Details

analyze683.0ms (21.1%)

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
16.4%	83.4%	0.2%	9
21.4%	78.4%	0.2%	10
25.9%	73.3%	0.8%	11
28%	70.2%	1.9%	12
39.6%	55.8%	4.6%	13
43.9%	50.4%	5.8%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	63×	body	80	invalid

Compiler

Compiled 19 to 21 computations (-10.5% saved)

simplify64.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	735	13
1	735	13

prune5.0ms (0.2%)

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: 10.4b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
0.0b	(*.f64 y (-.f64 z x))
10.4b	(/.f64 (*.f64 y (-.f64 z x)) t)

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `associate-r_binary64`
4×	`associate-*r/_binary64`
3×	`associate-/r_binary64` `associate-l*_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 59

Calls

3 calls:

11.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
7.0ms	(*.f64 y (-.f64 z x))
5.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

series33.0ms (1%)

Counts

3 → 9

Calls

3 calls:

13.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
12.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
8.0ms	(*.f64 y (-.f64 z x))

simplify70.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5614	847

prune49.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 0.0b

Counts

69 → 5

Compiler

Compiled 979 to 273 computations (72.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
0.0b	(/.f64 t (-.f64 z x))
4.9b	(/.f64 y (/.f64 t (-.f64 z x)))

rewrite43.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
105×	`*-un-lft-identity_binary64`
103×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`
16×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
11×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 151

Calls

3 calls:

19.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
11.0ms	(/.f64 y (/.f64 t (-.f64 z x)))
6.0ms	(/.f64 t (-.f64 z x))

series33.0ms (1%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(/.f64 y (/.f64 t (-.f64 z x)))
11.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
8.0ms	(/.f64 t (-.f64 z x))

simplify90.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5041	3116

prune84.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	159	6	165

Merged error: 0b

Counts

165 → 6

Compiler

Compiled 2852 to 603 computations (78.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z x)))
5.0b	(*.f64 (/.f64 y t) (-.f64 z x))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64` `times-frac_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `pow1_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `associate-+r+_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

2 → 53

Calls

2 calls:

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

series25.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

14.0ms	(*.f64 (/.f64 y t) (-.f64 z x))
12.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z x)))

simplify60.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4992	866
1	4992	866

prune39.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	59	6	65

Merged error: 0b

Counts

65 → 6

Compiler

Compiled 942 to 250 computations (73.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 z x))
0.6b	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
1.3b	(/.f64 y (/.f64 t (cbrt.f64 (-.f64 z x))))
3.3b	(.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (/.f64 y (/.f64 t (cbrt.f64 (-.f64 z x)))))

rewrite89.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

353×	`times-frac_binary64`
249×	`add-sqr-sqrt_binary64`
238×	`*-un-lft-identity_binary64`
180×	`add-cube-cbrt_binary64`
139×	`cbrt-prod_binary64`
103×	`associate-r_binary64`
52×	`cbrt-div_binary64`
32×	`add-exp-log_binary64`
30×	`associate-/r*_binary64`
28×	`distribute-lft-out--_binary64`
26×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64`
21×	`add-cbrt-cube_binary64`
20×	`frac-times_binary64`
16×	`pow1_binary64` `associate-/r/_binary64`
14×	`associate-*l/_binary64`
10×	`swap-sqr_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
9×	`cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `div-exp_binary64`
8×	`unswap-sqr_binary64`
7×	`associate-*r/_binary64` `pow1/3_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/l*_binary64`
2×	`pow-prod-up_binary64` `pow-sqr_binary64` `*-commutative_binary64`
1×	`pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow2_binary64`

Counts

4 → 348

Calls

4 calls:

40.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (/.f64 y (/.f64 t (cbrt.f64 (-.f64 z x)))))
12.0ms	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
11.0ms	(/.f64 y (/.f64 t (cbrt.f64 (-.f64 z x))))
3.0ms	(cbrt.f64 (-.f64 z x))

series104.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
26.0ms	(/.f64 y (/.f64 t (cbrt.f64 (-.f64 z x))))
25.0ms	(cbrt.f64 (-.f64 z x))
19.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (/.f64 y (/.f64 t (cbrt.f64 (-.f64 z x)))))

simplify159.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

360 → 360

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5173	9417

prune191.0ms (5.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	360	0	360
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	360	6	366

Merged error: 0b

Counts

366 → 6

Compiler

Compiled 10703 to 2186 computations (79.6% saved)

regimes185.0ms (5.7%)

Compiler: Compiled 284 to 252 computations (11.3% saved)

bsearch24.0ms (0.7%)

Steps

Iters	Range		Point
6	2.976658784231234e-131	2.558016872431392e-130	3.5767859404124596e-131
6	-1.3441203867706141e-86	-9.032331141875034e-88	-8.815637691747206e-87

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	40
1	35	40

end0.0ms (0%)

sample1.1s (34.3%)

Algorithm

1×

intervals

Results

240.0ms	8000×	body	80	valid
59.0ms	1990×	body	80	invalid

Compiler

Compiled 120 to 96 computations (20% saved)

Details

analyze683.0ms (21.1%)

sample20.0ms (0.6%)

simplify64.0ms (2%)

prune5.0ms (0.2%)

localize6.0ms (0.2%)

rewrite24.0ms (0.8%)

series33.0ms (1%)

simplify70.0ms (2.2%)

prune49.0ms (1.5%)

localize6.0ms (0.2%)

rewrite43.0ms (1.3%)

series33.0ms (1%)

simplify90.0ms (2.8%)

prune84.0ms (2.6%)

localize6.0ms (0.2%)

rewrite16.0ms (0.5%)

series25.0ms (0.8%)

simplify60.0ms (1.8%)

prune39.0ms (1.2%)

localize10.0ms (0.3%)

rewrite89.0ms (2.8%)

series104.0ms (3.2%)

simplify159.0ms (4.9%)

prune191.0ms (5.9%)

regimes185.0ms (5.7%)

bsearch24.0ms (0.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (34.3%)

Profiling