Details

analyze99.0ms (2.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

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)

sample74.0ms (1.5%)

Algorithm

1×

intervals

Results

27.0ms	96×	body	1024	valid
23.0ms	34×	body	2048	valid
11.0ms	62×	body	512	valid
3.0ms	47×	body	128	valid
3.0ms	17×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (0.1%)

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

Error

35.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.5b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.1b	(sin.f64 (+.f64 x eps))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163`
3×	`cancel-sign-sub-inv_binary64_2090` `add-cube-cbrt_binary64_2159`
2×	`pow1_binary64_2185` `sin-sum_binary64_2257` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-sin_binary64_2274` `diff-log_binary64_2216` `associate--l+_binary64_2061` `sub-neg_binary64_2117`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

series52.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

35.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
17.0ms	(sin.f64 (+.f64 x eps))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5196	441

prune27.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Error

0.4b

Counts

33 → 3

Compiler

Compiled 428 to 129 computations (69.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.1b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2124`
8×	`add-log-exp_binary64_2163`
7×	`add-sqr-sqrt_binary64_2146`
5×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sum-log_binary64_2215` `distribute-lft-out_binary64_2075` `associate-l_binary64_2065` `associate-r_binary64_2064`
1×	`pow-prod-down_binary64_2195` `sin-cos-mult_binary64_2280` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `associate-+r+_binary64_2056` `prod-exp_binary64_2173` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `flip-+_binary64_2098` `cbrt-unprod_binary64_2157`

Counts

3 → 41

Calls

3 calls:

7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series84.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
23.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
16.0ms	(+.f64 x (+.f64 x eps))

simplify80.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5266	830

prune64.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Error

0.3b

Counts

53 → 9

Compiler

Compiled 1173 to 768 computations (34.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
4.1b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_2155`
24×	`add-sqr-sqrt_binary64_2146`
15×	`add-cube-cbrt_binary64_2159` `associate-r_binary64_2064` `*-un-lft-identity_binary64_2124`
10×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
7×	`pow1_binary64_2185` `add-exp-log_binary64_2162`
6×	`add-cbrt-cube_binary64_2160`
5×	`unswap-sqr_binary64_2092`
4×	`add-log-exp_binary64_2163` `sqr-pow_binary64_2096`
3×	`unpow3_binary64_2190` `pow-unpow_binary64_2201` `cube-mult_binary64_2154` `associate-l_binary64_2065`
1×	`pow-prod-down_binary64_2195` `pow-pow_binary64_2196` `rem-cbrt-cube_binary64_2148` `pow-exp_binary64_2192` `*-commutative_binary64_2055` `pow1/3_binary64_2206` `prod-exp_binary64_2173` `pow-to-exp_binary64_2193` `cbrt-unprod_binary64_2157` `rem-cube-cbrt_binary64_2147`

Counts

4 → 85

Calls

4 calls:

12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

series146.0ms (3%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
50.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
19.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
18.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4910	1942
1	4910	1942

prune129.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	97	9	106

Error

0.3b

Counts

106 → 9

Compiler

Compiled 2429 to 1612 computations (33.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
4.1b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite42.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2146`
12×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`log-prod_binary64_2210` `exp-prod_binary64_2176`
8×	`log-pow_binary64_2213` `pow1_binary64_2185`
7×	`associate-r_binary64_2064`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`add-log-exp_binary64_2163`
3×	`associate-l_binary64_2065` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
1×	`pow-prod-down_binary64_2195` `rem-log-exp_binary64_2165` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `rem-exp-log_binary64_2164` `cbrt-unprod_binary64_2157`

Counts

4 → 61

Calls

4 calls:

14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
8.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series204.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
56.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
34.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
19.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4989	1476
1	4989	1476

prune89.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	6	6
Picked	0	1	1
Done	1	1	2
Total	72	10	82

Error

0.3b

Counts

82 → 10

Compiler

Compiled 1660 to 1086 computations (34.6% saved)

regimes229.0ms (4.8%)

Accuracy

Total 0.1b remaining (20.8%)

Threshold costs 0.1b (20.8%)

Compiler

Compiled 1590 to 1253 computations (21.2% saved)

bsearch51.0ms (1.1%)

Steps

Iters	Range		Point
9	1.1941300066793848e-12	0.0007794748927502307	2.9552866203194552e-08
4	-0.00017806805562616074	-0.00010248124561627069	-0.0001039683686927335

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	57
1	47	57

end0.0ms (0%)

sample3.1s (64.2%)

Algorithm

1×

intervals

Results

992.0ms	3451×	body	1024	valid
649.0ms	1263×	body	2048	valid
268.0ms	576×	body	256	valid
259.0ms	1383×	body	512	valid
87.0ms	1326×	body	128	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 581 to 459 computations (21% saved)

Details

analyze99.0ms (2.1%)

sample74.0ms (1.5%)

simplify10.0ms (0.2%)

prune2.0ms (0.1%)

localize7.0ms (0.1%)

rewrite12.0ms (0.3%)

series52.0ms (1.1%)

simplify62.0ms (1.3%)

prune27.0ms (0.6%)

localize11.0ms (0.2%)

rewrite22.0ms (0.5%)

series84.0ms (1.7%)

simplify80.0ms (1.7%)

prune64.0ms (1.3%)

localize14.0ms (0.3%)

rewrite32.0ms (0.7%)

series146.0ms (3%)

simplify85.0ms (1.8%)

prune129.0ms (2.7%)

localize14.0ms (0.3%)

rewrite42.0ms (0.9%)

series204.0ms (4.2%)

simplify79.0ms (1.6%)

prune89.0ms (1.8%)

regimes229.0ms (4.8%)

bsearch51.0ms (1.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.1s (64.2%)

Profiling