Details

analyze1.2s (0.2%)

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%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample70.0ms (0%)

Algorithm

1×

intervals

Results

15.0ms	44×	body	1024	valid
14.0ms	165×	body	128	valid
9.0ms	29×	body	1024	nan
7.0ms	27×	body	512	valid
4.0ms	45×	body	128	nan
4.0ms	20×	body	256	valid
3.0ms	12×	body	512	nan
2.0ms	12×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify219.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5192	41

prune6.0ms (0%)

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: 41.5b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
11.6b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
18.4b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite104.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_100`
13×	`sqrt-prod_binary64_94`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
7×	`pow1_binary64_139`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `associate-r_binary64_18` `flip--_binary64_53`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `associate--l+_binary64_15` `unswap-sqr_binary64_46` `associate-/r/_binary64_24`
1×	`distribute-lft-in_binary64_27` `-commutative_binary64_9` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `pow-prod-down_binary64_149` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 80

Calls

4 calls:

36.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
27.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
10.0ms	(*.f64 (sqrt.f64 2) t)

series2.0s (0.3%)

Counts

4 → 12

Calls

4 calls:

1.1s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
470.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
339.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
44.0ms	(*.f64 (sqrt.f64 2) t)

simplify79.0ms (0%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5269	3058

prune652.0ms (0.1%)

Pruning

43 alts after pruning (42 fresh and 1 done)

	Pruned	Kept	Total
New	50	42	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	43	93

Merged error: 5.4b

Counts

93 → 43

Compiler

Compiled 5313 to 3278 computations (38.3% saved)

localize31.0ms (0%)

Local error

Found 4 expressions with local error:

3.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
4.3b	(/.f64 (*.f64 l l) x)
7.1b	(/.f64 (*.f64 t t) x)
24.5b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
8×	`associate-*r/_binary64_20`
6×	`add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`frac-add_binary64_86` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `sqrt-div_binary64_95` `flip3-+_binary64_81`
3×	`sqrt-prod_binary64_94`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-+r+_binary64_10` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `distribute-lft-in_binary64_27` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `pow1/2_binary64_158` `sum-log_binary64_169`

Counts

4 → 74

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
8.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)

series226.0ms (0%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
69.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
13.0ms	(/.f64 (*.f64 t t) x)
13.0ms	(/.f64 (*.f64 l l) x)

simplify117.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4990	1973
1	4990	1973

prune1.2s (0.2%)

Pruning

74 alts after pruning (73 fresh and 1 done)

	Pruned	Kept	Total
New	51	35	86
Fresh	3	38	41
Picked	1	0	1
Done	0	1	1
Total	55	74	129

Merged error: 4.3b

Counts

129 → 74

Compiler

Compiled 5974 to 3256 computations (45.5% saved)

localize34.0ms (0%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
3.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
7.1b	(/.f64 (*.f64 t t) x)
24.5b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite53.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `associate-*r/_binary64_20`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`flip-+_binary64_52` `pow1_binary64_139` `flip3-+_binary64_81`
4×	`frac-add_binary64_86` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-+r+_binary64_10` `sum-log_binary64_169`
1×	`distribute-lft-in_binary64_27` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 64

Calls

4 calls:

15.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))
15.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
9.0ms	(/.f64 (*.f64 t t) x)
5.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))

series199.0ms (0%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))
47.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
29.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
14.0ms	(/.f64 (*.f64 t t) x)

simplify102.0ms (0%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4966	2011
1	4966	2011

prune1.1s (0.2%)

Pruning

86 alts after pruning (85 fresh and 1 done)

	Pruned	Kept	Total
New	53	23	76
Fresh	10	62	72
Picked	1	0	1
Done	0	1	1
Total	64	86	150

Merged error: 4.3b

Counts

150 → 86

Compiler

Compiled 6242 to 3420 computations (45.2% saved)

localize39.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
3.0b	(+.f64 (.f64 4 (.f64 (/.f64 t (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))) (.f64 2 (+.f64 (.f64 t t) (.f64 l (/.f64 l x)))))
24.5b	(sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))) (.f64 2 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))))

rewrite62.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`associate-*r/_binary64_20`
22×	`add-sqr-sqrt_binary64_100`
16×	`cbrt-prod_binary64_109`
13×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
12×	`frac-add_binary64_86` `pow1_binary64_139`
9×	`flip-+_binary64_52` `flip3-+_binary64_81`
8×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
6×	`associate-l_binary64_19` `swap-sqr_binary64_45` `pow1/3_binary64_160` `associate-r_binary64_18` `add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `frac-times_binary64_88` `associate-*l/_binary64_21` `unswap-sqr_binary64_46`
3×	`sqrt-prod_binary64_94`
2×	`+-commutative_binary64_8` `pow-sqr_binary64_51` `associate-+r+_binary64_10` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149` `sum-log_binary64_169`
1×	`pow2_binary64_159` `distribute-lft-in_binary64_27` `*-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `pow-plus_binary64_141` `pow1/2_binary64_158`

Counts

4 → 91

Calls

4 calls:

21.0ms	(+.f64 (.f64 4 (.f64 (/.f64 t (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))) (.f64 2 (+.f64 (.f64 t t) (.f64 l (/.f64 l x)))))
16.0ms	(sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))) (.f64 2 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))))
7.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
5.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))

series512.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))) (.f64 2 (+.f64 (.f64 t t) (.f64 l (/.f64 l x))))))
150.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
103.0ms	(+.f64 (.f64 4 (.f64 (/.f64 t (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 t (cbrt.f64 x)))) (.f64 2 (+.f64 (.f64 t t) (.f64 l (/.f64 l x)))))
45.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))

simplify160.0ms (0%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4943	2875
1	4943	2875

prune1.9s (0.3%)

Pruning

115 alts after pruning (113 fresh and 2 done)

	Pruned	Kept	Total
New	62	41	103
Fresh	12	72	84
Picked	0	1	1
Done	0	1	1
Total	74	115	189

Merged error: 4.3b

Counts

189 → 115

Compiler

Compiled 4057 to 1609 computations (60.3% saved)

regimes7.6s (1.3%)

Compiler: Compiled 65988 to 43677 computations (33.8% saved)

bsearch9.7min (97%)

Steps

Iters	Range		Point
9	6.553056853359995e+117	2.0405494163677858e+123	7.443333160970164e+118
8	7.304855387291916e-160	1.2455879138501324e-155	7.461029769105877e-160
5	6.196010096559689e-219	1.3824996933640603e-218	1.3625553722859779e-218
10	-9.428170475410259e+110	-3.416520553836596e+98	-1.9365101723127776e+110

Compiler

Compiled 1 to 3 computations (-200% saved)

Details

analyze1.2s (0.2%)

sample70.0ms (0%)

simplify219.0ms (0%)

prune6.0ms (0%)

localize23.0ms (0%)

rewrite104.0ms (0%)

series2.0s (0.3%)

simplify79.0ms (0%)

prune652.0ms (0.1%)

localize31.0ms (0%)

rewrite34.0ms (0%)

series226.0ms (0%)

simplify117.0ms (0%)

prune1.2s (0.2%)

localize34.0ms (0%)

rewrite53.0ms (0%)

series199.0ms (0%)

simplify102.0ms (0%)

prune1.1s (0.2%)

localize39.0ms (0%)

rewrite62.0ms (0%)

series512.0ms (0.1%)

simplify160.0ms (0%)

prune1.9s (0.3%)

regimes7.6s (1.3%)

bsearch9.7min (97%)

Profiling