Details

analyze674.0ms (6.5%)

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
7.8%	92%	0.2%	8
16.4%	83.4%	0.2%	9
23.8%	76%	0.2%	10
25.1%	74.7%	0.2%	11
38.1%	59.4%	2.5%	12
41.8%	55.3%	2.9%	13
46.5%	50.3%	3.1%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample24.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
2.0ms	56×	body	128	invalid

Compiler

Compiled 23 to 25 computations (-8.7% saved)

simplify367.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (264.0ms)

Iter	Nodes	Cost
0	1484	16
1	1484	16

prune2.0ms (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

Error

4.6b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

4.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
0.0b	(/.f64 t (-.f64 1 z))
0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.0b	(/.f64 t (-.f64 1 z))
4.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

rewrite80.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

111×	`add-sqr-sqrt_binary64_13399`
107×	`*-un-lft-identity_binary64_13377`
88×	`times-frac_binary64_13383`
72×	`cancel-sign-sub-inv_binary64_13343`
46×	`add-cube-cbrt_binary64_13412`
34×	`difference-of-squares_binary64_13346`
25×	`distribute-rgt-in_binary64_13327` `distribute-lft-in_binary64_13326`
21×	`distribute-lft-out--_binary64_13329`
10×	`associate-r_binary64_13317`
8×	`associate-/r/_binary64_13323`
7×	`add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
6×	`associate-/r*_binary64_13321` `flip3--_binary64_13381` `flip--_binary64_13352`
5×	`pow1_binary64_13438` `add-log-exp_binary64_13416`
4×	`div-inv_binary64_13374`
3×	`associate-l_binary64_13318` `associate-r/_binary64_13319` `associate-/l_binary64_13322` `sub-neg_binary64_13370`
2×	`frac-sub_binary64_13386`
1×	`prod-exp_binary64_13426` `diff-log_binary64_13469` `clear-num_binary64_13376` `cbrt-unprod_binary64_13410` `unswap-sqr_binary64_13345` `pow-prod-down_binary64_13448` `*-commutative_binary64_13308` `div-exp_binary64_13428` `cbrt-undiv_binary64_13411` `frac-2neg_binary64_13388`

Counts

3 → 162

Calls

6 calls:

29.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
28.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
6.0ms	(/.f64 t (-.f64 1 z))
0.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.0ms	(/.f64 t (-.f64 1 z))

series528.0ms (5.1%)

Counts

3 → 54

Calls

3 calls:

300.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
166.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
62.0ms	(/.f64 t (-.f64 1 z))

Compiler

Compiled 948 to 816 computations (13.9% saved)

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5234	3709

prune213.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	207	9	216
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	207	10	217

Error

1.0b

Counts

217 → 10

Compiler

Compiled 3670 to 1743 computations (52.5% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 t (-.f64 1 z))
0.0b	(/.f64 t (-.f64 1 z))
0.0b	(/.f64 t (-.f64 1 z))
0.0b	(-.f64 (/.f64 y z) (.f64 (.f64 (cbrt.f64 (/.f64 t (-.f64 1 z))) (cbrt.f64 (/.f64 t (-.f64 1 z)))) (cbrt.f64 (/.f64 t (-.f64 1 z)))))
4.4b	(.f64 x (-.f64 (/.f64 y z) (.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 1 z))) (cbrt.f64 (/.f64 t (-.f64 1 z)))) (cbrt.f64 (/.f64 t (-.f64 1 z))))))
12.3b	(cbrt.f64 (/.f64 t (-.f64 1 z)))
12.3b	(cbrt.f64 (/.f64 t (-.f64 1 z)))
12.3b	(cbrt.f64 (/.f64 t (-.f64 1 z)))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`cbrt-prod_binary64_13408`
65×	`add-sqr-sqrt_binary64_13399`
63×	`*-un-lft-identity_binary64_13377`
54×	`times-frac_binary64_13383`
36×	`add-cube-cbrt_binary64_13412`
18×	`difference-of-squares_binary64_13346`
15×	`cbrt-div_binary64_13409`
12×	`associate-*r/_binary64_13319`
9×	`distribute-lft-out--_binary64_13329`
7×	`frac-sub_binary64_13386`
6×	`pow1_binary64_13438` `add-exp-log_binary64_13415` `associate-/r/_binary64_13323` `add-cbrt-cube_binary64_13413`
5×	`associate-*l/_binary64_13320` `frac-times_binary64_13387`
4×	`flip3--_binary64_13381` `flip--_binary64_13352` `add-log-exp_binary64_13416`
3×	`associate-r_binary64_13317` `div-inv_binary64_13374` `pow1/3_binary64_13459` `associate-l_binary64_13318`
2×	`distribute-rgt-in_binary64_13327` `distribute-lft-in_binary64_13326` `sub-neg_binary64_13370` `cancel-sign-sub-inv_binary64_13343`
1×	`prod-exp_binary64_13426` `cbrt-unprod_binary64_13410` `unswap-sqr_binary64_13345` `pow-prod-down_binary64_13448` `*-commutative_binary64_13308`

Counts

4 → 130

Calls

8 calls:

12.0ms	(.f64 x (-.f64 (/.f64 y z) (.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 1 z))) (cbrt.f64 (/.f64 t (-.f64 1 z)))) (cbrt.f64 (/.f64 t (-.f64 1 z))))))
6.0ms	(cbrt.f64 (/.f64 t (-.f64 1 z)))
6.0ms	(cbrt.f64 (/.f64 t (-.f64 1 z)))
6.0ms	(cbrt.f64 (/.f64 t (-.f64 1 z)))
0.0ms	(-.f64 (/.f64 y z) (.f64 (.f64 (cbrt.f64 (/.f64 t (-.f64 1 z))) (cbrt.f64 (/.f64 t (-.f64 1 z)))) (cbrt.f64 (/.f64 t (-.f64 1 z)))))

series990.0ms (9.5%)

Counts

4 → 53

Calls

4 calls:

346.0ms	(.f64 x (-.f64 (/.f64 y z) (.f64 (*.f64 (cbrt.f64 (/.f64 t (-.f64 1 z))) (cbrt.f64 (/.f64 t (-.f64 1 z)))) (cbrt.f64 (/.f64 t (-.f64 1 z))))))
222.0ms	(cbrt.f64 (/.f64 t (-.f64 1 z)))
215.0ms	(cbrt.f64 (/.f64 t (-.f64 1 z)))
207.0ms	(cbrt.f64 (/.f64 t (-.f64 1 z)))

Compiler

Compiled 2314 to 1921 computations (17% saved)

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4964	3618
1	4964	3618

prune283.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	185	8	193

Error

0.3b

Counts

193 → 8

Compiler

Compiled 5632 to 3478 computations (38.2% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 t (-.f64 1 z))
0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
4.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
5.8b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
5.8b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
5.8b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))

rewrite121.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64_13399`
55×	`*-un-lft-identity_binary64_13377`
48×	`cancel-sign-sub-inv_binary64_13343`
44×	`times-frac_binary64_13383`
26×	`add-cube-cbrt_binary64_13412`
25×	`distribute-rgt-in_binary64_13327` `distribute-lft-in_binary64_13326`
16×	`difference-of-squares_binary64_13346`
12×	`associate-*r/_binary64_13319`
10×	`associate-r_binary64_13317` `distribute-lft-out--_binary64_13329`
9×	`cbrt-div_binary64_13409`
6×	`pow1_binary64_13438` `flip3--_binary64_13381` `flip--_binary64_13352` `add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
4×	`frac-sub_binary64_13386` `add-log-exp_binary64_13416` `associate-/r/_binary64_13323`
3×	`cbrt-prod_binary64_13408` `pow1/3_binary64_13459` `associate-l_binary64_13318`
2×	`div-inv_binary64_13374` `sub-neg_binary64_13370`
1×	`prod-exp_binary64_13426` `cbrt-unprod_binary64_13410` `unswap-sqr_binary64_13345` `pow-prod-down_binary64_13448` `*-commutative_binary64_13308`

Counts

4 → 114

Calls

8 calls:

32.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
25.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
23.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
23.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
0.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

series2.2s (20.7%)

Counts

4 → 85

Calls

4 calls:

620.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
618.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
602.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
316.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 8338 to 5847 computations (29.9% saved)

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4994	5183
1	4994	5183

prune432.0ms (4.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	198	9	207

Error

0.3b

Counts

207 → 9

Compiler

Compiled 9310 to 4982 computations (46.5% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.6b	(cbrt.f64 x)
0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.0b	(/.f64 t (-.f64 1 z))
0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
2.0b	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
2.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))

rewrite73.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_13399`
20×	`*-un-lft-identity_binary64_13377`
18×	`pow1_binary64_13438` `add-exp-log_binary64_13415`
11×	`associate-l_binary64_13318` `add-cbrt-cube_binary64_13413`
10×	`cbrt-prod_binary64_13408`
9×	`prod-exp_binary64_13426` `add-cube-cbrt_binary64_13412` `cbrt-unprod_binary64_13410` `pow-prod-down_binary64_13448`
8×	`times-frac_binary64_13383`
7×	`associate-r_binary64_13317`
6×	`associate-*l/_binary64_13320`
4×	`distribute-lft-out--_binary64_13329` `difference-of-squares_binary64_13346` `add-log-exp_binary64_13416`
3×	`associate-*r/_binary64_13319`
2×	`frac-sub_binary64_13386` `unswap-sqr_binary64_13345` `pow1/3_binary64_13459` `*-commutative_binary64_13308` `flip3--_binary64_13381` `flip--_binary64_13352`

Counts

4 → 79

Calls

8 calls:

33.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))
30.0ms	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

series1.0s (9.7%)

Counts

4 → 52

Calls

4 calls:

541.0ms	(*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x))
324.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))) (cbrt.f64 x)))
77.0ms	(cbrt.f64 x)
72.0ms	(cbrt.f64 x)

Compiler

Compiled 1456 to 1174 computations (19.4% saved)

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4947	2038
1	4947	2038

prune99.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	131	9	140

Error

0.3b

Counts

140 → 9

Compiler

Compiled 2512 to 994 computations (60.4% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	532	1150
1	532	1150

regimes560.0ms (5.4%)

Compiler: Compiled 5111 to 3909 computations (23.5% saved)

bsearch2.0ms (0%)

Compiler: Compiled 9 to 9 computations (0% saved)

regimes150.0ms (1.4%)

Compiler: Compiled 704 to 749 computations (-6.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 9 computations (0% saved)

regimes107.0ms (1%)

Compiler: Compiled 492 to 574 computations (-16.7% saved)

bsearch0.0ms (0%)

regimes159.0ms (1.5%)

Compiler: Compiled 156 to 236 computations (-51.3% saved)

bsearch35.0ms (0.3%)

Steps

Iters	Range		Point
8	2.3372972800024355e-05	0.00699379209196945	0.006930783671939834
6	-1.6834101773030716	-0.1322794553243022	-0.987684137996394

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes77.0ms (0.7%)

Compiler: Compiled 96 to 172 computations (-79.2% saved)

bsearch31.0ms (0.3%)

Steps

Iters	Range		Point
8	2.3372972800024355e-05	0.00699379209196945	0.006930783671939834
5	-8.189444581686234e-35	-3.0113749134299977e-35	-4.2658667193930415e-35

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes67.0ms (0.6%)

Compiler: Compiled 68 to 144 computations (-111.8% saved)

bsearch45.0ms (0.4%)

Steps

Iters	Range		Point
8	13530440.382379593	25561275006.735416	13708614.872476278
10	-5.017534419595682e-74	-1.8023189935569e-88	-4.1058533444088976e-74

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes40.0ms (0.4%)

Compiler: Compiled 40 to 116 computations (-190% saved)

bsearch0.0ms (0%)

regimes36.0ms (0.3%)

Accuracy

Total 2.5b remaining (88%)

Threshold costs 0b (0%)

Compiler

Compiled 20 to 92 computations (-360% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 252 to 159 computations (36.9% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	119	330
1	119	330

end0.0ms (0%)

sample1.5s (14.6%)

Algorithm

1×

intervals

Results

322.0ms	8000×	body	128	valid
73.0ms	1823×	body	128	invalid

Compiler

Compiled 1066 to 793 computations (25.6% saved)

Pareto

0.7464001207848057

Details

analyze674.0ms (6.5%)

sample24.0ms (0.2%)

simplify367.0ms (3.5%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite80.0ms (0.8%)

series528.0ms (5.1%)

simplify88.0ms (0.8%)

prune213.0ms (2%)

localize13.0ms (0.1%)

rewrite46.0ms (0.4%)

series990.0ms (9.5%)

simplify108.0ms (1%)

prune283.0ms (2.7%)

localize14.0ms (0.1%)

rewrite121.0ms (1.2%)

series2.2s (20.7%)

simplify106.0ms (1%)

prune432.0ms (4.1%)

localize13.0ms (0.1%)

rewrite73.0ms (0.7%)

series1.0s (9.7%)

simplify92.0ms (0.9%)

prune99.0ms (0.9%)

simplify22.0ms (0.2%)

regimes560.0ms (5.4%)

bsearch2.0ms (0%)

regimes150.0ms (1.4%)

bsearch1.0ms (0%)

regimes107.0ms (1%)

bsearch0.0ms (0%)

regimes159.0ms (1.5%)

bsearch35.0ms (0.3%)

regimes77.0ms (0.7%)

bsearch31.0ms (0.3%)

regimes67.0ms (0.6%)

bsearch45.0ms (0.4%)

regimes40.0ms (0.4%)

bsearch0.0ms (0%)

regimes36.0ms (0.3%)

bsearch9.0ms (0.1%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample1.5s (14.6%)

Profiling