Details

analyze581.0ms (11%)

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
21.8%	78%	0.1%	7
26.5%	73.3%	0.1%	8
36.7%	63.2%	0.1%	9
41.3%	49.9%	8.7%	10
47.2%	43.3%	9.5%	11
54.4%	35.5%	10.1%	12
57.9%	27.4%	14.7%	13
61.7%	23.2%	15.1%	14

Compiler

Compiled 8 to 8 computations (0% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	19×	body	128	invalid

Compiler

Compiled 15 to 18 computations (-20% saved)

simplify211.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	569	10
1	569	10

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
6×	`cancel-sign-sub-inv_binary64_726` `associate-r_binary64_700`
5×	`add-cube-cbrt_binary64_795`
4×	`distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `frac-times_binary64_770` `associate-l_binary64_701`
3×	`flip3-+_binary64_763` `add-exp-log_binary64_798` `flip-+_binary64_734` `add-cbrt-cube_binary64_796` `pow1_binary64_821` `flip--_binary64_735` `flip3--_binary64_764`
2×	`associate-l/_binary64_703` `difference-of-squares_binary64_729` `associate-r/_binary64_702` `sub-neg_binary64_753`
1×	`unswap-sqr_binary64_728` `distribute-lft-out_binary64_711` `prod-exp_binary64_809` `add-log-exp_binary64_799` `distribute-lft-out--_binary64_712` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

1 → 38

Calls

1 calls:

18.0ms

(*.f64 (+.f64 x y) (-.f64 1 z))

series46.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

46.0ms

(*.f64 (+.f64 x y) (-.f64 1 z))

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5049	608

prune67.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0b

Counts

42 → 3

Compiler

Compiled 593 to 273 computations (54% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`associate-r_binary64_700`
8×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
7×	`add-log-exp_binary64_799`
6×	`associate-*l/_binary64_703` `flip3-+_binary64_763` `add-cube-cbrt_binary64_795` `flip-+_binary64_734`
4×	`add-exp-log_binary64_798` `frac-add_binary64_768` `add-cbrt-cube_binary64_796` `associate-l_binary64_701` `pow1_binary64_821`
3×	`distribute-lft-neg-in_binary64_717` `sum-log_binary64_851` `distribute-rgt-neg-in_binary64_718`
2×	`distribute-rgt-neg-out_binary64_720`
1×	`neg-mul-1_binary64_756` `unswap-sqr_binary64_728` `distribute-lft-out_binary64_711` `prod-exp_binary64_809` `associate-+l+_binary64_693` `unsub-neg_binary64_754` `+-commutative_binary64_690` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

2 → 47

Calls

2 calls:

16.0ms	(*.f64 (+.f64 x y) (neg.f64 z))
13.0ms	(+.f64 (+.f64 x y) (*.f64 (+.f64 x y) (neg.f64 z)))

series123.0ms (2.3%)

Counts

2 → 6

Calls

2 calls:

68.0ms	(+.f64 (+.f64 x y) (*.f64 (+.f64 x y) (neg.f64 z)))
55.0ms	(*.f64 (+.f64 x y) (neg.f64 z))

simplify115.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5091	787

prune69.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	53	3	56

Merged error: 0b

Counts

56 → 3

Compiler

Compiled 852 to 260 computations (69.5% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 x y) (-.f64 1 z))
0.0b	(sqrt.f64 (*.f64 (+.f64 x y) (-.f64 1 z)))
0.0b	(sqrt.f64 (*.f64 (+.f64 x y) (-.f64 1 z)))
0.3b	(.f64 (sqrt.f64 (.f64 (+.f64 x y) (-.f64 1 z))) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 1 z))))

rewrite134.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

160×	`sqrt-div_binary64_777`
148×	`frac-times_binary64_770`
63×	`flip3-+_binary64_763` `flip-+_binary64_734` `flip--_binary64_735` `flip3--_binary64_764`
61×	`pow1_binary64_821`
50×	`associate-l/_binary64_703` `associate-r/_binary64_702`
32×	`sqrt-pow1_binary64_778`
23×	`pow-prod-down_binary64_831`
19×	`add-sqr-sqrt_binary64_782`
17×	`*-un-lft-identity_binary64_760`
12×	`add-cube-cbrt_binary64_795` `pow1/2_binary64_840`
10×	`associate-r_binary64_700` `pow-prod-up_binary64_830`
8×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `associate-l_binary64_701`
6×	`sqrt-prod_binary64_776` `cancel-sign-sub-inv_binary64_726` `pow-sqr_binary64_733`
4×	`distribute-lft-in_binary64_709` `add-log-exp_binary64_799` `distribute-rgt-in_binary64_710` `swap-sqr_binary64_727`
2×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `difference-of-squares_binary64_729` `cbrt-unprod_binary64_793` `sub-neg_binary64_753` `*-commutative_binary64_691`
1×	`pow2_binary64_841` `distribute-lft-out_binary64_711` `rem-square-sqrt_binary64_772` `pow-plus_binary64_823` `sqrt-unprod_binary64_780` `distribute-lft-out--_binary64_712`

Counts

4 → 205

Calls

4 calls:

41.0ms	(.f64 (sqrt.f64 (.f64 (+.f64 x y) (-.f64 1 z))) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 1 z))))
18.0ms	(*.f64 (+.f64 x y) (-.f64 1 z))
12.0ms	(sqrt.f64 (*.f64 (+.f64 x y) (-.f64 1 z)))
12.0ms	(sqrt.f64 (*.f64 (+.f64 x y) (-.f64 1 z)))

series593.0ms (11.3%)

Counts

4 → 12

Calls

4 calls:

280.0ms	(.f64 (sqrt.f64 (.f64 (+.f64 x y) (-.f64 1 z))) (sqrt.f64 (*.f64 (+.f64 x y) (-.f64 1 z))))
141.0ms	(sqrt.f64 (*.f64 (+.f64 x y) (-.f64 1 z)))
125.0ms	(sqrt.f64 (*.f64 (+.f64 x y) (-.f64 1 z)))
47.0ms	(*.f64 (+.f64 x y) (-.f64 1 z))

simplify219.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5087	6874

prune485.0ms (9.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	217	3	220

Merged error: 0b

Counts

220 → 3

Compiler

Compiled 6208 to 3040 computations (51% saved)

localize30.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 (+.f64 1 (+.f64 z (.f64 z z))) (-.f64 x y))
2.0b	(-.f64 (.f64 x x) (.f64 y y))
2.6b	(.f64 (-.f64 1 (pow.f64 z 3)) (-.f64 (.f64 x x) (*.f64 y y)))
34.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 z 3)) (-.f64 (.f64 x x) (.f64 y y))) (.f64 (+.f64 1 (+.f64 z (*.f64 z z))) (-.f64 x y)))

rewrite135.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_782`
20×	`*-un-lft-identity_binary64_760` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
19×	`flip--_binary64_735` `flip3--_binary64_764`
16×	`frac-times_binary64_770` `associate-l_binary64_701`
11×	`difference-of-squares_binary64_729`
10×	`add-cube-cbrt_binary64_795`
9×	`cancel-sign-sub-inv_binary64_726` `associate-r_binary64_700`
8×	`associate-l/_binary64_703` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `associate-r/_binary64_702` `pow1_binary64_821`
6×	`prod-exp_binary64_809` `flip3-+_binary64_763` `distribute-lft-in_binary64_709` `add-log-exp_binary64_799` `distribute-rgt-in_binary64_710` `flip-+_binary64_734` `cbrt-unprod_binary64_793`
5×	`sub-neg_binary64_753`
4×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
2×	`unswap-sqr_binary64_728` `distribute-lft-out--_binary64_712` `sqr-pow_binary64_732` `cube-prod_binary64_788` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `unpow-prod-down_binary64_839`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `distribute-lft-out_binary64_711` `associate-/r_binary64_704` `div-inv_binary64_757` `associate-/l_binary64_705` `clear-num_binary64_759` `times-frac_binary64_766`

Counts

4 → 127

Calls

4 calls:

44.0ms	(/.f64 (.f64 (-.f64 1 (pow.f64 z 3)) (-.f64 (.f64 x x) (.f64 y y))) (.f64 (+.f64 1 (+.f64 z (*.f64 z z))) (-.f64 x y)))
32.0ms	(.f64 (-.f64 1 (pow.f64 z 3)) (-.f64 (.f64 x x) (*.f64 y y)))
22.0ms	(.f64 (+.f64 1 (+.f64 z (.f64 z z))) (-.f64 x y))
7.0ms	(-.f64 (.f64 x x) (.f64 y y))

series446.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(/.f64 (.f64 (-.f64 1 (pow.f64 z 3)) (-.f64 (.f64 x x) (.f64 y y))) (.f64 (+.f64 1 (+.f64 z (*.f64 z z))) (-.f64 x y)))
123.0ms	(.f64 (-.f64 1 (pow.f64 z 3)) (-.f64 (.f64 x x) (*.f64 y y)))
51.0ms	(.f64 (+.f64 1 (+.f64 z (.f64 z z))) (-.f64 x y))
39.0ms	(-.f64 (.f64 x x) (.f64 y y))

simplify192.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	5101	3432

prune296.0ms (5.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	3	142

Merged error: 0b

Counts

142 → 3

Compiler

Compiled 4535 to 1939 computations (57.2% saved)

regimes224.0ms (4.2%)

Compiler: Compiled 812 to 692 computations (14.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms (0%)

sample1.1s (20.4%)

Algorithm

1×

intervals

Results

369.0ms	7998×	body	128	valid
28.0ms	632×	body	128	invalid
0.0ms	2×	body	1024	valid

Compiler

Compiled 145 to 125 computations (13.8% saved)

Details

analyze581.0ms (11%)

sample25.0ms (0.5%)

simplify211.0ms (4%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite22.0ms (0.4%)

series46.0ms (0.9%)

simplify96.0ms (1.8%)

prune67.0ms (1.3%)

localize11.0ms (0.2%)

rewrite35.0ms (0.7%)

series123.0ms (2.3%)

simplify115.0ms (2.2%)

prune69.0ms (1.3%)

localize19.0ms (0.4%)

rewrite134.0ms (2.5%)

series593.0ms (11.3%)

simplify219.0ms (4.2%)

prune485.0ms (9.2%)

localize30.0ms (0.6%)

rewrite135.0ms (2.6%)

series446.0ms (8.5%)

simplify192.0ms (3.6%)

prune296.0ms (5.6%)

regimes224.0ms (4.2%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (20.4%)

Profiling