Details

analyze78.0ms (2.2%)

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
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	18.7%	12.6%	7
68.7%	12.5%	18.8%	8
68.7%	12.5%	18.8%	9
68.7%	9.4%	22%	10
68.7%	9.4%	22%	11
68.7%	7.8%	23.5%	12
68.7%	7.8%	23.5%	13
68.7%	7%	24.3%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample15.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
1.0ms	25×	body	128	overflowed

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify168.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	13
1	8	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: 1.5b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
1.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_2143`
12×	`times-frac_binary64_2149`
11×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178`
5×	`distribute-lft-out_binary64_2094`
4×	`add-log-exp_binary64_2182` `associate-/r*_binary64_2087` `add-cbrt-cube_binary64_2179`
3×	`associate-/l*_binary64_2088` `add-exp-log_binary64_2181`
2×	`pow1_binary64_2204` `associate-/r/_binary64_2089` `flip3-+_binary64_2146` `flip-+_binary64_2117`
1×	`cbrt-undiv_binary64_2177` `+-commutative_binary64_2073` `clear-num_binary64_2142` `div-inv_binary64_2140` `sum-log_binary64_2234` `div-exp_binary64_2194` `frac-2neg_binary64_2154`

Counts

2 → 45

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

series131.0ms (3.6%)

Counts

2 → 6

Calls

2 calls:

96.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
34.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify66.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5503	899

prune81.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	5	52

Merged error: 1.4b

Counts

52 → 5

Compiler

Compiled 1375 to 523 computations (62% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
1.3b	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
4.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_2143`
13×	`add-sqr-sqrt_binary64_2165`
9×	`pow1_binary64_2204` `add-log-exp_binary64_2182` `add-cube-cbrt_binary64_2178`
8×	`log-prod_binary64_2229` `cancel-sign-sub-inv_binary64_2109`
7×	`exp-sum_binary64_2189`
6×	`exp-prod_binary64_2195` `log-div_binary64_2230`
5×	`add-exp-log_binary64_2181` `log-pow_binary64_2232`
4×	`associate--r-_binary64_2082` `distribute-lft-out--_binary64_2095` `associate--r+_binary64_2079` `flip3-+_binary64_2146` `flip-+_binary64_2117` `add-cbrt-cube_binary64_2179`
3×	`distribute-lft-out_binary64_2094`
2×	`diff-log_binary64_2235` `sub-neg_binary64_2136` `rem-exp-log_binary64_2183` `difference-of-squares_binary64_2112`
1×	`+-commutative_binary64_2073` `flip--_binary64_2118` `rem-log-exp_binary64_2184` `sum-log_binary64_2234` `flip3--_binary64_2147` `exp-diff_binary64_2191`

Counts

4 → 74

Calls

4 calls:

9.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
7.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
5.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

series270.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
77.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
65.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
35.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify64.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5765	1300

prune59.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	86	5	91

Merged error: 1.4b

Counts

91 → 5

Compiler

Compiled 1263 to 348 computations (72.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
0.3b	(*.f64 (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
1.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
1.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite75.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`*-un-lft-identity_binary64_2143`
98×	`sqrt-prod_binary64_2159`
96×	`add-sqr-sqrt_binary64_2165`
92×	`times-frac_binary64_2149`
62×	`add-cube-cbrt_binary64_2178`
29×	`swap-sqr_binary64_2110`
27×	`distribute-lft-out_binary64_2094`
21×	`associate-r_binary64_2083` `associate-l_binary64_2084`
19×	`pow1_binary64_2204`
12×	`associate-/r/_binary64_2089`
10×	`add-cbrt-cube_binary64_2179`
9×	`unswap-sqr_binary64_2111`
8×	`pow1/2_binary64_2223` `associate-/r*_binary64_2087` `add-exp-log_binary64_2181` `sqrt-pow1_binary64_2161`
7×	`flip3-+_binary64_2146` `flip-+_binary64_2117`
6×	`add-log-exp_binary64_2182` `associate-/l*_binary64_2088` `div-inv_binary64_2140`
5×	`pow-prod-up_binary64_2213`
4×	`rem-sqrt-square_binary64_2156` `sqrt-div_binary64_2160`
3×	`pow-sqr_binary64_2116` `pow-prod-down_binary64_2214`
2×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `sqr-abs_binary64_2158` `div-exp_binary64_2194` `frac-2neg_binary64_2154`
1×	`+-commutative_binary64_2073` `pow2_binary64_2224` `sqrt-unprod_binary64_2163` `frac-times_binary64_2153` `pow-plus_binary64_2206` `cbrt-unprod_binary64_2176` `sum-log_binary64_2234` `prod-exp_binary64_2192` `associate-l/_binary64_2086` `associate-r/_binary64_2085` `rem-square-sqrt_binary64_2155` `*-commutative_binary64_2074`

Counts

4 → 188

Calls

4 calls:

31.0ms	(*.f64 (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
8.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
8.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

series323.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(*.f64 (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
95.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
93.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
33.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify113.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4942	4272
1	4942	4272

prune168.0ms (4.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	200	5	205

Merged error: 1.4b

Counts

205 → 5

Compiler

Compiled 4689 to 662 computations (85.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
1.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
1.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
1.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite85.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

137×	`*-un-lft-identity_binary64_2143`
102×	`times-frac_binary64_2149`
96×	`cbrt-prod_binary64_2174`
95×	`add-sqr-sqrt_binary64_2165`
71×	`add-cube-cbrt_binary64_2178`
30×	`distribute-lft-out_binary64_2094`
27×	`swap-sqr_binary64_2110`
21×	`associate-r_binary64_2083` `associate-l_binary64_2084`
14×	`associate-/r/_binary64_2089`
12×	`associate-/r*_binary64_2087`
11×	`pow1_binary64_2204`
10×	`add-cbrt-cube_binary64_2179`
9×	`associate-/l*_binary64_2088` `add-exp-log_binary64_2181` `unswap-sqr_binary64_2111`
7×	`div-inv_binary64_2140` `flip3-+_binary64_2146` `flip-+_binary64_2117`
6×	`pow1/3_binary64_2225`
4×	`add-log-exp_binary64_2182` `cbrt-div_binary64_2175`
3×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `div-exp_binary64_2194` `frac-2neg_binary64_2154`
2×	`pow-sqr_binary64_2116` `pow-prod-up_binary64_2213` `pow-prod-down_binary64_2214`
1×	`pow2_binary64_2224` `frac-times_binary64_2153` `pow-plus_binary64_2206` `cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `associate-l/_binary64_2086` `associate-r/_binary64_2085` `*-commutative_binary64_2074`

Counts

4 → 198

Calls

4 calls:

29.0ms	(*.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
10.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
8.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
8.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series886.0ms (24.5%)

Counts

4 → 12

Calls

4 calls:

407.0ms	(*.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
282.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
102.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
95.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

simplify109.0ms (3%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4976	6026
1	4976	6026

prune224.0ms (6.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	210	5	215

Merged error: 1.4b

Counts

215 → 5

Compiler

Compiled 7857 to 887 computations (88.7% saved)

regimes70.0ms (1.9%)

Compiler: Compiled 520 to 286 computations (45% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	15
1	20	15

end0.0ms (0%)

sample552.0ms (15.3%)

Algorithm

1×

intervals

Results

253.0ms	8000×	body	128	valid
18.0ms	702×	body	128	overflowed

Compiler

Compiled 98 to 63 computations (35.7% saved)

Details

analyze78.0ms (2.2%)

sample15.0ms (0.4%)

simplify168.0ms (4.6%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

rewrite16.0ms (0.4%)

series131.0ms (3.6%)

simplify66.0ms (1.8%)

prune81.0ms (2.2%)

localize9.0ms (0.2%)

rewrite32.0ms (0.9%)

series270.0ms (7.5%)

simplify64.0ms (1.8%)

prune59.0ms (1.6%)

localize8.0ms (0.2%)

rewrite75.0ms (2.1%)

series323.0ms (8.9%)

simplify113.0ms (3.1%)

prune168.0ms (4.6%)

localize9.0ms (0.3%)

rewrite85.0ms (2.3%)

series886.0ms (24.5%)

simplify109.0ms (3%)

prune224.0ms (6.2%)

regimes70.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample552.0ms (15.3%)

Profiling