Details

analyze272.0ms (7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample71.0ms (1.8%)

Algorithm

1×

intervals

Results

34.0ms	72×	body	1280	valid
14.0ms	53×	body	640	valid
9.0ms	27×	body	2560	valid
4.0ms	23×	body	320	valid
3.0ms	72×	body	80	valid
1.0ms	9×	body	160	valid

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

prune4.0ms (0.1%)

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: 52.9b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

1.1b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
1.8b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
15.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 42

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

series23.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

13.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

simplify42.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5075	600

prune83.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
0.1b	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`associate-r_binary64`
49×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`unpow-prod-down_binary64` `cube-prod_binary64`
20×	`sqrt-prod_binary64`
10×	`add-exp-log_binary64`
8×	`unswap-sqr_binary64`
6×	`add-log-exp_binary64`
4×	`add-cbrt-cube_binary64` `prod-exp_binary64`
3×	`associate-r/_binary64` `associate-l*_binary64` `cube-div_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64` `div-inv_binary64` `frac-sub_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 90

Calls

2 calls:

18.0ms	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))
15.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))

series36.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

21.0ms	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))
15.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))

simplify31.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	4998	1131
1	4998	1131

prune159.0ms (4.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Merged error: 0b

Counts

100 → 4

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3))))
0.2b	(/.f64 0.125 (pow.f64 x 3))
10.9b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))))

rewrite77.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
18×	`add-log-exp_binary64`
13×	`unpow-prod-down_binary64` `cube-prod_binary64`
12×	`associate-/r*_binary64`
10×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `sum-log_binary64`
4×	`diff-log_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `log-div_binary64` `associate-+r+_binary64` `frac-sub_binary64` `associate--l+_binary64`
1×	`pow-to-exp_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 123

Calls

4 calls:

23.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3))))
22.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))))
22.0ms	(-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))
5.0ms	(/.f64 0.125 (pow.f64 x 3))

series28.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))))
6.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3))))
5.0ms	(/.f64 0.125 (pow.f64 x 3))
5.0ms	(-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4984	1775
1	4984	1775

prune171.0ms (4.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	135	4	139

Merged error: 0b

Counts

139 → 4

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 0.0625 (pow.f64 x 5))
0.2b	(/.f64 0.125 (pow.f64 x 3))
12.6b	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
20.1b	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

rewrite87.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

36.0ms	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))
36.0ms	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
5.0ms	(/.f64 0.125 (pow.f64 x 3))
5.0ms	(/.f64 0.0625 (pow.f64 x 5))

series31.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
7.0ms	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))
6.0ms	(/.f64 0.0625 (pow.f64 x 5))
5.0ms	(/.f64 0.125 (pow.f64 x 3))

simplify58.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5361	2493

prune268.0ms (6.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	171	4	175

Merged error: 0b

Counts

175 → 4

regimes40.0ms (1%)

Accuracy

Total 0.2b remaining (79.8%)

Threshold costs 0.2b (79.8%)

bsearch29.0ms (0.8%)

Steps

Iters	Range		Point
10	1.4332844389409512e-13	15.167647912522936	0.887192876086426
10	-270.7734377663163	-7.923252455646139e-14	-1.010460937713024

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	55
1	117	55

end0.0ms (0%)

sample2.2s (57%)

Algorithm

1×

intervals

Results

1.1s	2411×	body	1280	valid
436.0ms	1555×	body	640	valid
275.0ms	832×	body	2560	valid
126.0ms	763×	body	320	valid
89.0ms	2076×	body	80	valid
35.0ms	363×	body	160	valid

Details

analyze272.0ms (7%)

sample71.0ms (1.8%)

simplify5.0ms (0.1%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

rewrite18.0ms (0.5%)

series23.0ms (0.6%)

simplify42.0ms (1.1%)

prune83.0ms (2.1%)

localize9.0ms (0.2%)

rewrite36.0ms (0.9%)

series36.0ms (0.9%)

simplify31.0ms (0.8%)

prune159.0ms (4.1%)

localize13.0ms (0.3%)

rewrite77.0ms (2%)

series28.0ms (0.7%)

simplify50.0ms (1.3%)

prune171.0ms (4.4%)

localize14.0ms (0.4%)

rewrite87.0ms (2.3%)

series31.0ms (0.8%)

simplify58.0ms (1.5%)

prune268.0ms (6.9%)

regimes40.0ms (1%)

bsearch29.0ms (0.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (57%)

Profiling