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)

sample76.0ms (1.9%)

Algorithm

1×

intervals

Results

61.0ms	182×	body	1280	valid
8.0ms	46×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	4×	body	80	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify107.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4754	13
1	4754	13

prune3.0ms (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: 30.6b

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)
3.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
4×	`frac-add_binary64` `add-sqr-sqrt_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `pow1_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `neg-sub0_binary64` `add-cube-cbrt_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` `associate-+l-_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

2 → 33

Calls

2 calls:

8.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

series8.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
2.0ms	(-.f64 (exp.f64 x) 2)

simplify115.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4832	627
1	4832	627

prune39.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	2	40

Merged error: 0.0b

Counts

40 → 2

Compiler

Compiled 580 to 312 computations (46.2% saved)

localize11.0ms (0.3%)

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))

rewrite26.0ms (0.7%)

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

series30.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
7.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
5.0ms	(*.f64 1/360 (pow.f64 x 6))
4.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify92.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5024	1259

prune69.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	86	2	88

Merged error: 0.0b

Counts

88 → 2

Compiler

Compiled 1756 to 1235 computations (29.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) -2)
0.0b	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
0.0b	(pow.f64 (exp.f64 x) -3)
3.5b	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
11×	`unpow-prod-down_binary64`
9×	`pow-unpow_binary64` `pow-pow_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `exp-prod_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cube-prod_binary64`
3×	`pow-to-exp_binary64` `sqr-pow_binary64` `pow-exp_binary64`
2×	`cube-div_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `rem-cube-cbrt_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 81

Calls

4 calls:

15.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))
6.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
4.0ms	(pow.f64 (exp.f64 x) -2)
3.0ms	(pow.f64 (exp.f64 x) -3)

series49.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))
8.0ms	(pow.f64 (exp.f64 x) -3)
7.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
6.0ms	(pow.f64 (exp.f64 x) -2)

simplify69.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	6182	1157

prune96.0ms (2.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	93	2	95

Merged error: 0b

Counts

95 → 2

Compiler

Compiled 3273 to 1934 computations (40.9% saved)

localize28.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3)
0.1b	(pow.f64 (exp.f64 x) -6)
0.1b	(pow.f64 (-.f64 (exp.f64 x) 2) 6)
3.4b	(+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 x) -3) 3))

rewrite63.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`unpow-prod-down_binary64`
36×	`*-un-lft-identity_binary64`
30×	`cube-prod_binary64`
26×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
9×	`pow-unpow_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `pow-pow_binary64` `pow-exp_binary64`
5×	`distribute-lft-out_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
4×	`pow-to-exp_binary64` `cube-div_binary64`
3×	`unpow3_binary64` `exp-prod_binary64` `cube-mult_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `sum-cubes_binary64` `rem-cube-cbrt_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 109

Calls

4 calls:

39.0ms	(+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 x) -3) 3))
9.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 6)
8.0ms	(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3)
4.0ms	(pow.f64 (exp.f64 x) -6)

series159.0ms (4%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 x) -3) 3))
12.0ms	(pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3)
11.0ms	(pow.f64 (exp.f64 x) -6)
9.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 6)

simplify94.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5093	2163

prune303.0ms (7.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	121	2	123

Merged error: 0b

Counts

123 → 2

Compiler

Compiled 7737 to 5027 computations (35% saved)

regimes16.0ms (0.4%)

Compiler: Compiled 75 to 55 computations (26.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample2.4s (61.6%)

Algorithm

1×

intervals

Results

1.8s	5683×	body	1280	valid
220.0ms	1232×	body	640	valid
70.0ms	611×	body	320	valid
23.0ms	295×	body	160	valid
7.0ms	179×	body	80	valid

Compiler

Compiled 105 to 82 computations (21.9% saved)

Details

analyze4.0ms (0.1%)

sample76.0ms (1.9%)

simplify107.0ms (2.7%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

rewrite13.0ms (0.3%)

series8.0ms (0.2%)

simplify115.0ms (2.9%)

prune39.0ms (1%)

localize11.0ms (0.3%)

rewrite26.0ms (0.7%)

series30.0ms (0.8%)

simplify92.0ms (2.3%)

prune69.0ms (1.7%)

localize14.0ms (0.4%)

rewrite29.0ms (0.7%)

series49.0ms (1.2%)

simplify69.0ms (1.7%)

prune96.0ms (2.4%)

localize28.0ms (0.7%)

rewrite63.0ms (1.6%)

series159.0ms (4%)

simplify94.0ms (2.4%)

prune303.0ms (7.6%)

regimes16.0ms (0.4%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.4s (61.6%)

Profiling