64_100`
51×	`cbrt-prod_binary64_109`
39×	`unpow-prod-down_binary64_157`
25×	`*-un-lft-identity_binary64_78`
20×	`unswap-sqr_binary64_46`
15×	`add-cube-cbrt_binary64_113`
14×	`associate-l_binary64_19`
13×	`sqr-pow_binary64_50`
11×	`associate-r_binary64_18`
10×	`add-exp-log_binary64_116`
7×	`unpow2_binary64_143`
6×	`difference-of-squares_binary64_47` `pow1_binary64_139`
5×	`add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117`
3×	`prod-exp_binary64_127` `distribute-lft-out--_binary64_30` `times-frac_binary64_84` `pow-unpow_binary64_155`
2×	`cbrt-div_binary64_110` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `pow1/3_binary64_160` `distribute-lft-out_binary64_29`
1×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `flip-+_binary64_52` `pow-pow_binary64_150` `pow-prod-down_binary64_149` `flip3-+_binary64_81`

Counts

4 → 112

Calls

8 calls:

27.0ms	(*.f64 (cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2)) (pow.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))) 1))
11.0ms	(pow.f64 (-.f64 x (/.f64 x z)) 2)
9.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
8.0ms	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))
0.0ms	(+.f64 x (/.f64 (-.f64 y x) z))

series2.1s (2.1%)

Counts

4 → 60

Calls

4 calls:

1.4s	(*.f64 (cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2)) (pow.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))) 1))
315.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
236.0ms	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))
123.0ms	(pow.f64 (-.f64 x (/.f64 x z)) 2)

Compiler

Compiled 6181 to 4749 computations (23.2% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4963	5492
1	4963	5492

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.3b	(cbrt.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
0.5b	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))) (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))

rewrite68.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`cbrt-prod_binary64_109`
36×	`*-un-lft-identity_binary64_78`
24×	`add-sqr-sqrt_binary64_100`
18×	`cbrt-div_binary64_110`
16×	`add-cube-cbrt_binary64_113`
11×	`pow1_binary64_139`
9×	`flip-+_binary64_52` `swap-sqr_binary64_45` `pow1/3_binary64_160` `distribute-lft-out_binary64_29` `flip3-+_binary64_81`
7×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94` `add-log-exp_binary64_117` `frac-times_binary64_88` `unswap-sqr_binary64_46`
2×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `sqrt-div_binary64_95` `associate-r/_binary64_20`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-plus_binary64_141`

Counts

4 → 98

Calls

8 calls:

24.0ms	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))) (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
11.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
10.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
9.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
0.0ms	(+.f64 x (/.f64 (-.f64 y x) z))

series2.2s (2.2%)

Counts

4 → 80

Calls

4 calls:

883.0ms	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))) (cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))
450.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
433.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
417.0ms	(cbrt.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 y x) z))))

Compiler

Compiled 10246 to 6796 computations (33.7% saved)

simplify103.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4998	6449
1	4998	6449

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (-.f64 y x) z)
0.0b	(/.f64 (-.f64 y x) z)
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
0.6b	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
27.5b	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))
27.5b	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))

rewrite44.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`cbrt-prod_binary64_109`
20×	`add-sqr-sqrt_binary64_100`
18×	`*-un-lft-identity_binary64_78`
12×	`unpow-prod-down_binary64_157`
10×	`add-cube-cbrt_binary64_113`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `add-log-exp_binary64_117` `pow1/3_binary64_160` `add-exp-log_binary64_116` `difference-of-squares_binary64_47` `pow1_binary64_139`
2×	`flip-+_binary64_52` `distribute-lft-out--_binary64_30` `unpow2_binary64_143` `sqr-pow_binary64_50` `times-frac_binary64_84` `distribute-lft-out_binary64_29` `flip3-+_binary64_81`

Counts

4 → 66

Calls

8 calls:

9.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
9.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
8.0ms	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))
8.0ms	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))
0.0ms	(+.f64 x (/.f64 (-.f64 y x) z))

series914.0ms (0.9%)

Counts

4 → 42

Calls

4 calls:

236.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
231.0ms	(cbrt.f64 (+.f64 x (/.f64 (-.f64 y x) z)))
224.0ms	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))
222.0ms	(cbrt.f64 (pow.f64 (-.f64 x (/.f64 x z)) 2))

Compiler

Compiled 4158 to 2972 computations (28.5% saved)

simplify59.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5137	1910

prune28.5s (28.3%)

Pruning

706 alts after pruning (690 fresh and 16 done)

	Pruned	Kept	Total
New	292	200	492
Fresh	6	490	496
Picked	0	0	0
Done	0	16	16
Total	298	706	1004

Error

Counts

1004 → 706

Compiler

Compiled 15522 to 4620 computations (70.2% saved)

simplify989.0ms (1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5010	60935

regimes8.3s (8.3%)

Compiler: Compiled 104240 to 55386 computations (46.9% saved)

bsearch0.0ms (0%)

regimes99.0ms (0.1%)

Compiler: Compiled 84 to 135 computations (-60.7% saved)

bsearch32.0ms (0%)

Steps

Iters	Range		Point
10	0.0076469624820881005	1164791561.378084	1.0096100883260688
9	-5980.431163081977	-0.0014782792412844793	-1.0081080980265853

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes97.0ms (0.1%)

Compiler: Compiled 69 to 120 computations (-73.9% saved)

bsearch25.0ms (0%)

Steps

Iters	Range		Point
7	1.9461079290483738e-149	1.0523406905049641e-147	1.4187696900043743e-148
7	-5.882054483126471e-130	-3.123111168601651e-132	-1.5516536084389152e-130

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes145.0ms (0.1%)

Compiler: Compiled 54 to 105 computations (-94.4% saved)

bsearch92.0ms (0.1%)

Steps

Iters	Range		Point
10	9.122322027680646e-37	3.544941500751211e-26	9.251475128363361e-37
7	1.1592027721361184e-118	2.1880296394937085e-116	1.735832671204082e-117
7	3.974180417246785e-128	1.932162029454285e-126	1.2944207908337052e-127
9	-4.053363126824742e-155	-5.245801461287932e-160	-9.577831527727277e-158
9	-5.19797493518702e-133	-2.1765158765526175e-138	-1.0843876553453599e-137
9	-2.5862353259953647e-70	-1.5405031060407144e-76	-2.408078771633287e-74

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes103.0ms (0.1%)

Compiler: Compiled 39 to 90 computations (-130.8% saved)

bsearch64.0ms (0.1%)

Steps

Iters	Range		Point
10	0.0076469624820881005	1164791561.378084	3078.309954677097
7	-1.1703115925899998e-190	-8.223428388591964e-193	-2.960284388334264e-191
10	-2.0954773458638973e-20	-8.423762986789772e-35	-1.9604328605987303e-30
10	-6.27597266419544e+48	-6.665832863616659e+38	-4.334045885144298e+42

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes75.0ms (0.1%)

Compiler: Compiled 27 to 75 computations (-177.8% saved)

bsearch30.0ms (0%)

Steps

Iters	Range		Point
10	9.122322027680646e-37	3.544941500751211e-26	3.79913320538792e-30
9	-2.5862353259953647e-70	-1.5405031060407144e-76	-7.18768673884761e-75

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes27.0ms (0%)

Compiler: Compiled 18 to 63 computations (-250% saved)

bsearch0.0ms (0%)

regimes24.0ms (0%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch7.0ms (0%)

Compiler: Compiled 149 to 91 computations (38.9% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	127	179
1	127	179

end0.0ms (0%)

sample16.8s (16.7%)

Algorithm

1×

intervals

Results

207.0ms	8000×	body	128	valid
33.0ms	1338×	body	128	invalid

Compiler

Compiled 26309 to 14041 computations (46.6% saved)

Pareto

0.35908932251068665