Details

analyze1.9s (16.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample119.0ms (1%)

Algorithm

1×

intervals

Results

60.0ms	71×	body	1024	valid
20.0ms	135×	body	128	valid
12.0ms	26×	body	512	valid
7.0ms	24×	body	256	valid
4.0ms	24×	body	128	invalid
0.0ms	2×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify310.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5787	32

prune9.0ms (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: 13.8b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
8.1b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
16.6b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

16.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 F (sin.f64 B))

series749.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

291.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
219.0ms	(/.f64 x (tan.f64 B))
138.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
101.0ms	(/.f64 F (sin.f64 B))

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4930	2525
1	4930	2525

prune210.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	13	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Merged error: 0.0b

Counts

129 → 13

Compiler

Compiled 3876 to 1880 computations (51.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
16.6b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

series695.0ms (6%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
207.0ms	(/.f64 x (tan.f64 B))
115.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
111.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5181	2141

prune146.0ms (1.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	104	14	118

Merged error: 0.0b

Counts

118 → 14

Compiler

Compiled 3189 to 1729 computations (45.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 F (.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2)))
0.7b	(.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x))) -1/2))
16.6b	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))
16.6b	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))

rewrite80.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
44×	`unpow-prod-down_binary64`
39×	`add-exp-log_binary64`
28×	`prod-exp_binary64` `sqrt-prod_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
17×	`unswap-sqr_binary64`
13×	`associate-l_binary64`
12×	`pow-to-exp_binary64` `swap-sqr_binary64` `sqr-pow_binary64` `pow-exp_binary64`
11×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `sqrt-div_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 126

Calls

4 calls:

26.0ms	(.f64 F (.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2)))
22.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x))) -1/2))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))

series299.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(.f64 F (.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2)))
90.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x))) -1/2))
59.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))
47.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4960	3805
1	4960	3805

prune259.0ms (2.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	139	13	152

Merged error: 0.0b

Counts

152 → 13

Compiler

Compiled 5341 to 3180 computations (40.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 F)
0.6b	(cbrt.f64 F)
0.6b	(cbrt.f64 F)
16.6b	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))
1.0ms	(cbrt.f64 F)
1.0ms	(cbrt.f64 F)
1.0ms	(cbrt.f64 F)

series507.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt.f64 F)
149.0ms	(cbrt.f64 F)
146.0ms	(cbrt.f64 F)
52.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)))

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4924	626
1	4924	626

prune73.0ms (0.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	60	13	73

Merged error: 0.0b

Counts

73 → 13

Compiler

Compiled 1882 to 798 computations (57.6% saved)

regimes637.0ms (5.5%)

Compiler: Compiled 6632 to 5000 computations (24.6% saved)

bsearch186.0ms (1.6%)

Steps

Iters	Range		Point
10	8.370040452892694e-12	6390017.534609873	3893804.8260155115
9	-12556370876301.305	-10440157.942140756	-14573622.064940056

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	98	95
1	98	95

end0.0ms (0%)

sample4.8s (41.7%)

Algorithm

1×

intervals

Results

1.6s	2207×	body	1024	valid
602.0ms	4125×	body	128	valid
515.0ms	1109×	body	512	valid
167.0ms	553×	body	256	valid
102.0ms	658×	body	128	invalid
13.0ms	130×	body	128	nan
8.0ms	6×	body	2048	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 1733 to 1297 computations (25.2% saved)

Details

analyze1.9s (16.6%)

sample119.0ms (1%)

simplify310.0ms (2.7%)

prune9.0ms (0.1%)

localize21.0ms (0.2%)

rewrite46.0ms (0.4%)

series749.0ms (6.5%)

simplify96.0ms (0.8%)

prune210.0ms (1.8%)

localize23.0ms (0.2%)

rewrite46.0ms (0.4%)

series695.0ms (6%)

simplify62.0ms (0.5%)

prune146.0ms (1.3%)

localize23.0ms (0.2%)

rewrite80.0ms (0.7%)

series299.0ms (2.6%)

simplify87.0ms (0.8%)

prune259.0ms (2.3%)

localize20.0ms (0.2%)

rewrite15.0ms (0.1%)

series507.0ms (4.4%)

simplify66.0ms (0.6%)

prune73.0ms (0.6%)

regimes637.0ms (5.5%)

bsearch186.0ms (1.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.8s (41.7%)

Profiling