Details

analyze882.0ms (15.1%)

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
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
33.3%	66.5%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify274.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4896	16
1	4896	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

Merged error: 1.6b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
1.8b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64_17622`
71×	`*-un-lft-identity_binary64_17601`
51×	`times-frac_binary64_17607`
31×	`associate-r_binary64_17543`
27×	`add-cube-cbrt_binary64_17633`
22×	`distribute-lft-out--_binary64_17555` `difference-of-squares_binary64_17570`
10×	`add-cbrt-cube_binary64_17634` `add-exp-log_binary64_17636`
5×	`associate-/r_binary64_17547` `add-log-exp_binary64_17637` `pow1_binary64_17659` `associate-/l_binary64_17548`
4×	`associate-/r/_binary64_17549`
3×	`flip--_binary64_17576` `associate-l_binary64_17544` `flip3--_binary64_17605`
2×	`prod-exp_binary64_17647` `cbrt-undiv_binary64_17632` `unswap-sqr_binary64_17569` `associate-/l/_binary64_17550` `cbrt-unprod_binary64_17631` `div-inv_binary64_17598` `div-exp_binary64_17649`
1×	`associate-r/_binary64_17545` `flip-+_binary64_17575` `+-commutative_binary64_17533` `flip3-+_binary64_17604` `div-sub_binary64_17606` `clear-num_binary64_17600` `-commutative_binary64_17534` `sum-log_binary64_17689` `frac-2neg_binary64_17612` `pow-prod-down_binary64_17669`

Counts

3 → 113

Calls

3 calls:

18.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
10.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

series447.0ms (7.6%)

Counts

3 → 9

Calls

3 calls:

227.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
155.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
66.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6250	2068

prune110.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Merged error: 0b

Counts

123 → 7

Compiler

Compiled 2337 to 511 computations (78.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 z (-.f64 z a))
0.0b	(+.f64 x (*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))))
0.0b	(-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))
1.8b	(*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))))

rewrite104.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64_17601`
62×	`add-sqr-sqrt_binary64_17622`
51×	`times-frac_binary64_17607`
28×	`distribute-lft-out--_binary64_17555`
20×	`add-cube-cbrt_binary64_17633`
18×	`associate-r_binary64_17543`
16×	`difference-of-squares_binary64_17570`
10×	`associate-/r/_binary64_17549`
8×	`add-log-exp_binary64_17637` `add-cbrt-cube_binary64_17634` `add-exp-log_binary64_17636`
7×	`flip--_binary64_17576` `flip3--_binary64_17605`
6×	`distribute-rgt-out--_binary64_17557` `pow1_binary64_17659`
5×	`associate-/r*_binary64_17547` `div-inv_binary64_17598` `sub-neg_binary64_17594`
4×	`associate-*r/_binary64_17545`
3×	`associate-/l_binary64_17548` `associate-l*_binary64_17544`
2×	`frac-sub_binary64_17610` `distribute-lft-in_binary64_17552` `sub-div_binary64_17608` `distribute-rgt-in_binary64_17553` `associate-+r+_binary64_17535`
1×	`prod-exp_binary64_17647` `cbrt-undiv_binary64_17632` `flip-+_binary64_17575` `+-commutative_binary64_17533` `diff-log_binary64_17690` `flip3-+_binary64_17604` `unswap-sqr_binary64_17569` `clear-num_binary64_17600` `cbrt-unprod_binary64_17631` `*-commutative_binary64_17534` `sum-log_binary64_17689` `frac-2neg_binary64_17612` `pow-prod-down_binary64_17669` `div-exp_binary64_17649`

Counts

4 → 117

Calls

4 calls:

40.0ms	(*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))))
37.0ms	(-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))
8.0ms	(+.f64 x (*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))))
6.0ms	(/.f64 z (-.f64 z a))

series822.0ms (14%)

Counts

4 → 12

Calls

4 calls:

335.0ms	(*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))))
240.0ms	(+.f64 x (*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))))
190.0ms	(-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))
56.0ms	(/.f64 z (-.f64 z a))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5040	2330

prune101.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	131	5	136

Merged error: 0b

Counts

136 → 5

Compiler

Compiled 2878 to 602 computations (79.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 z a))
0.5b	(cbrt.f64 (-.f64 z a))
0.5b	(cbrt.f64 (-.f64 z a))
5.4b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))

rewrite75.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64_17622`
60×	`*-un-lft-identity_binary64_17601`
50×	`times-frac_binary64_17607`
46×	`associate-r_binary64_17543`
42×	`cbrt-prod_binary64_17629`
28×	`add-cube-cbrt_binary64_17633`
25×	`add-exp-log_binary64_17636`
20×	`cbrt-div_binary64_17630`
18×	`add-cbrt-cube_binary64_17634`
16×	`distribute-lft-out--_binary64_17555` `difference-of-squares_binary64_17570`
15×	`associate-l_binary64_17544`
10×	`flip--_binary64_17576` `associate-/r/_binary64_17549` `flip3--_binary64_17605`
8×	`prod-exp_binary64_17647` `cbrt-unprod_binary64_17631`
7×	`cbrt-undiv_binary64_17632` `div-exp_binary64_17649`
6×	`pow1_binary64_17659` `unswap-sqr_binary64_17569`
5×	`frac-times_binary64_17611`
4×	`add-log-exp_binary64_17637`
3×	`associate-r/_binary64_17545` `associate-l/_binary64_17546` `pow1/3_binary64_17680`
2×	`div-inv_binary64_17598`
1×	`*-commutative_binary64_17534` `pow-prod-down_binary64_17669`

Counts

4 → 136

Calls

4 calls:

46.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))
4.0ms	(cbrt.f64 (-.f64 z a))
4.0ms	(cbrt.f64 (-.f64 z a))
4.0ms	(cbrt.f64 (-.f64 z a))

series930.0ms (15.9%)

Counts

4 → 12

Calls

4 calls:

275.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))
224.0ms	(cbrt.f64 (-.f64 z a))
216.0ms	(cbrt.f64 (-.f64 z a))
216.0ms	(cbrt.f64 (-.f64 z a))

simplify88.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4947	3456
1	4947	3456

prune138.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	148	5	153

Merged error: 0b

Counts

153 → 5

Compiler

Compiled 4287 to 780 computations (81.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
0.0b	(/.f64 y (-.f64 z a))
7.4b	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_17622`
39×	`*-un-lft-identity_binary64_17601`
31×	`times-frac_binary64_17607`
23×	`add-cube-cbrt_binary64_17633`
21×	`associate-l_binary64_17544`
10×	`add-cbrt-cube_binary64_17634` `add-exp-log_binary64_17636`
8×	`distribute-lft-out--_binary64_17555` `difference-of-squares_binary64_17570`
5×	`associate-/r_binary64_17547` `add-log-exp_binary64_17637` `pow1_binary64_17659` `associate-r*_binary64_17543`
4×	`flip--_binary64_17576` `associate-/r/_binary64_17549` `sub-neg_binary64_17594` `flip3--_binary64_17605`
3×	`associate-/l*_binary64_17548`
2×	`associate-*r/_binary64_17545` `prod-exp_binary64_17647` `frac-times_binary64_17611` `cbrt-undiv_binary64_17632` `unswap-sqr_binary64_17569` `distribute-lft-in_binary64_17552` `cbrt-unprod_binary64_17631` `div-inv_binary64_17598` `distribute-rgt-in_binary64_17553` `div-exp_binary64_17649` `associate-+r+_binary64_17535`
1×	`associate-l/_binary64_17546` `flip-+_binary64_17575` `+-commutative_binary64_17533` `flip3-+_binary64_17604` `clear-num_binary64_17600` `-commutative_binary64_17534` `sum-log_binary64_17689` `frac-2neg_binary64_17612` `pow-prod-down_binary64_17669`

Counts

3 → 98

Calls

3 calls:

19.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))
6.0ms	(/.f64 y (-.f64 z a))
4.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))

series576.0ms (9.8%)

Counts

3 → 9

Calls

3 calls:

257.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))
251.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
68.0ms	(/.f64 y (-.f64 z a))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4967	1655
1	4967	1655

prune69.0ms (1.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Merged error: 0b

Counts

112 → 5

Compiler

Compiled 1868 to 417 computations (77.7% saved)

regimes77.0ms (1.3%)

Compiler: Compiled 390 to 330 computations (15.4% saved)

bsearch39.0ms (0.7%)

Steps

Iters	Range		Point
8	6.774575129630024e-111	3.102171530431565e-106	1.3883953432163486e-108
8	-1.4636702452871036e-19	-8.162948217039944e-24	-6.850122719949887e-23

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	66
1	59	66

end0.0ms (0%)

sample753.0ms (12.9%)

Algorithm

1×

intervals

Results

315.0ms	7999×	body	128	valid
30.0ms	727×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 144 to 106 computations (26.4% saved)

Details

analyze882.0ms (15.1%)

sample22.0ms (0.4%)

simplify274.0ms (4.7%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite45.0ms (0.8%)

series447.0ms (7.6%)

simplify75.0ms (1.3%)

prune110.0ms (1.9%)

localize10.0ms (0.2%)

rewrite104.0ms (1.8%)

series822.0ms (14%)

simplify76.0ms (1.3%)

prune101.0ms (1.7%)

localize13.0ms (0.2%)

rewrite75.0ms (1.3%)

series930.0ms (15.9%)

simplify88.0ms (1.5%)

prune138.0ms (2.4%)

localize9.0ms (0.1%)

rewrite39.0ms (0.7%)

series576.0ms (9.8%)

simplify72.0ms (1.2%)

prune69.0ms (1.2%)

regimes77.0ms (1.3%)

bsearch39.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample753.0ms (12.9%)

Profiling