Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample25.0ms (0.2%)

Algorithm

1×

intervals

Results

7.0ms	47×	body	1024	valid
5.0ms	130×	body	128	valid
5.0ms	46×	body	512	valid
2.0ms	33×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify127.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune4.0ms (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

11.0b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
3.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite157.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`*-un-lft-identity_binary64_419`
53×	`times-frac_binary64_425`
43×	`add-sqr-sqrt_binary64_441`
26×	`add-cube-cbrt_binary64_454` `cancel-sign-sub-inv_binary64_385`
17×	`distribute-lft-out_binary64_370`
14×	`distribute-lft-out--_binary64_371` `associate-+l+_binary64_352`
10×	`add-log-exp_binary64_458`
9×	`div-inv_binary64_416`
7×	`add-exp-log_binary64_457`
6×	`difference-of-squares_binary64_388`
5×	`add-cbrt-cube_binary64_455`
4×	`associate-/r*_binary64_363` `pow1_binary64_480`
3×	`frac-add_binary64_427` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `sub-neg_binary64_412` `sum-log_binary64_510` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip-+_binary64_393` `diff-log_binary64_511` `flip--_binary64_394` `div-exp_binary64_470` `frac-sub_binary64_428`
1×	`clear-num_binary64_418` `1-exp_binary64_463` `inv-pow_binary64_504` `associate-+l-_binary64_354` `rec-exp_binary64_469` `frac-2neg_binary64_430` `pow-flip_binary64_493` `+-commutative_binary64_349` `cbrt-undiv_binary64_453`

Counts

3 → 112

Calls

3 calls:

82.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
44.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
11.0ms	(/.f64 1 (+.f64 x 1))

series128.0ms (1%)

Counts

3 → 9

Calls

3 calls:

87.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
26.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
15.0ms	(/.f64 1 (+.f64 x 1))

simplify132.0ms (1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5039	2123

prune195.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	3	122

Error

0.4b

Counts

122 → 3

Compiler

Compiled 2553 to 2057 computations (19.4% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))
0.3b	(*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
6.2b	(-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1)))
16.7b	(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))

rewrite822.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Rules

1125×	`times-frac_binary64_425`
1051×	`*-un-lft-identity_binary64_419`
960×	`add-sqr-sqrt_binary64_441`
341×	`difference-of-squares_binary64_388`
308×	`distribute-lft-out--_binary64_371`
283×	`add-cube-cbrt_binary64_454`
247×	`cancel-sign-sub-inv_binary64_385`
100×	`difference-of-sqr-1_binary64_389`
93×	`div-inv_binary64_416`
58×	`frac-sub_binary64_428`
45×	`flip3--_binary64_423` `flip--_binary64_394`
39×	`associate-/r/_binary64_365`
35×	`associate-/l*_binary64_364`
28×	`associate--l+_binary64_356` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
27×	`frac-times_binary64_429`
24×	`distribute-lft-out_binary64_370`
23×	`associate-/r*_binary64_363`
21×	`swap-sqr_binary64_386`
18×	`associate-/l/_binary64_366`
17×	`add-exp-log_binary64_457`
14×	`pow1_binary64_480`
13×	`associate-r_binary64_359` `associate-l_binary64_360` `add-cbrt-cube_binary64_455`
9×	`associate-l/_binary64_362` `associate-r/_binary64_361`
7×	`div-exp_binary64_470`
6×	`add-log-exp_binary64_458`
5×	`sub-neg_binary64_412`
4×	`cbrt-undiv_binary64_453`
2×	`clear-num_binary64_418` `pow-div_binary64_494` `frac-2neg_binary64_430`
1×	`pow-prod-down_binary64_490` `1-exp_binary64_463` `inv-pow_binary64_504` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `rec-exp_binary64_469` `pow-plus_binary64_482` `*-commutative_binary64_350` `pow-flip_binary64_493` `diff-log_binary64_511` `pow-sqr_binary64_392` `pow-prod-up_binary64_489` `pow2_binary64_500` `div-sub_binary64_424`

Counts

4 → 791

Calls

4 calls:

237.0ms	(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))
151.0ms	(-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1)))
92.0ms	(*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
27.0ms	(/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))

series371.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

258.0ms	(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))
67.0ms	(-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1)))
34.0ms	(*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
12.0ms	(/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))

simplify460.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

803 → 803

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5004	36837

prune7.5s (56.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	802	1	803
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	802	4	806

Error

0.4b

Counts

806 → 4

Compiler

Compiled 47554 to 37793 computations (20.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (+.f64 1 x))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
18.9b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite125.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_419`
44×	`associate-*r/_binary64_361`
32×	`frac-add_binary64_427`
30×	`flip3--_binary64_423` `flip--_binary64_394`
28×	`add-sqr-sqrt_binary64_441`
21×	`times-frac_binary64_425`
20×	`flip3-+_binary64_422` `add-cube-cbrt_binary64_454` `frac-times_binary64_429` `flip-+_binary64_393`
18×	`associate-/l/_binary64_366`
10×	`associate-l/_binary64_362` `associate-l*_binary64_360` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`distribute-lft-out_binary64_370`
8×	`unpow3_binary64_485` `pow1_binary64_480` `distribute-rgt-out_binary64_372`
7×	`associate-r_binary64_359` `associate-/r*_binary64_363`
6×	`add-log-exp_binary64_458` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`distribute-lft-neg-in_binary64_376` `sub-neg_binary64_412` `neg-mul-1_binary64_415` `distribute-rgt-neg-in_binary64_377` `cancel-sign-sub-inv_binary64_385` `associate-+l+_binary64_352`
3×	`associate-/l*_binary64_364`
2×	`associate-+r+_binary64_351` `pow-prod-down_binary64_490` `difference-of-squares_binary64_388` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r/_binary64_365` `*-commutative_binary64_350`
1×	`clear-num_binary64_418` `difference-of-sqr-1_binary64_389` `div-inv_binary64_416` `sum-log_binary64_510` `distribute-lft-out--_binary64_371` `frac-2neg_binary64_430` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 153

Calls

4 calls:

48.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
21.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
17.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
13.0ms	(*.f64 x (+.f64 1 x))

series75.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
26.0ms	(*.f64 x (+.f64 1 x))
12.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
5.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5412	6096

prune441.0ms (3.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	167	2	169

Error

0.4b

Counts

169 → 2

Compiler

Compiled 6902 to 4747 computations (31.2% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

0.4b	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_419`
21×	`times-frac_binary64_425`
13×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
8×	`unpow3_binary64_485` `distribute-lft-out_binary64_370` `distribute-rgt-out_binary64_372`
7×	`associate-/r*_binary64_363`
4×	`distribute-lft-neg-in_binary64_376` `neg-mul-1_binary64_415` `distribute-rgt-neg-in_binary64_377`
3×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `associate-/l*_binary64_364`
2×	`associate-/r/_binary64_365`
1×	`flip3-+_binary64_422` `clear-num_binary64_418` `add-log-exp_binary64_458` `div-inv_binary64_416` `frac-2neg_binary64_430` `flip-+_binary64_393` `pow1_binary64_480` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

1 → 45

Calls

1 calls:

19.0ms

(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

series30.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

30.0ms

(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4913	775
1	4913	775

prune89.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Error

Counts

50 → 5

Compiler

Compiled 661 to 498 computations (24.7% saved)

regimes186.0ms (1.4%)

Accuracy

Total 0.1b remaining (96.8%)

Threshold costs 0.1b (96.8%)

Compiler

Compiled 1708 to 1422 computations (16.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	13
1	9	13

end0.0ms (0%)

sample2.2s (16.2%)

Algorithm

1×

intervals

Results

275.0ms	1310×	body	1024	valid
244.0ms	4434×	body	128	valid
232.0ms	1492×	body	512	valid
82.0ms	764×	body	256	valid

Compiler

Compiled 872 to 726 computations (16.7% saved)

Details

analyze9.0ms (0.1%)

sample25.0ms (0.2%)

simplify127.0ms (1%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite157.0ms (1.2%)

series128.0ms (1%)

simplify132.0ms (1%)

prune195.0ms (1.5%)

localize26.0ms (0.2%)

rewrite822.0ms (6.2%)

series371.0ms (2.8%)

simplify460.0ms (3.5%)

prune7.5s (56.6%)

localize16.0ms (0.1%)

rewrite125.0ms (0.9%)

series75.0ms (0.6%)

simplify92.0ms (0.7%)

prune441.0ms (3.3%)

localize5.0ms (0%)

rewrite26.0ms (0.2%)

series30.0ms (0.2%)

simplify67.0ms (0.5%)

prune89.0ms (0.7%)

regimes186.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (16.2%)

Profiling