Details

analyze1.2s (11.1%)

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
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.2%	83.5%	0.3%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	219×	body	128	valid
2.0ms	13×	body	1024	valid
2.0ms	16×	body	512	valid
1.0ms	36×	body	128	invalid
1.0ms	7×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify250.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5014	19

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: 21.5b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y x) (-.f64 z t))
1.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
14.7b	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_18275` `add-sqr-sqrt_binary64_18296`
13×	`flip3--_binary64_18279` `flip--_binary64_18250`
10×	`add-exp-log_binary64_18310` `add-cbrt-cube_binary64_18308`
8×	`associate-/l/_binary64_18224` `frac-times_binary64_18285`
7×	`add-cube-cbrt_binary64_18307`
5×	`associate-l_binary64_18218` `associate-r_binary64_18217` `times-frac_binary64_18281` `add-log-exp_binary64_18311` `pow1_binary64_18333` `associate-/r*_binary64_18221`
4×	`associate-l/_binary64_18220` `associate-r/_binary64_18219` `distribute-lft-out--_binary64_18229` `difference-of-squares_binary64_18244`
2×	`sub-neg_binary64_18268` `div-exp_binary64_18323` `cbrt-undiv_binary64_18306` `associate-/r/_binary64_18223` `cbrt-unprod_binary64_18305` `prod-exp_binary64_18321`
1×	`clear-num_binary64_18274` `pow-prod-down_binary64_18343` `distribute-rgt-in_binary64_18227` `distribute-lft-in_binary64_18226` `unswap-sqr_binary64_18243` `flip-+_binary64_18249` `+-commutative_binary64_18207` `div-inv_binary64_18272` `-commutative_binary64_18208` `frac-2neg_binary64_18286` `associate-/l_binary64_18222` `distribute-lft-out_binary64_18228` `flip3-+_binary64_18278` `sum-log_binary64_18363`

Counts

3 → 79

Calls

3 calls:

15.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
11.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
9.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

series972.0ms (9.1%)

Counts

3 → 9

Calls

3 calls:

518.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
372.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
83.0ms	(*.f64 (-.f64 y x) (-.f64 z t))

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	6765	1609

prune100.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 3.2b

Counts

89 → 11

Compiler

Compiled 2019 to 552 computations (72.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
1.8b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
3.5b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

rewrite129.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

330×	`times-frac_binary64_18281`
323×	`*-un-lft-identity_binary64_18275`
321×	`add-sqr-sqrt_binary64_18296`
113×	`add-cube-cbrt_binary64_18307`
104×	`distribute-lft-out--_binary64_18229` `difference-of-squares_binary64_18244`
36×	`associate-/r*_binary64_18221`
15×	`associate-/r/_binary64_18223`
10×	`add-exp-log_binary64_18310` `associate-/l*_binary64_18222` `add-cbrt-cube_binary64_18308`
9×	`flip3--_binary64_18279` `flip--_binary64_18250`
8×	`div-inv_binary64_18272`
5×	`add-log-exp_binary64_18311`
4×	`associate-/l/_binary64_18224` `div-exp_binary64_18323` `cbrt-undiv_binary64_18306`
3×	`pow1_binary64_18333` `div-sub_binary64_18280`
2×	`clear-num_binary64_18274` `frac-2neg_binary64_18286`
1×	`flip-+_binary64_18249` `+-commutative_binary64_18207` `associate-+r-_binary64_18211` `distribute-lft-out_binary64_18228` `flip3-+_binary64_18278` `sum-log_binary64_18363`

Counts

3 → 274

Calls

3 calls:

55.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
19.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
10.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

series1.2s (10.8%)

Counts

3 → 9

Calls

3 calls:

544.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
523.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
94.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

simplify122.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4987	8451
1	4987	8451

prune228.0ms (2.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	278	5	283
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	281	13	294

Merged error: 3.2b

Counts

294 → 13

Compiler

Compiled 7248 to 1051 computations (85.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
3.5b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
3.5b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
7.8b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))) (cbrt.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))) (cbrt.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))))

rewrite215.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

915×	`times-frac_binary64_18281`
850×	`*-un-lft-identity_binary64_18275` `add-sqr-sqrt_binary64_18296`
298×	`add-cube-cbrt_binary64_18307`
276×	`distribute-lft-out--_binary64_18229` `difference-of-squares_binary64_18244`
93×	`associate-/r*_binary64_18221`
39×	`associate-/r/_binary64_18223`
21×	`flip3--_binary64_18279` `div-inv_binary64_18272` `flip--_binary64_18250`
19×	`add-exp-log_binary64_18310` `add-cbrt-cube_binary64_18308`
15×	`associate-/l*_binary64_18222`
9×	`div-exp_binary64_18323` `cbrt-undiv_binary64_18306`
6×	`add-log-exp_binary64_18311` `associate-/l/_binary64_18224`
4×	`pow1_binary64_18333`
3×	`clear-num_binary64_18274` `frac-2neg_binary64_18286` `div-sub_binary64_18280`
1×	`flip-+_binary64_18249` `+-commutative_binary64_18207` `flip3-+_binary64_18278` `sum-log_binary64_18363`

Counts

4 → 638

Calls

4 calls:

20.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
20.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
20.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
4.0ms	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))) (cbrt.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))) (cbrt.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))))

series2.1s (19.8%)

Counts

4 → 12

Calls

4 calls:

558.0ms	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))) (cbrt.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))) (cbrt.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))))
536.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
519.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
517.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

simplify251.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

650 → 650

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4966	21540
1	4966	21540

prune727.0ms (6.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	650	0	650
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	650	13	663

Merged error: 3.2b

Counts

663 → 13

Compiler

Compiled 34322 to 2396 computations (93% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a t))
0.6b	(cbrt.f64 (-.f64 a t))
3.2b	(.f64 (/.f64 (-.f64 y x) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
7.8b	(+.f64 x (.f64 (/.f64 (-.f64 y x) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))))

rewrite80.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64_18296`
59×	`*-un-lft-identity_binary64_18275`
52×	`times-frac_binary64_18281`
46×	`associate-r_binary64_18217`
37×	`cbrt-prod_binary64_18303`
27×	`add-cube-cbrt_binary64_18307`
25×	`add-exp-log_binary64_18310`
18×	`cbrt-div_binary64_18304` `add-cbrt-cube_binary64_18308`
17×	`associate-l_binary64_18218`
16×	`distribute-lft-out--_binary64_18229` `difference-of-squares_binary64_18244`
10×	`associate-/r/_binary64_18223`
9×	`flip3--_binary64_18279` `flip--_binary64_18250`
8×	`cbrt-unprod_binary64_18305` `prod-exp_binary64_18321`
7×	`div-exp_binary64_18323` `cbrt-undiv_binary64_18306`
6×	`add-log-exp_binary64_18311` `unswap-sqr_binary64_18243` `pow1_binary64_18333`
5×	`frac-times_binary64_18285`
3×	`associate-l/_binary64_18220` `associate-r/_binary64_18219`
2×	`pow1/3_binary64_18354` `div-inv_binary64_18272`
1×	`pow-prod-down_binary64_18343` `flip-+_binary64_18249` `+-commutative_binary64_18207` `*-commutative_binary64_18208` `flip3-+_binary64_18278` `sum-log_binary64_18363`

Counts

4 → 134

Calls

4 calls:

48.0ms	(.f64 (/.f64 (-.f64 y x) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
5.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y x) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))))
4.0ms	(cbrt.f64 (-.f64 a t))
4.0ms	(cbrt.f64 (-.f64 a t))

series1.5s (13.7%)

Counts

4 → 12

Calls

4 calls:

528.0ms	(.f64 (/.f64 (-.f64 y x) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
514.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y x) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))))
219.0ms	(cbrt.f64 (-.f64 a t))
210.0ms	(cbrt.f64 (-.f64 a t))

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5317	3969

prune127.0ms (1.2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	146	13	159

Merged error: 3.2b

Counts

159 → 13

Compiler

Compiled 4454 to 708 computations (84.1% saved)

regimes189.0ms (1.8%)

Compiler: Compiled 1495 to 890 computations (40.5% saved)

bsearch63.0ms (0.6%)

Steps

Iters	Range		Point
7	2.3333570559780574e-214	1.5857394658940334e-212	8.086779230574728e-213
11	-3.381672303726889e-160	-1.4952301374919493e-179	-9.273760752644893e-169

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	52
1	83	52

end0.0ms (0%)

sample1.1s (9.9%)

Algorithm

1×

intervals

Results

296.0ms	6667×	body	128	valid
59.0ms	399×	body	1024	valid
56.0ms	510×	body	512	valid
48.0ms	1212×	body	128	invalid
27.0ms	355×	body	256	valid
13.0ms	69×	body	2048	valid

Compiler

Compiled 393 to 235 computations (40.2% saved)

Details

analyze1.2s (11.1%)

sample27.0ms (0.3%)

simplify250.0ms (2.3%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite43.0ms (0.4%)

series972.0ms (9.1%)

simplify64.0ms (0.6%)

prune100.0ms (0.9%)

localize10.0ms (0.1%)

rewrite129.0ms (1.2%)

series1.2s (10.8%)

simplify122.0ms (1.1%)

prune228.0ms (2.1%)

localize19.0ms (0.2%)

rewrite215.0ms (2%)

series2.1s (19.8%)

simplify251.0ms (2.3%)

prune727.0ms (6.8%)

localize13.0ms (0.1%)

rewrite80.0ms (0.7%)

series1.5s (13.7%)

simplify69.0ms (0.6%)

prune127.0ms (1.2%)

regimes189.0ms (1.8%)

bsearch63.0ms (0.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.1s (9.9%)

Profiling