Details

analyze820.0ms (9.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
15.6%	84.2%	0.2%	8
15.6%	84.2%	0.2%	9
20.3%	79.5%	0.2%	10
25.3%	74.5%	0.2%	11
34.2%	65.6%	0.2%	12
37.4%	62%	0.6%	13
41.7%	57.7%	0.6%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample30.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
4.0ms	94×	body	128	invalid

Compiler

Compiled 31 to 31 computations (0% saved)

simplify463.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (365.0ms)

Iter	Nodes	Cost
0	4800	16
1	4800	16

prune5.0ms (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

Error

0.1b

Counts

2 → 2

Compiler

Compiled 37 to 33 computations (10.8% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

2.9b	(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))
0.4b	(/.f64 -1/3 z)
0.0b	(-.f64 y (/.f64 t y))
0.0b	(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
0.0b	(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
0.0b	(-.f64 y (/.f64 t y))
0.4b	(/.f64 -1/3 z)
2.9b	(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64_18408`
66×	`times-frac_binary64_18392`
65×	`cancel-sign-sub-inv_binary64_18352`
59×	`*-un-lft-identity_binary64_18386`
55×	`add-cube-cbrt_binary64_18421`
28×	`distribute-lft-in_binary64_18335` `distribute-rgt-in_binary64_18336` `associate-+r+_binary64_18318`
13×	`associate-l_binary64_18327`
11×	`add-cbrt-cube_binary64_18422` `add-exp-log_binary64_18424`
8×	`add-log-exp_binary64_18425`
7×	`div-inv_binary64_18383`
6×	`pow1_binary64_18447` `associate-r_binary64_18326`
5×	`sub-neg_binary64_18379`
4×	`difference-of-squares_binary64_18355`
3×	`associate-/r_binary64_18330` `flip--_binary64_18361` `flip3--_binary64_18390` `associate-/l_binary64_18331`
2×	`frac-times_binary64_18396` `unswap-sqr_binary64_18354` `prod-exp_binary64_18435` `associate-*r/_binary64_18328` `distribute-lft-out--_binary64_18338` `cbrt-undiv_binary64_18420` `cbrt-unprod_binary64_18419` `div-exp_binary64_18437`
1×	`diff-log_binary64_18478` `pow-prod-down_binary64_18457` `flip3-+_binary64_18389` `+-commutative_binary64_18316` `flip-+_binary64_18360` `sum-log_binary64_18477` `frac-2neg_binary64_18397` `associate-l/_binary64_18329` `clear-num_binary64_18385` `-commutative_binary64_18317`

Counts

4 → 160

Calls

8 calls:

16.0ms	(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))
7.0ms	(-.f64 y (/.f64 t y))
7.0ms	(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
3.0ms	(/.f64 -1/3 z)
0.0ms	(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))

series683.0ms (7.8%)

Counts

4 → 57

Calls

4 calls:

376.0ms	(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
218.0ms	(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))
73.0ms	(-.f64 y (/.f64 t y))
16.0ms	(/.f64 -1/3 z)

Compiler

Compiled 1007 to 938 computations (6.9% saved)

simplify94.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4967	2901
1	4967	2901

prune200.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	212	5	217
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	213	6	219

Error

0.0b

Counts

219 → 6

Compiler

Compiled 3540 to 1603 computations (54.7% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

2.9b	(.f64 (.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)))
0.4b	(*.f64 -1/3 (/.f64 1 z))
0.0b	(-.f64 y (/.f64 t y))
0.0b	(+.f64 x (.f64 (.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y))))
0.0b	(+.f64 x (.f64 (.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y))))
0.0b	(-.f64 y (/.f64 t y))
0.4b	(*.f64 -1/3 (/.f64 1 z))
2.9b	(.f64 (.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`cancel-sign-sub-inv_binary64_18352` `add-sqr-sqrt_binary64_18408`
58×	`times-frac_binary64_18392`
53×	`*-un-lft-identity_binary64_18386`
48×	`add-cube-cbrt_binary64_18421`
28×	`distribute-lft-in_binary64_18335` `distribute-rgt-in_binary64_18336` `add-exp-log_binary64_18424` `associate-+r+_binary64_18318`
19×	`associate-r_binary64_18326`
18×	`add-cbrt-cube_binary64_18422`
13×	`prod-exp_binary64_18435`
11×	`pow1_binary64_18447`
8×	`add-log-exp_binary64_18425`
7×	`cbrt-unprod_binary64_18419`
6×	`div-inv_binary64_18383` `associate-*r/_binary64_18328`
5×	`sub-neg_binary64_18379`
4×	`frac-times_binary64_18396` `flip--_binary64_18361` `un-div-inv_binary64_18384` `pow-prod-down_binary64_18457` `associate-l_binary64_18327` `difference-of-squares_binary64_18355` `flip3--_binary64_18390` `div-exp_binary64_18437`
3×	`unswap-sqr_binary64_18354`
2×	`1-exp_binary64_18430` `distribute-lft-out--_binary64_18338` `cbrt-undiv_binary64_18420` `associate-l/_binary64_18329` `rec-exp_binary64_18436` `-commutative_binary64_18317`
1×	`diff-log_binary64_18478` `flip3-+_binary64_18389` `+-commutative_binary64_18316` `flip-+_binary64_18360` `sum-log_binary64_18477`

Counts

4 → 163

Calls

8 calls:

15.0ms	(.f64 (.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)))
8.0ms	(+.f64 x (.f64 (.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y))))
8.0ms	(-.f64 y (/.f64 t y))
8.0ms	(*.f64 -1/3 (/.f64 1 z))
0.0ms	(+.f64 x (.f64 (.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y))))

series665.0ms (7.6%)

Counts

4 → 57

Calls

4 calls:

361.0ms	(+.f64 x (.f64 (.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y))))
213.0ms	(.f64 (.f64 -1/3 (/.f64 1 z)) (-.f64 y (/.f64 t y)))
74.0ms	(-.f64 y (/.f64 t y))
16.0ms	(*.f64 -1/3 (/.f64 1 z))

Compiler

Compiled 1043 to 974 computations (6.6% saved)

simplify98.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4969	2821
1	4969	2821

prune184.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	220	6	226

Error

0.0b

Counts

226 → 6

Compiler

Compiled 3677 to 1739 computations (52.7% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 y (*.f64 z 3))
0.2b	(.f64 (.f64 z 3) y)
0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))
0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
0.2b	(.f64 (.f64 z 3) y)
0.2b	(/.f64 y (*.f64 z 3))
6.4b	(/.f64 t (.f64 (.f64 z 3) y))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-cbrt-cube_binary64_18422` `add-exp-log_binary64_18424`
13×	`add-sqr-sqrt_binary64_18408` `*-un-lft-identity_binary64_18386`
11×	`add-cube-cbrt_binary64_18421`
9×	`pow1_binary64_18447` `times-frac_binary64_18392`
7×	`cancel-sign-sub-inv_binary64_18352` `prod-exp_binary64_18435` `cbrt-unprod_binary64_18419`
6×	`add-log-exp_binary64_18425` `associate-/l*_binary64_18331`
5×	`cbrt-undiv_binary64_18420` `div-exp_binary64_18437`
3×	`div-inv_binary64_18383` `pow-prod-down_binary64_18457` `associate-r_binary64_18326`
2×	`associate-/r*_binary64_18330` `frac-2neg_binary64_18397` `clear-num_binary64_18385`
1×	`flip--_binary64_18361` `diff-log_binary64_18478` `sub-neg_binary64_18379` `associate-l_binary64_18327` `difference-of-squares_binary64_18355` `distribute-lft-out--_binary64_18338` `flip3--_binary64_18390` `*-commutative_binary64_18317`

Counts

4 → 82

Calls

8 calls:

6.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
6.0ms	(/.f64 t (.f64 (.f64 z 3) y))
5.0ms	(.f64 (.f64 z 3) y)
4.0ms	(/.f64 y (*.f64 z 3))
0.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 t (.f64 (*.f64 z 3) y)))

series369.0ms (4.2%)

Counts

4 → 39

Calls

4 calls:

130.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
127.0ms	(/.f64 t (.f64 (.f64 z 3) y))
56.0ms	(/.f64 y (*.f64 z 3))
56.0ms	(.f64 (.f64 z 3) y)

Compiler

Compiled 997 to 873 computations (12.4% saved)

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5366	1209

prune128.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	120	7	127

Error

Counts

127 → 7

Compiler

Compiled 2194 to 1379 computations (37.1% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.6b	(/.f64 1 (/.f64 (*.f64 z 3) (/.f64 t y)))
0.2b	(/.f64 y (*.f64 z 3))
0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
0.0b	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 1 (/.f64 (.f64 z 3) (/.f64 t y))))
0.0b	(-.f64 x (/.f64 y (*.f64 z 3)))
0.2b	(/.f64 y (*.f64 z 3))
0.6b	(/.f64 1 (/.f64 (*.f64 z 3) (/.f64 t y)))
3.6b	(/.f64 (*.f64 z 3) (/.f64 t y))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

179×	`times-frac_binary64_18392`
75×	`add-sqr-sqrt_binary64_18408` `*-un-lft-identity_binary64_18386`
73×	`add-cube-cbrt_binary64_18421`
65×	`add-exp-log_binary64_18424`
39×	`add-cbrt-cube_binary64_18422`
36×	`div-exp_binary64_18437`
32×	`associate-/r*_binary64_18330`
19×	`cbrt-undiv_binary64_18420`
14×	`div-inv_binary64_18383`
9×	`prod-exp_binary64_18435`
7×	`cancel-sign-sub-inv_binary64_18352` `associate-/l*_binary64_18331`
6×	`add-log-exp_binary64_18425` `associate-/r/_binary64_18332`
5×	`pow1_binary64_18447` `1-exp_binary64_18430` `cbrt-unprod_binary64_18419` `rec-exp_binary64_18436`
3×	`frac-2neg_binary64_18397` `clear-num_binary64_18385`
1×	`inv-pow_binary64_18471` `flip--_binary64_18361` `diff-log_binary64_18478` `pow-flip_binary64_18460` `sub-neg_binary64_18379` `difference-of-squares_binary64_18355` `distribute-lft-out--_binary64_18338` `flip3--_binary64_18390`

Counts

4 → 195

Calls

8 calls:

10.0ms	(/.f64 1 (/.f64 (*.f64 z 3) (/.f64 t y)))
7.0ms	(/.f64 (*.f64 z 3) (/.f64 t y))
6.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
4.0ms	(/.f64 y (*.f64 z 3))
0.0ms	(+.f64 (-.f64 x (/.f64 y (.f64 z 3))) (/.f64 1 (/.f64 (.f64 z 3) (/.f64 t y))))

series451.0ms (5.1%)

Counts

4 → 42

Calls

4 calls:

133.0ms	(-.f64 x (/.f64 y (*.f64 z 3)))
132.0ms	(/.f64 (*.f64 z 3) (/.f64 t y))
129.0ms	(/.f64 1 (/.f64 (*.f64 z 3) (/.f64 t y)))
57.0ms	(/.f64 y (*.f64 z 3))

Compiler

Compiled 1201 to 1065 computations (11.3% saved)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4908	3405
1	4908	3405

prune235.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	237	7	244

Error

Counts

244 → 7

Compiler

Compiled 4931 to 2723 computations (44.8% saved)

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	2006	1010
1	2006	1010

regimes505.0ms (5.7%)

Accuracy

Total 0.8b remaining (99.1%)

Threshold costs 0.8b (99.1%)

Compiler

Compiled 3534 to 2975 computations (15.8% saved)

bsearch45.0ms (0.5%)

Steps

Iters	Range		Point
7	4.920833073152757e-49	4.485652948537715e-47	1.4493721208221e-48
7	-3.880709402827725e+108	-2.355788145412525e+106	-2.408599115432412e+106

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	72
1	71	72

end0.0ms (0%)

sample3.4s (38.3%)

Algorithm

1×

intervals

Results

377.0ms	8000×	body	128	valid
148.0ms	3050×	body	128	invalid

Compiler

Compiled 2163 to 1779 computations (17.8% saved)

Pareto

0.04040763358020919

Details

analyze820.0ms (9.3%)

sample30.0ms (0.3%)

simplify463.0ms (5.3%)

prune5.0ms (0.1%)

localize9.0ms (0.1%)

rewrite48.0ms (0.5%)

series683.0ms (7.8%)

simplify94.0ms (1.1%)

prune200.0ms (2.3%)

localize10.0ms (0.1%)

rewrite57.0ms (0.6%)

series665.0ms (7.6%)

simplify98.0ms (1.1%)

prune184.0ms (2.1%)

localize10.0ms (0.1%)

rewrite27.0ms (0.3%)

series369.0ms (4.2%)

simplify66.0ms (0.7%)

prune128.0ms (1.5%)

localize11.0ms (0.1%)

rewrite46.0ms (0.5%)

series451.0ms (5.1%)

simplify92.0ms (1%)

prune235.0ms (2.7%)

simplify68.0ms (0.8%)

regimes505.0ms (5.7%)

bsearch45.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (38.3%)

Profiling