Details

analyze1.1s (9%)

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)

sample28.0ms (0.2%)

Algorithm

1×

intervals

Results

9.0ms	212×	body	128	valid
2.0ms	18×	body	512	valid
2.0ms	46×	body	128	invalid
1.0ms	18×	body	256	valid
1.0ms	6×	body	1024	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify257.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4917	19
1	4917	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: 24.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y x) (-.f64 z t))
3.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
16.7b	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_17623` `add-sqr-sqrt_binary64_17645`
13×	`flip3--_binary64_17627` `flip--_binary64_17598`
10×	`add-cbrt-cube_binary64_17659` `add-exp-log_binary64_17661`
9×	`add-cube-cbrt_binary64_17658`
8×	`frac-times_binary64_17633` `associate-/l/_binary64_17570`
6×	`cancel-sign-sub-inv_binary64_17589`
5×	`associate-/r_binary64_17567` `associate-l_binary64_17564` `associate-r*_binary64_17563` `times-frac_binary64_17629` `add-log-exp_binary64_17662` `pow1_binary64_17684`
4×	`distribute-lft-out--_binary64_17575` `associate-l/_binary64_17566` `associate-r/_binary64_17565` `distribute-lft-in_binary64_17572` `difference-of-squares_binary64_17592` `distribute-rgt-in_binary64_17573`
2×	`prod-exp_binary64_17672` `associate-/r/_binary64_17569` `cbrt-undiv_binary64_17657` `cbrt-unprod_binary64_17656` `sub-neg_binary64_17616` `div-exp_binary64_17674`
1×	`-commutative_binary64_17554` `sum-log_binary64_17714` `frac-2neg_binary64_17634` `distribute-lft-out_binary64_17574` `unswap-sqr_binary64_17591` `div-inv_binary64_17620` `associate-/l_binary64_17568` `flip3-+_binary64_17626` `pow-prod-down_binary64_17694` `flip-+_binary64_17597` `+-commutative_binary64_17553` `clear-num_binary64_17622`

Counts

3 → 85

Calls

3 calls:

16.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
16.0ms	(*.f64 (-.f64 y x) (-.f64 z t))
10.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

series978.0ms (8.4%)

Counts

3 → 9

Calls

3 calls:

520.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))
385.0ms	(/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))
73.0ms	(*.f64 (-.f64 y x) (-.f64 z t))

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6921	1705

prune543.0ms (4.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 4.7b

Counts

95 → 10

Compiler

Compiled 11382 to 6403 computations (43.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
2.0b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
3.0b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))

rewrite126.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

330×	`times-frac_binary64_17629`
323×	`*-un-lft-identity_binary64_17623`
321×	`add-sqr-sqrt_binary64_17645`
113×	`add-cube-cbrt_binary64_17658`
104×	`distribute-lft-out--_binary64_17575` `difference-of-squares_binary64_17592`
36×	`associate-/r*_binary64_17567`
15×	`associate-/r/_binary64_17569`
10×	`add-cbrt-cube_binary64_17659` `associate-/l*_binary64_17568` `add-exp-log_binary64_17661`
9×	`flip3--_binary64_17627` `flip--_binary64_17598`
8×	`div-inv_binary64_17620`
5×	`add-log-exp_binary64_17662`
4×	`associate-/l/_binary64_17570` `cbrt-undiv_binary64_17657` `div-exp_binary64_17674`
3×	`div-sub_binary64_17628` `pow1_binary64_17684`
2×	`frac-2neg_binary64_17634` `clear-num_binary64_17622`
1×	`sum-log_binary64_17714` `distribute-lft-out_binary64_17574` `flip3-+_binary64_17626` `associate-+r-_binary64_17557` `flip-+_binary64_17597` `+-commutative_binary64_17553`

Counts

3 → 274

Calls

3 calls:

52.0ms	(+.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)))
9.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

series1.1s (9.8%)

Counts

3 → 9

Calls

3 calls:

533.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))
511.0ms	(+.f64 x (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))))
99.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

simplify140.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4980	8451
1	4980	8451

prune689.0ms (5.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	276	7	283
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	281	12	293

Merged error: 4.2b

Counts

293 → 12

Compiler

Compiled 17509 to 7066 computations (59.6% 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))
2.6b	(/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))
9.4b	(+.f64 x (/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t))))

rewrite664.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Rules

1737×	`times-frac_binary64_17629`
1010×	`*-un-lft-identity_binary64_17623`
1008×	`add-sqr-sqrt_binary64_17645`
568×	`cbrt-div_binary64_17655`
460×	`cbrt-prod_binary64_17654`
442×	`add-cube-cbrt_binary64_17658`
413×	`associate-/r/_binary64_17569`
302×	`flip3--_binary64_17627` `flip--_binary64_17598`
283×	`distribute-lft-out--_binary64_17575` `difference-of-squares_binary64_17592`
188×	`frac-times_binary64_17633`
94×	`associate-l/_binary64_17566` `associate-r/_binary64_17565`
66×	`div-inv_binary64_17620`
46×	`associate-/r*_binary64_17567`
25×	`add-exp-log_binary64_17661`
18×	`add-cbrt-cube_binary64_17659`
17×	`associate-/l*_binary64_17568`
13×	`cbrt-undiv_binary64_17657` `div-exp_binary64_17674`
6×	`add-log-exp_binary64_17662`
4×	`div-sub_binary64_17628` `pow1_binary64_17684`
2×	`prod-exp_binary64_17672` `cbrt-unprod_binary64_17656` `pow1/3_binary64_17705`
1×	`sum-log_binary64_17714` `frac-2neg_binary64_17634` `distribute-lft-out_binary64_17574` `flip3-+_binary64_17626` `associate-/l/_binary64_17570` `associate-+r-_binary64_17557` `flip-+_binary64_17597` `+-commutative_binary64_17553` `clear-num_binary64_17622`

Counts

4 → 913

Calls

4 calls:

201.0ms	(+.f64 x (/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t))))
51.0ms	(/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))
3.0ms	(cbrt.f64 (-.f64 a t))
3.0ms	(cbrt.f64 (-.f64 a t))

series1.5s (13%)

Counts

4 → 12

Calls

4 calls:

539.0ms	(/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))
528.0ms	(+.f64 x (/.f64 (/.f64 (-.f64 y x) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t))))
225.0ms	(cbrt.f64 (-.f64 a t))
223.0ms	(cbrt.f64 (-.f64 a t))

simplify492.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

925 → 925

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5913	59440

prune1.2s (10.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	925	0	925
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	925	12	937

Merged error: 4.2b

Counts

937 → 12

Compiler

Compiled 42167 to 6295 computations (85.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 y x) (-.f64 a t))
3.8b	(+.f64 x (*.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t)))
7.0b	(*.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64_17645`
77×	`*-un-lft-identity_binary64_17623`
51×	`times-frac_binary64_17629`
31×	`associate-l_binary64_17564` `add-cube-cbrt_binary64_17658`
23×	`distribute-lft-out--_binary64_17575` `difference-of-squares_binary64_17592`
12×	`cancel-sign-sub-inv_binary64_17589`
10×	`add-cbrt-cube_binary64_17659` `add-exp-log_binary64_17661`
8×	`distribute-lft-in_binary64_17572` `associate-+r+_binary64_17555` `distribute-rgt-in_binary64_17573`
5×	`associate-/r_binary64_17567` `associate-/l_binary64_17568` `associate-r_binary64_17563` `flip3--_binary64_17627` `flip--_binary64_17598` `add-log-exp_binary64_17662` `pow1_binary64_17684`
4×	`associate-/r/_binary64_17569` `sub-neg_binary64_17616`
2×	`prod-exp_binary64_17672` `frac-times_binary64_17633` `unswap-sqr_binary64_17591` `div-inv_binary64_17620` `associate-/l/_binary64_17570` `cbrt-undiv_binary64_17657` `cbrt-unprod_binary64_17656` `associate-*r/_binary64_17565` `div-exp_binary64_17674`
1×	`-commutative_binary64_17554` `sum-log_binary64_17714` `frac-2neg_binary64_17634` `flip3-+_binary64_17626` `associate-l/_binary64_17566` `div-sub_binary64_17628` `pow-prod-down_binary64_17694` `flip-+_binary64_17597` `+-commutative_binary64_17553` `clear-num_binary64_17622`

Counts

3 → 135

Calls

3 calls:

22.0ms	(*.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t))
9.0ms	(/.f64 (-.f64 y x) (-.f64 a t))
5.0ms	(+.f64 x (*.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t)))

series1.2s (9.9%)

Counts

3 → 9

Calls

3 calls:

526.0ms	(*.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t))
503.0ms	(+.f64 x (*.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t)))
124.0ms	(/.f64 (-.f64 y x) (-.f64 a t))

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4950	2830
1	4950	2830

prune125.0ms (1.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	144	12	156

Merged error: 4.2b

Counts

156 → 12

Compiler

Compiled 3520 to 886 computations (74.8% saved)

regimes155.0ms (1.3%)

Compiler: Compiled 1010 to 780 computations (22.8% saved)

bsearch57.0ms (0.5%)

Steps

Iters	Range		Point
9	2.9594770662002505e-212	1.1694294431725161e-206	4.953885231570819e-211
7	-2.5940948294008662e-76	-1.8998431712792107e-78	-1.9298566122944367e-78

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 (9.1%)

Algorithm

1×

intervals

Results

280.0ms	6658×	body	128	valid
69.0ms	493×	body	512	valid
57.0ms	1231×	body	128	invalid
56.0ms	384×	body	1024	valid
31.0ms	405×	body	256	valid
11.0ms	60×	body	2048	valid

Compiler

Compiled 296 to 213 computations (28% saved)

Details

analyze1.1s (9%)

sample28.0ms (0.2%)

simplify257.0ms (2.2%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite50.0ms (0.4%)

series978.0ms (8.4%)

simplify68.0ms (0.6%)

prune543.0ms (4.7%)

localize9.0ms (0.1%)

rewrite126.0ms (1.1%)

series1.1s (9.8%)

simplify140.0ms (1.2%)

prune689.0ms (5.9%)

localize13.0ms (0.1%)

rewrite664.0ms (5.7%)

series1.5s (13%)

simplify492.0ms (4.2%)

prune1.2s (10.3%)

localize9.0ms (0.1%)

rewrite51.0ms (0.4%)

series1.2s (9.9%)

simplify55.0ms (0.5%)

prune125.0ms (1.1%)

regimes155.0ms (1.3%)

bsearch57.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.1s (9.1%)

Profiling