Details

analyze1.1s (12.9%)

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
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
13.1%	74.3%	12.7%	12
16.1%	70.5%	13.5%	13
18.6%	68%	13.5%	14

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample73.0ms (0.9%)

Algorithm

1×

intervals

Results

21.0ms	49×	body	1024	valid
10.0ms	134×	body	128	valid
9.0ms	10×	body	2048	valid
9.0ms	39×	body	512	valid
3.0ms	24×	body	256	valid
3.0ms	55×	body	128	nan
2.0ms	11×	body	512	nan
2.0ms	7×	body	1024	nan
1.0ms	20×	body	128	overflowed
0.0ms	2×	body	256	nan

Compiler

Compiled 27 to 29 computations (-7.4% saved)

simplify392.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (297.0ms)

Iter	Nodes	Cost
0	5254	20

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

24.8b

Counts

2 → 1

Compiler

Compiled 26 to 24 computations (7.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (exp.f64 z))
0.0b	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
1.8b	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
3.1b	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_9648`
17×	`add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
12×	`times-frac_binary64_9632`
11×	`pow1_binary64_9687`
9×	`add-log-exp_binary64_9665`
8×	`add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
5×	`log-pow_binary64_9715`
4×	`associate-/l*_binary64_9571` `associate-+l+_binary64_9559` `log-div_binary64_9713`
3×	`associate-l_binary64_9567` `log-prod_binary64_9712` `flip-+_binary64_9600` `cancel-sign-sub-inv_binary64_9592` `flip3-+_binary64_9629` `associate-r_binary64_9566` `associate-/r*_binary64_9570`
2×	`sum-log_binary64_9717` `div-sub_binary64_9631`
1×	`sub-neg_binary64_9619` `associate-+l-_binary64_9561` `diff-log_binary64_9718` `div-exp_binary64_9677` `rem-log-exp_binary64_9667` `prod-exp_binary64_9675` `+-commutative_binary64_9556` `pow-prod-down_binary64_9697` `*-commutative_binary64_9557` `cbrt-undiv_binary64_9660` `unswap-sqr_binary64_9594` `frac-2neg_binary64_9637` `div-inv_binary64_9623` `clear-num_binary64_9625` `cbrt-unprod_binary64_9659`

Counts

4 → 82

Calls

4 calls:

9.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
8.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
7.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
5.0ms	(*.f64 y (exp.f64 z))

series326.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
68.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
31.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
22.0ms	(*.f64 y (exp.f64 z))

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5129	1998

prune119.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	6	95

Error

4.4b

Counts

95 → 6

Compiler

Compiled 2113 to 1126 computations (46.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
3.5b	(log.f64 (+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (exp.f64 z) (cbrt.f64 y)))))
12.9b	(+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (exp.f64 z) (cbrt.f64 y))))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64_9665`
8×	`add-sqr-sqrt_binary64_9648` `add-cube-cbrt_binary64_9661` `*-un-lft-identity_binary64_9626`
6×	`cbrt-prod_binary64_9657`
5×	`pow1_binary64_9687` `add-exp-log_binary64_9664`
4×	`associate-+l+_binary64_9559` `add-cbrt-cube_binary64_9662`
3×	`log-prod_binary64_9712` `cancel-sign-sub-inv_binary64_9592`
2×	`pow1/3_binary64_9708` `flip-+_binary64_9600` `sum-log_binary64_9717` `log-div_binary64_9713` `flip3-+_binary64_9629`
1×	`sub-neg_binary64_9619` `associate-+l-_binary64_9561` `diff-log_binary64_9718` `rem-log-exp_binary64_9667` `+-commutative_binary64_9556` `log-pow_binary64_9715`

Counts

4 → 53

Calls

4 calls:

10.0ms	(+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (exp.f64 z) (cbrt.f64 y))))
8.0ms	(log.f64 (+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (exp.f64 z) (cbrt.f64 y)))))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series325.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(log.f64 (+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (exp.f64 z) (cbrt.f64 y)))))
91.0ms	(cbrt.f64 y)
86.0ms	(cbrt.f64 y)
51.0ms	(+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (exp.f64 z) (cbrt.f64 y))))

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5431	922

prune70.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	65	6	71

Error

4.4b

Counts

71 → 6

Compiler

Compiled 1576 to 770 computations (51.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
3.5b	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
6.9b	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)
8.5b	(.f64 y (.f64 z z))

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64_9664` `add-cbrt-cube_binary64_9662`
23×	`pow1_binary64_9687`
22×	`add-sqr-sqrt_binary64_9648`
21×	`*-un-lft-identity_binary64_9626`
18×	`add-cube-cbrt_binary64_9661`
13×	`prod-exp_binary64_9675` `pow-prod-down_binary64_9697` `cbrt-unprod_binary64_9659`
12×	`cancel-sign-sub-inv_binary64_9592`
9×	`times-frac_binary64_9632`
8×	`distribute-rgt-in_binary64_9576` `distribute-lft-in_binary64_9575` `associate-+r+_binary64_9558`
7×	`associate-r_binary64_9566`
6×	`add-log-exp_binary64_9665`
4×	`associate-l_binary64_9567` `sub-neg_binary64_9619`
3×	`associate-/l_binary64_9571` `associate-/r_binary64_9570`
2×	`difference-of-squares_binary64_9595` `-commutative_binary64_9557` `associate-/l/_binary64_9573` `flip-+_binary64_9600` `flip3-+_binary64_9629` `associate-r/_binary64_9568`
1×	`flip3--_binary64_9630` `div-exp_binary64_9677` `distribute-lft-out--_binary64_9578` `+-commutative_binary64_9556` `flip--_binary64_9601` `cbrt-undiv_binary64_9660` `unswap-sqr_binary64_9594` `frac-2neg_binary64_9637` `sum-log_binary64_9717` `div-inv_binary64_9623` `clear-num_binary64_9625`

Counts

4 → 104

Calls

4 calls:

15.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
8.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)
6.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
6.0ms	(.f64 y (.f64 z z))

series212.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(/.f64 (+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y))) t)
49.0ms	(+.f64 (.f64 y z) (.f64 (.f64 1/2 (.f64 y (*.f64 z z))) (-.f64 1 y)))
48.0ms	(.f64 (.f64 1/2 (.f64 y (.f64 z z))) (-.f64 1 y))
26.0ms	(.f64 y (.f64 z z))

simplify77.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5004	2470

prune141.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	110	6	116
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	111	11	122

Error

4.3b

Counts

122 → 11

Compiler

Compiled 3214 to 1626 computations (49.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 (.f64 z z) 1/2))))))
3.1b	(.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 (.f64 z z) 1/2))))
5.4b	(.f64 (-.f64 1 y) (.f64 (*.f64 z z) 1/2))
7.1b	(/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 (.f64 z z) 1/2)))))

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64_9632`
41×	`add-exp-log_binary64_9664`
32×	`add-sqr-sqrt_binary64_9648`
30×	`*-un-lft-identity_binary64_9626`
29×	`add-cbrt-cube_binary64_9662`
27×	`add-cube-cbrt_binary64_9661`
16×	`pow1_binary64_9687`
14×	`div-exp_binary64_9677`
12×	`associate-*r/_binary64_9568`
11×	`prod-exp_binary64_9675` `associate-/r/_binary64_9572`
10×	`associate-/r*_binary64_9570`
9×	`associate-l_binary64_9567` `cbrt-unprod_binary64_9659`
7×	`pow-prod-down_binary64_9697` `cbrt-undiv_binary64_9660`
6×	`flip-+_binary64_9600` `associate-/l*_binary64_9571` `div-inv_binary64_9623` `flip3-+_binary64_9629`
4×	`add-log-exp_binary64_9665` `associate-r_binary64_9566`
3×	`1-exp_binary64_9670` `rec-exp_binary64_9676`
2×	`associate-l/_binary64_9569` `difference-of-squares_binary64_9595` `-commutative_binary64_9557` `frac-2neg_binary64_9637` `clear-num_binary64_9625`
1×	`distribute-rgt-in_binary64_9576` `flip3--_binary64_9630` `inv-pow_binary64_9711` `distribute-lft-out--_binary64_9578` `pow-flip_binary64_9700` `flip--_binary64_9601` `unswap-sqr_binary64_9594` `distribute-lft-in_binary64_9575`

Counts

4 → 135

Calls

4 calls:

15.0ms	(.f64 (-.f64 1 y) (.f64 (*.f64 z z) 1/2))
10.0ms	(/.f64 1 (/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 (.f64 z z) 1/2))))))
7.0ms	(/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 (.f64 z z) 1/2)))))
6.0ms	(.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 (.f64 z z) 1/2))))

series346.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 (.f64 z z) 1/2)))))
122.0ms	(/.f64 1 (/.f64 t (.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 (.f64 z z) 1/2))))))
53.0ms	(.f64 y (+.f64 z (.f64 (-.f64 1 y) (.f64 (.f64 z z) 1/2))))
36.0ms	(.f64 (-.f64 1 y) (.f64 (*.f64 z z) 1/2))

simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5315	3772

prune183.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	149	9	158

Error

3.2b

Counts

158 → 9

Compiler

Compiled 3882 to 2293 computations (40.9% saved)

regimes1.2s (14.1%)

Accuracy

Total 7.6b remaining (69%)

Threshold costs 0b (0%)

Compiler

Compiled 11504 to 8917 computations (22.5% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 13 to 12 computations (7.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	230	338
1	230	338

end0.0ms (0%)

sample3.4s (40.9%)

Algorithm

1×

intervals

Results

760.0ms	1767×	body	1024	valid
318.0ms	1295×	body	512	valid
290.0ms	3868×	body	128	valid
270.0ms	305×	body	2048	valid
117.0ms	765×	body	256	valid
77.0ms	1553×	body	128	nan
56.0ms	212×	body	1024	nan
47.0ms	812×	body	128	overflowed
43.0ms	257×	body	512	nan
17.0ms	152×	body	256	nan
1.0ms	20×	body	128	invalid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 1484 to 1097 computations (26.1% saved)

Details

analyze1.1s (12.9%)

sample73.0ms (0.9%)

simplify392.0ms (4.7%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite36.0ms (0.4%)

series326.0ms (3.9%)

simplify80.0ms (0.9%)

prune119.0ms (1.4%)

localize14.0ms (0.2%)

rewrite29.0ms (0.3%)

series325.0ms (3.9%)

simplify55.0ms (0.7%)

prune70.0ms (0.8%)

localize12.0ms (0.1%)

rewrite47.0ms (0.6%)

series212.0ms (2.5%)

simplify77.0ms (0.9%)

prune141.0ms (1.7%)

localize12.0ms (0.1%)

rewrite53.0ms (0.6%)

series346.0ms (4.1%)

simplify66.0ms (0.8%)

prune183.0ms (2.2%)

regimes1.2s (14.1%)

bsearch6.0ms (0.1%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample3.4s (40.9%)

Profiling