Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample80.0ms (1%)

Algorithm

1×

intervals

Results

30.0ms	132×	body	1024	valid
28.0ms	57×	body	2048	valid
11.0ms	42×	body	512	valid
2.0ms	17×	body	256	valid
0.0ms	8×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

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

40.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.2b	(cos.f64 (+.f64 x eps))
0.8b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
0.8b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.2b	(cos.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
4×	`add-log-exp_binary64_799`
3×	`cancel-sign-sub-inv_binary64_726` `add-cube-cbrt_binary64_795`
2×	`cos-sum_binary64_894` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
1×	`diff-log_binary64_852` `associate--l-_binary64_698` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `diff-cos_binary64_911` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

2 → 26

Calls

4 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))
0.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
0.0ms	(cos.f64 (+.f64 x eps))

series121.0ms (1.5%)

Counts

2 → 23

Calls

2 calls:

77.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
44.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 379 to 301 computations (20.6% saved)

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4917	732
1	4917	732

prune64.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Error

0.2b

Counts

50 → 6

Compiler

Compiled 696 to 248 computations (64.4% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.0b	(+.f64 x (+.f64 x eps))
0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_760`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
9×	`add-log-exp_binary64_799` `add-sqr-sqrt_binary64_782`
7×	`add-cube-cbrt_binary64_795`
6×	`associate-l_binary64_701`
4×	`prod-exp_binary64_809` `associate-r_binary64_700` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
3×	`distribute-lft-out_binary64_711` `sum-log_binary64_851`
2×	`sin-mult_binary64_915` `*-commutative_binary64_691`
1×	`unswap-sqr_binary64_728` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-+r+_binary64_692` `+-commutative_binary64_690` `associate-*r/_binary64_702`

Counts

4 → 60

Calls

8 calls:

11.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))
0.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))

series394.0ms (4.9%)

Counts

4 → 48

Calls

4 calls:

152.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
122.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
61.0ms	(+.f64 x (+.f64 x eps))
59.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Compiler

Compiled 1176 to 1059 computations (9.9% saved)

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4932	2050
1	4932	2050

prune122.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	105	9	114

Error

0.2b

Counts

114 → 9

Compiler

Compiled 2208 to 1478 computations (33.1% saved)

localize18.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.6b	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.0b	(+.f64 x (+.f64 x eps))
0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.6b	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
3.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.5b	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_791`
24×	`add-sqr-sqrt_binary64_782`
15×	`-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `associate-r*_binary64_700`
10×	`cube-prod_binary64_788` `unpow-prod-down_binary64_839`
7×	`add-exp-log_binary64_798` `pow1_binary64_821`
6×	`add-cbrt-cube_binary64_796`
5×	`unswap-sqr_binary64_728`
4×	`add-log-exp_binary64_799` `sqr-pow_binary64_732`
3×	`cube-mult_binary64_790` `unpow3_binary64_826` `associate-l_binary64_701` `pow-unpow_binary64_837`
1×	`pow1/3_binary64_842` `rem-cbrt-cube_binary64_784` `prod-exp_binary64_809` `pow-exp_binary64_828` `rem-cube-cbrt_binary64_783` `pow-to-exp_binary64_829` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 85

Calls

8 calls:

15.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
8.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
0.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))))

series415.0ms (5.2%)

Counts

4 → 47

Calls

4 calls:

183.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
120.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
57.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
54.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Compiler

Compiled 1466 to 1293 computations (11.8% saved)

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5001	2916

prune182.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	132	9	141

Error

0.2b

Counts

141 → 9

Compiler

Compiled 3289 to 2236 computations (32% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

2.8b	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (.f64 (sin.f64 x) (sin.f64 eps))))
0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.1b	(+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))
0.1b	(*.f64 (cos.f64 x) (cos.f64 eps))
0.1b	(*.f64 (cos.f64 x) (cos.f64 eps))
0.1b	(+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
2.8b	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (.f64 (sin.f64 x) (sin.f64 eps))))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_782`
11×	`add-log-exp_binary64_799`
9×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
8×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
6×	`associate-r_binary64_700` `associate-l_binary64_701`
3×	`cancel-sign-sub-inv_binary64_726` `cos-mult_binary64_914`
2×	`diff-log_binary64_852` `unswap-sqr_binary64_728` `prod-exp_binary64_809` `flip3-+_binary64_763` `flip-+_binary64_734` `sum-log_binary64_851` `frac-sub_binary64_769` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`+-commutative_binary64_690` `sin-mult_binary64_915` `associate--r+_binary64_696` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 67

Calls

8 calls:

8.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (.f64 (sin.f64 x) (sin.f64 eps))))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
4.0ms	(*.f64 (cos.f64 x) (cos.f64 eps))
4.0ms	(+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))
0.0ms	(*.f64 (cos.f64 x) (cos.f64 eps))

series482.0ms (6%)

Counts

4 → 40

Calls

4 calls:

187.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (.f64 (sin.f64 x) (sin.f64 eps))))
116.0ms	(+.f64 (cos.f64 x) (*.f64 (sin.f64 x) (sin.f64 eps)))
93.0ms	(*.f64 (cos.f64 x) (cos.f64 eps))
85.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

Compiler

Compiled 1019 to 742 computations (27.2% saved)

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5313	1848

prune107.0ms (1.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	100	16	116

Error

0.1b

Counts

116 → 16

Compiler

Compiled 1996 to 467 computations (76.6% saved)

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	1998	1395
1	1998	1395

regimes373.0ms (4.6%)

Compiler: Compiled 2655 to 1951 computations (26.5% saved)

bsearch64.0ms (0.8%)

Steps

Iters	Range		Point
9	2.13199055564998e-08	16.724583358149186	0.00015167359697961248
8	-1.0000069373194402	-2.5070953418002607e-05	-0.0001675426203356274

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes230.0ms (2.9%)

Compiler: Compiled 1203 to 1054 computations (12.4% saved)

bsearch61.0ms (0.8%)

Steps

Iters	Range		Point
9	2.13199055564998e-08	16.724583358149186	0.00015167359697961248
8	-1.0000069373194402	-2.5070953418002607e-05	-0.00018218815574185185

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes211.0ms (2.6%)

Compiler: Compiled 1119 to 1000 computations (10.6% saved)

bsearch65.0ms (0.8%)

Steps

Iters	Range		Point
9	2.13199055564998e-08	16.724583358149186	0.00015167359697961248
8	-1.0000069373194402	-2.5070953418002607e-05	-0.00018218815574185185

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes109.0ms (1.4%)

Compiler: Compiled 678 to 625 computations (7.8% saved)

bsearch0.0ms (0%)

regimes96.0ms (1.2%)

Compiler: Compiled 231 to 248 computations (-7.4% saved)

bsearch53.0ms (0.7%)

Steps

Iters	Range		Point
9	2.13199055564998e-08	16.724583358149186	0.10441087167263563
7	-2.5070953418002607e-05	-9.594598602840287e-07	-2.4794567668379724e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes94.0ms (1.2%)

Compiler: Compiled 198 to 221 computations (-11.6% saved)

bsearch42.0ms (0.5%)

Steps

Iters	Range		Point
6	4.005367464346597e-09	2.13199055564998e-08	4.073923632484895e-09
7	-2.5070953418002607e-05	-9.594598602840287e-07	-9.767339696354591e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes77.0ms (1%)

Compiler: Compiled 114 to 137 computations (-20.2% saved)

bsearch41.0ms (0.5%)

Steps

Iters	Range		Point
6	4.005367464346597e-09	2.13199055564998e-08	2.1045680883946606e-08
7	-2.5070953418002607e-05	-9.594598602840287e-07	-1.1735105876753362e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes44.0ms (0.5%)

Compiler: Compiled 28 to 46 computations (-64.3% saved)

bsearch41.0ms (0.5%)

Steps

Iters	Range		Point
6	4.005367464346597e-09	2.13199055564998e-08	2.1045680883946606e-08
7	-2.5070953418002607e-05	-9.594598602840287e-07	-5.674656834469873e-06

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes19.0ms (0.2%)

Compiler: Compiled 18 to 36 computations (-100% saved)

bsearch0.0ms (0%)

regimes30.0ms (0.4%)

Compiler: Compiled 10 to 26 computations (-160% saved)

bsearch66.0ms (0.8%)

Steps

Iters	Range		Point
9	3.5968630408344143e-69	2.688913657805818e-60	6.397017030345022e-67
6	-5.484201987079943e-68	-3.686454326587784e-69	-3.8977243412453404e-69

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes17.0ms (0.2%)

Accuracy

Total 0.4b remaining (78.7%)

Threshold costs 0.4b (78.7%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch14.0ms (0.2%)

Compiler: Compiled 296 to 198 computations (33.1% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	190	405
1	190	405

end0.0ms (0%)

sample3.6s (45%)

Algorithm

1×

intervals

Results

1.0s	2027×	body	2048	valid
936.0ms	3872×	body	1024	valid
211.0ms	1347×	body	512	valid
56.0ms	512×	body	256	valid
14.0ms	240×	body	128	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 1137 to 830 computations (27% saved)

Pareto

0.4564991154350679

Details

analyze2.0ms (0%)

sample80.0ms (1%)

simplify91.0ms (1.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite13.0ms (0.2%)

series121.0ms (1.5%)

simplify59.0ms (0.7%)

prune64.0ms (0.8%)

localize14.0ms (0.2%)

rewrite39.0ms (0.5%)

series394.0ms (4.9%)

simplify93.0ms (1.2%)

prune122.0ms (1.5%)

localize18.0ms (0.2%)

rewrite46.0ms (0.6%)

series415.0ms (5.2%)

simplify90.0ms (1.1%)

prune182.0ms (2.3%)

localize12.0ms (0.2%)

rewrite27.0ms (0.3%)

series482.0ms (6%)

simplify85.0ms (1.1%)

prune107.0ms (1.3%)

simplify98.0ms (1.2%)

regimes373.0ms (4.6%)

bsearch64.0ms (0.8%)

regimes230.0ms (2.9%)

bsearch61.0ms (0.8%)

regimes211.0ms (2.6%)

bsearch65.0ms (0.8%)

regimes109.0ms (1.4%)

bsearch0.0ms (0%)

regimes96.0ms (1.2%)

bsearch53.0ms (0.7%)

regimes94.0ms (1.2%)

bsearch42.0ms (0.5%)

regimes77.0ms (1%)

bsearch41.0ms (0.5%)

regimes44.0ms (0.5%)

bsearch41.0ms (0.5%)

regimes19.0ms (0.2%)

bsearch0.0ms (0%)

regimes30.0ms (0.4%)

bsearch66.0ms (0.8%)

regimes17.0ms (0.2%)

bsearch14.0ms (0.2%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample3.6s (45%)

Profiling