Details

analyze608.0ms (10.3%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
5.0ms	117×	body	128	invalid

Compiler

Compiled 31 to 26 computations (16.1% saved)

simplify170.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4898	19
1	4898	19

prune6.0ms (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

10.6b

Counts

2 → 2

Compiler

Compiled 41 to 31 computations (24.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

11.1b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
1.8b	(-.f64 (.f64 z z) (.f64 x x))
1.8b	(-.f64 (.f64 z z) (.f64 x x))
11.1b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac_binary64_13383`
11×	`add-cube-cbrt_binary64_13412` `*-un-lft-identity_binary64_13377` `add-sqr-sqrt_binary64_13399`
5×	`difference-of-squares_binary64_13346`
4×	`add-log-exp_binary64_13416` `add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413` `associate-/l*_binary64_13322`
3×	`associate-/r*_binary64_13321`
2×	`associate-/l/_binary64_13324` `pow1_binary64_13438` `flip3--_binary64_13381` `flip--_binary64_13352`
1×	`diff-log_binary64_13469` `div-inv_binary64_13374` `clear-num_binary64_13376` `div-sub_binary64_13382` `div-exp_binary64_13428` `cbrt-undiv_binary64_13411` `frac-2neg_binary64_13388` `sub-neg_binary64_13370` `cancel-sign-sub-inv_binary64_13343`

Counts

2 → 47

Calls

4 calls:

8.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
5.0ms	(-.f64 (.f64 z z) (.f64 x x))
0.0ms	(-.f64 (.f64 z z) (.f64 x x))
0.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series298.0ms (5.1%)

Counts

2 → 27

Calls

2 calls:

203.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
95.0ms	(-.f64 (.f64 z z) (.f64 x x))

Compiler

Compiled 538 to 496 computations (7.8% saved)

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4963	1124
1	4963	1124

prune98.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	70	6	76

Error

0.0b

Counts

76 → 6

Compiler

Compiled 1374 to 421 computations (69.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_13399`
38×	`*-un-lft-identity_binary64_13377`
31×	`times-frac_binary64_13383`
22×	`add-cube-cbrt_binary64_13412`
19×	`associate-r_binary64_13317`
9×	`add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
7×	`distribute-lft-out--_binary64_13329` `difference-of-squares_binary64_13346`
5×	`associate-/l*_binary64_13322`
4×	`pow1_binary64_13438` `associate-l_binary64_13318`
3×	`associate-/r*_binary64_13321`
2×	`prod-exp_binary64_13426` `associate-/l/_binary64_13324` `div-inv_binary64_13374` `associate-*l/_binary64_13320` `cbrt-unprod_binary64_13410` `unswap-sqr_binary64_13345` `frac-times_binary64_13387` `div-exp_binary64_13428` `add-log-exp_binary64_13416` `cbrt-undiv_binary64_13411` `flip-+_binary64_13351` `flip3-+_binary64_13380`
1×	`clear-num_binary64_13376` `pow-prod-down_binary64_13448` `-commutative_binary64_13308` `distribute-lft-out_binary64_13328` `div-sub_binary64_13382` `flip3--_binary64_13381` `flip--_binary64_13352` `associate-r/_binary64_13319` `frac-2neg_binary64_13388`

Counts

2 → 81

Calls

4 calls:

14.0ms	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))
7.0ms	(/.f64 (-.f64 z x) y)
0.0ms	(/.f64 (-.f64 z x) y)
0.0ms	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))

series327.0ms (5.6%)

Counts

2 → 30

Calls

2 calls:

212.0ms	(*.f64 (+.f64 z x) (/.f64 (-.f64 z x) y))
115.0ms	(/.f64 (-.f64 z x) y)

Compiler

Compiled 656 to 544 computations (17.1% saved)

simplify92.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4973	1506
1	4973	1506

prune95.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	110	7	117

Error

Counts

117 → 7

Compiler

Compiled 2074 to 626 computations (69.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
0.0b	(/.f64 y (-.f64 z x))
0.0b	(/.f64 y (-.f64 z x))
0.4b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`times-frac_binary64_13383`
161×	`*-un-lft-identity_binary64_13377`
117×	`add-sqr-sqrt_binary64_13399`
79×	`add-cube-cbrt_binary64_13412`
26×	`associate-/r*_binary64_13321`
22×	`distribute-lft-out_binary64_13328`
19×	`distribute-lft-out--_binary64_13329` `difference-of-squares_binary64_13346`
13×	`associate-/r/_binary64_13323`
9×	`add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
7×	`div-inv_binary64_13374` `associate-/l*_binary64_13322`
6×	`flip3--_binary64_13381` `flip--_binary64_13352`
4×	`div-exp_binary64_13428` `cbrt-undiv_binary64_13411`
2×	`associate-/l/_binary64_13324` `clear-num_binary64_13376` `pow1_binary64_13438` `add-log-exp_binary64_13416` `frac-2neg_binary64_13388`
1×	`flip-+_binary64_13351` `flip3-+_binary64_13380`

Counts

2 → 163

Calls

4 calls:

13.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
6.0ms	(/.f64 y (-.f64 z x))
0.0ms	(/.f64 y (-.f64 z x))
0.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

series533.0ms (9.1%)

Counts

2 → 42

Calls

2 calls:

405.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
127.0ms	(/.f64 y (-.f64 z x))

Compiler

Compiled 1003 to 795 computations (20.7% saved)

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4982	4571
1	4982	4571

prune165.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	205	7	212

Error

Counts

212 → 7

Compiler

Compiled 4569 to 1242 computations (72.8% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_13408`
23×	`add-sqr-sqrt_binary64_13399`
15×	`add-cube-cbrt_binary64_13412` `*-un-lft-identity_binary64_13377`
11×	`pow1_binary64_13438`
9×	`pow1/3_binary64_13459`
6×	`swap-sqr_binary64_13344` `associate-r_binary64_13317` `add-exp-log_binary64_13415` `associate-l_binary64_13318`
4×	`unswap-sqr_binary64_13345` `add-log-exp_binary64_13416` `add-cbrt-cube_binary64_13413`
2×	`pow-prod-down_binary64_13448` `pow-sqr_binary64_13350` `pow-prod-up_binary64_13447`
1×	`prod-exp_binary64_13426` `cbrt-unprod_binary64_13410` `pow-plus_binary64_13440` `*-commutative_binary64_13308` `pow2_binary64_13458`

Counts

4 → 73

Calls

8 calls:

7.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)
0.0ms	(/.f64 (+.f64 z x) (*.f64 (cbrt.f64 y) (cbrt.f64 y)))

series305.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
80.0ms	(cbrt.f64 y)
73.0ms	(cbrt.f64 y)
69.0ms	(cbrt.f64 y)

Compiler

Compiled 538 to 406 computations (24.5% saved)

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune79.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	85	7	92

Error

Counts

92 → 7

Compiler

Compiled 1913 to 599 computations (68.7% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	391	811
1	391	811

regimes386.0ms (6.6%)

Compiler: Compiled 4016 to 2675 computations (33.4% saved)

bsearch0.0ms (0%)

regimes124.0ms (2.1%)

Compiler: Compiled 465 to 487 computations (-4.7% saved)

bsearch0.0ms (0%)

regimes199.0ms (3.4%)

Compiler: Compiled 400 to 437 computations (-9.3% saved)

bsearch42.0ms (0.7%)

Steps

Iters	Range		Point
9	22.64377946160851	18176197239.016254	724227.9020631777
8	-3.989740375762617e-13	-1.4077725901979837e-15	-1.4502890771219212e-15

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes162.0ms (2.8%)

Compiler: Compiled 195 to 250 computations (-28.2% saved)

bsearch113.0ms (1.9%)

Steps

Iters	Range		Point
10	7.699818039358096e+133	1.0298446419944856e+144	1.0170312198005829e+144
9	22.64377946160851	18176197239.016254	30.5176369781239
8	-3.989740375762617e-13	-1.4077725901979837e-15	-7.292625313747265e-15
11	-8.255342438864258e+172	-2.166032747925588e+153	-1.3512482171332066e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes140.0ms (2.4%)

Compiler: Compiled 123 to 174 computations (-41.5% saved)

bsearch103.0ms (1.7%)

Steps

Iters	Range		Point
9	9.18044574974965e+147	1.7772298817752564e+156	1.341976696412328e+154
8	2.106528432160388e-95	6.447971974562053e-92	2.7611911349035228e-92
4	-3.712567143078006e-149	-2.1075035317617728e-149	-2.458611196737199e-149
9	-3.8456683870585264e+86	-1.1201164401222231e+79	-3.7848748461932285e+86

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes41.0ms (0.7%)

Compiler: Compiled 60 to 106 computations (-76.7% saved)

bsearch0.0ms (0%)

regimes24.0ms (0.4%)

Accuracy

Total 0.1b remaining (69.9%)

Threshold costs 0.1b (69.9%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch9.0ms (0.2%)

Compiler: Compiled 193 to 115 computations (40.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	141	200
1	141	200

end0.0ms (0%)

sample1.3s (22.8%)

Algorithm

1×

intervals

Results

327.0ms	8000×	body	128	valid
119.0ms	2885×	body	128	invalid

Compiler

Compiled 707 to 491 computations (30.6% saved)

Pareto

0.24493217032218897

Details

analyze608.0ms (10.3%)

sample30.0ms (0.5%)

simplify170.0ms (2.9%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

rewrite20.0ms (0.3%)

series298.0ms (5.1%)

simplify66.0ms (1.1%)

prune98.0ms (1.7%)

localize11.0ms (0.2%)

rewrite29.0ms (0.5%)

series327.0ms (5.6%)

simplify92.0ms (1.6%)

prune95.0ms (1.6%)

localize9.0ms (0.2%)

rewrite38.0ms (0.7%)

series533.0ms (9.1%)

simplify76.0ms (1.3%)

prune165.0ms (2.8%)

localize13.0ms (0.2%)

rewrite17.0ms (0.3%)

series305.0ms (5.2%)

simplify83.0ms (1.4%)

prune79.0ms (1.3%)

simplify15.0ms (0.3%)

regimes386.0ms (6.6%)

bsearch0.0ms (0%)

regimes124.0ms (2.1%)

bsearch0.0ms (0%)

regimes199.0ms (3.4%)

bsearch42.0ms (0.7%)

regimes162.0ms (2.8%)

bsearch113.0ms (1.9%)

regimes140.0ms (2.4%)

bsearch103.0ms (1.7%)

regimes41.0ms (0.7%)

bsearch0.0ms (0%)

regimes24.0ms (0.4%)

bsearch9.0ms (0.2%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.3s (22.8%)

Profiling