Details

Time bar (total: 11.1s)

analyze2.1s (18.6%)

Algorithm
search
Search
TrueOtherFalseIter
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 31 to 24 computations (22.6% saved)

sample5.1s (46.5%)

Results
2.6s2335×body1024valid
1.1s4283×body128valid
815.0ms1111×body512valid
300.0ms515×body256valid
197.0ms827×body128invalid
20.0ms12×body2048valid
Compiler

Compiled 92 to 71 computations (22.8% saved)

simplify52.0ms (0.5%)

Algorithm
egg-herbie
Rules
640×distribute-rgt-neg-in_binary64
474×fma-neg_binary64
418×distribute-lft-neg-in_binary64
379×div-sub_binary64
378×fma-def_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02335
14928
210028
319528
439128
5107528
6254328
7420028
8495528

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
15.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
15.2b
(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (*.f64 F F) 2) (*.f64 2 x)) (neg.f64 (/.f64 1 2)))))
15.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 x (tan.f64 B)))
Compiler

Compiled 153 to 108 computations (29.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 F (sin.f64 B))
0.1b
(/.f64 x (tan.f64 B))
7.4b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
18.1b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series180.0ms (1.6%)

Counts
4 → 80
Calls

4 calls:

97.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
39.0ms
(/.f64 x (tan.f64 B))
28.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
16.0ms
(/.f64 F (sin.f64 B))

rewrite97.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
270×expm1-udef_binary64
270×log1p-udef_binary64
151×add-sqr-sqrt_binary64
141×log1p-expm1-u_binary64
141×expm1-log1p-u_binary64
Counts
4 → 113
Calls

4 calls:

95.0ms
(/.f64 F (sin.f64 B))
95.0ms
(/.f64 x (tan.f64 B))
95.0ms
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
95.0ms
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01444
129944
2365744
3492044
4492644
000
100

simplify93.0ms (0.8%)

Algorithm
egg-herbie
Rules
965×times-frac_binary64
300×fma-def_binary64
196×+-commutative_binary64
187×fma-neg_binary64
166×*-commutative_binary64
Counts
193 → 212
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03333644
110303471
235483471
350223471

prune261.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New20111212
Fresh101
Picked101
Done000
Total20311214
Error
0.0b
Counts
214 → 11
Alt Table
StatusErrorProgram
15.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (*.f64 (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/4) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/4))) (/.f64 x (tan.f64 B)))
40.4b
(-.f64 (-.f64 (/.f64 1 (sin.f64 B)) (+.f64 (/.f64 x (*.f64 (sin.f64 B) (pow.f64 F 2))) (/.f64 1 (*.f64 (sin.f64 B) (pow.f64 F 2))))) (/.f64 x (tan.f64 B)))
15.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (cbrt.f64 (/.f64 x (tan.f64 B)))))
38.7b
(-.f64 (/.f64 (/.f64 (*.f64 F (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))) (/.f64 x (tan.f64 B)))
39.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
15.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
12.5b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
34.5b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
15.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
36.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (tan.f64 B)))))
42.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (sqrt.f64 (tan.f64 B))) (/.f64 x (sqrt.f64 (tan.f64 B)))))
Compiler

Compiled 8310 to 4950 computations (40.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 x (tan.f64 B))
0.3b
(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
0.3b
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
18.1b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series147.0ms (1.3%)

Counts
2 → 56
Calls

2 calls:

99.0ms
(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
47.0ms
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))

rewrite64.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
622×log-prod_binary64
228×expm1-udef_binary64
228×log1p-udef_binary64
205×log-pow_binary64
131×prod-diff_binary64
Counts
2 → 83
Calls

2 calls:

61.0ms
(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)))
61.0ms
(/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01237
125835
2315435
3562035
000
100

simplify91.0ms (0.8%)

Algorithm
egg-herbie
Rules
559×fma-neg_binary64
528×times-frac_binary64
474×cancel-sign-sub-inv_binary64
273×neg-mul-1_binary64
230×sub-neg_binary64
Counts
139 → 165
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02342803
17372637
225022493
345872489
451092489

prune337.0ms (3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2664270
Fresh2810
Picked011
Done000
Total26813281
Error
0.0b
Counts
281 → 13
Alt Table
StatusErrorProgram
12.5b
(-.f64 (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))))) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
36.0b
(-.f64 (/.f64 F (neg.f64 (*.f64 F (sin.f64 B)))) (/.f64 x (tan.f64 B)))
40.4b
(-.f64 (-.f64 (/.f64 1 (sin.f64 B)) (+.f64 (/.f64 x (*.f64 (sin.f64 B) (pow.f64 F 2))) (/.f64 1 (*.f64 (sin.f64 B) (pow.f64 F 2))))) (/.f64 x (tan.f64 B)))
15.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (cbrt.f64 (/.f64 x (tan.f64 B)))))
39.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
15.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
36.0b
(-.f64 (/.f64 F (*.f64 (sin.f64 B) F)) (/.f64 x (tan.f64 B)))
34.5b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
15.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
36.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (tan.f64 B)))))
42.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (sqrt.f64 (tan.f64 B))) (/.f64 x (sqrt.f64 (tan.f64 B)))))
26.8b
(-.f64 (/.f64 F (cbrt.f64 (pow.f64 (*.f64 (sin.f64 B) (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))) 3))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 10511 to 6262 computations (40.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 x (tan.f64 B))
0.2b
(/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))))
0.4b
(*.f64 (/.f64 1 (sin.f64 B)) (/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))))
18.1b
(sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))

series156.0ms (1.4%)

Counts
3 → 60
Calls

3 calls:

97.0ms
(*.f64 (/.f64 1 (sin.f64 B)) (/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))))
40.0ms
(/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))))
19.0ms
(sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))

rewrite67.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
625×log-prod_binary64
229×expm1-udef_binary64
229×log1p-udef_binary64
211×log-pow_binary64
138×log-div_binary64
Counts
3 → 120
Calls

3 calls:

64.0ms
(/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))))
64.0ms
(*.f64 (/.f64 1 (sin.f64 B)) (/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))))
64.0ms
(sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01344
126744
2321144
3571044
000
100

simplify73.0ms (0.7%)

Algorithm
egg-herbie
Rules
501×times-frac_binary64
470×cancel-sign-sub-inv_binary64
354×sub-neg_binary64
233×fma-def_binary64
217×fma-neg_binary64
Counts
180 → 220
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02702923
18352749
228392747
350562747

prune317.0ms (2.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New2621263
Fresh11011
Picked011
Done011
Total26313276
Error
0.0b
Counts
276 → 13
Alt Table
StatusErrorProgram
12.5b
(-.f64 (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))))) (/.f64 x (tan.f64 B)))
12.5b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
36.0b
(-.f64 (/.f64 F (*.f64 (sin.f64 B) F)) (/.f64 x (tan.f64 B)))
34.5b
(-.f64 (*.f64 (/.f64 1 (sin.f64 B)) 1) (/.f64 x (tan.f64 B)))
15.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (cbrt.f64 (/.f64 x (tan.f64 B)))))
39.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (/.f64 x (tan.f64 B)))
15.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 x (/.f64 1 (tan.f64 B))))
34.5b
(-.f64 (/.f64 -1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
36.0b
(-.f64 (/.f64 F (neg.f64 (*.f64 F (sin.f64 B)))) (/.f64 x (tan.f64 B)))
15.1b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
36.6b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (tan.f64 B)))))
42.0b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 1 (sqrt.f64 (tan.f64 B))) (/.f64 x (sqrt.f64 (tan.f64 B)))))
26.8b
(-.f64 (/.f64 F (cbrt.f64 (pow.f64 (*.f64 (sin.f64 B) (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))) 3))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 9058 to 5369 computations (40.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 F (sin.f64 B))
0.1b
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
7.4b
(*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))
18.1b
(pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)

series22.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

22.0ms
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))

rewrite71.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
716×log1p-expm1-u_binary64
716×expm1-log1p-u_binary64
137×expm1-udef_binary64
137×log1p-udef_binary64
75×add-sqr-sqrt_binary64
Counts
1 → 26
Calls

1 calls:

70.0ms
(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
114411
2185111
3498811
4499011
000
100

simplify146.0ms (1.3%)

Algorithm
egg-herbie
Rules
824×unswap-sqr_binary64
470×distribute-rgt-neg-in_binary64
466×fma-def_binary64
424×sub-neg_binary64
384×distribute-lft-neg-in_binary64
Counts
50 → 33
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
027293
174291
2203284
3598282
41913282
52728282
63782282
74069282
84971282
94788282
104989282
114742282

prune240.0ms (2.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1975202
Fresh5510
Picked101
Done022
Total20312215
Error
0.0b
Counts
215 → 12
Alt Table
StatusErrorProgram
12.5b
(-.f64 (*.f64 (/.f64 1 (sin.f64 B)) (/.f64 F (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2))))) (/.f64 x (tan.f64 B)))
34.5b
(-.f64 (/.f64 -1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
12.5b
(-.f64 (/.f64 F (/.f64 (sin.f64 B) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2))) (/.f64 x (tan.f64 B)))
36.0b
(-.f64 (/.f64 F (*.f64 (sin.f64 B) F)) (/.f64 x (tan.f64 B)))
34.5b
(-.f64 (*.f64 (/.f64 1 (sin.f64 B)) 1) (/.f64 x (tan.f64 B)))
15.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (/.f64 (*.f64 x (cos.f64 B)) (pow.f64 (cbrt.f64 (sin.f64 B)) 2)) (cbrt.f64 (sin.f64 B))))
36.0b
(-.f64 (/.f64 F (neg.f64 (*.f64 F (sin.f64 B)))) (/.f64 x (tan.f64 B)))
39.3b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (/.f64 1 F)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
40.5b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (/.f64 (*.f64 x (cos.f64 B)) (sqrt.f64 (sin.f64 B))) (sqrt.f64 (sin.f64 B))))
15.7b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (tan.f64 B)) 2)) (cbrt.f64 (/.f64 x (tan.f64 B)))))
15.2b
(-.f64 (*.f64 (/.f64 F (sin.f64 B)) (pow.f64 (fma.f64 x 2 (fma.f64 F F 2)) -1/2)) (/.f64 (cos.f64 B) (/.f64 (sin.f64 B) x)))
26.8b
(-.f64 (/.f64 F (cbrt.f64 (pow.f64 (*.f64 (sin.f64 B) (sqrt.f64 (fma.f64 x 2 (fma.f64 F F 2)))) 3))) (/.f64 x (tan.f64 B)))
Compiler

Compiled 8301 to 4612 computations (44.4% saved)

regimes997.0ms (9%)

Accuracy

Total 0.2b remaining (76.5%)

Threshold costs 0.2b (76.5%)

Counts
165 → 3
Compiler

Compiled 15628 to 10944 computations (30% saved)

bsearch154.0ms (1.4%)

Steps
ItersRangePoint
9
0.44020137540811566
31893389.003689665
31465108.153329495
6
-4.324819827133507e+151
-2.3452629262293073e+147
-1.0847063455858735e+151
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
20×+-commutative_binary64
18×*-commutative_binary64
18×sub-neg_binary64
15×neg-sub0_binary64
15×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039105
161105
294105
3129105
4147105
5155105
6156105
7154105

end219.0ms (2%)

Compiler

Compiled 409 to 264 computations (35.5% saved)

Profiling

Loading profile data...