Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample107.0ms (1.5%)

Algorithm

1×

intervals

Results

81.0ms	144×	body	2048	valid
16.0ms	65×	body	1024	valid
3.0ms	25×	body	512	valid
1.0ms	11×	body	256	valid
0.0ms	11×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4770	13
1	4770	13

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: 27.5b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
3.4b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64`
6×	`cancel-sign-sub-inv_binary64` `add-sqr-sqrt_binary64`
4×	`frac-add_binary64` `add-cube-cbrt_binary64` `associate-+l+_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `pow1_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `neg-sub0_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-diff_binary64` `distribute-lft-out--_binary64` `exp-neg_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `associate-+l-_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

2 → 39

Calls

2 calls:

10.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
5.0ms	(-.f64 (exp.f64 x) 2)

series83.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

66.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
16.0ms	(-.f64 (exp.f64 x) 2)

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4877	664
1	4877	664

prune81.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	3	46

Merged error: 0.0b

Counts

46 → 3

Compiler

Compiled 1235 to 778 computations (37% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64` `add-exp-log_binary64`
11×	`add-log-exp_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
6×	`associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`pow1_binary64` `sqr-pow_binary64` `sum-log_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`associate-+r+_binary64`

Counts

4 → 74

Calls

4 calls:

8.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
8.0ms	(*.f64 1/12 (pow.f64 x 4))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
5.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))

series342.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
62.0ms	(*.f64 1/360 (pow.f64 x 6))
55.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
47.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4979	1259
1	4979	1259

prune96.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	86	3	89

Merged error: 0.0b

Counts

89 → 3

Compiler

Compiled 1753 to 1231 computations (29.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
0.1b	(pow.f64 (exp.f64 x) 3)
0.3b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))
3.1b	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
4×	`flip3-+_binary64` `associate-*r/_binary64` `pow-pow_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `associate-r_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `associate-/l*_binary64` `times-frac_binary64` `exp-prod_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-+r+_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `associate-/r_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `pow-exp_binary64` `unpow3_binary64` `sum-log_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))
7.0ms	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
4.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))
4.0ms	(pow.f64 (exp.f64 x) 3)

series707.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

462.0ms	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (.f64 (exp.f64 x) (+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))
126.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))
78.0ms	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
40.0ms	(pow.f64 (exp.f64 x) 3)

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5013	2508

prune155.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	98	3	101

Merged error: 0b

Counts

101 → 3

Compiler

Compiled 3537 to 2084 computations (41.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(exp.f64 (-.f64 (log.f64 (/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))) x))
0.2b	(log.f64 (/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))
0.2b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
3.1b	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
30×	`log-prod_binary64` `add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
27×	`times-frac_binary64`
19×	`exp-sum_binary64`
15×	`associate--l+_binary64`
9×	`add-exp-log_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `exp-prod_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `cancel-sign-sub-inv_binary64` `associate-/l_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `rem-log-exp_binary64` `log-pow_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `associate-+r+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `log-div_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 105

Calls

4 calls:

12.0ms	(exp.f64 (-.f64 (log.f64 (/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))) x))
8.0ms	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
6.0ms	(log.f64 (/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))
4.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))

series1.4s (19.3%)

Counts

4 → 12

Calls

4 calls:

691.0ms	(log.f64 (/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))))
339.0ms	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
229.0ms	(exp.f64 (-.f64 (log.f64 (/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3))))) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))) x))
122.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))

simplify108.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4956	5620
1	4956	5620

prune204.0ms (2.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	117	3	120

Merged error: 0b

Counts

120 → 3

Compiler

Compiled 4725 to 2948 computations (37.6% saved)

regimes22.0ms (0.3%)

Compiler: Compiled 120 to 92 computations (23.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample3.3s (46.7%)

Algorithm

1×

intervals

Results

2.4s	4148×	body	2048	valid
501.0ms	2003×	body	1024	valid
133.0ms	977×	body	512	valid
44.0ms	498×	body	256	valid
17.0ms	374×	body	128	valid

Compiler

Compiled 83 to 67 computations (19.3% saved)

Details

analyze4.0ms (0.1%)

sample107.0ms (1.5%)

simplify88.0ms (1.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite17.0ms (0.2%)

series83.0ms (1.2%)

simplify93.0ms (1.3%)

prune81.0ms (1.1%)

localize10.0ms (0.1%)

rewrite34.0ms (0.5%)

series342.0ms (4.8%)

simplify73.0ms (1%)

prune96.0ms (1.3%)

localize13.0ms (0.2%)

rewrite35.0ms (0.5%)

series707.0ms (9.9%)

simplify97.0ms (1.4%)

prune155.0ms (2.2%)

localize18.0ms (0.2%)

rewrite45.0ms (0.6%)

series1.4s (19.3%)

simplify108.0ms (1.5%)

prune204.0ms (2.8%)

regimes22.0ms (0.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (46.7%)

Profiling