Details

Time bar (total: 8.5s)

analyze1.8s (21.4%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
3.1%96.5%0.3%9
4.7%95%0.3%10
4.7%95%0.3%11
5.1%82.1%12.8%12
6.2%74.7%19%13
6.4%74.5%19%14
Compiler

Compiled 34 to 30 computations (11.8% saved)

sample74.0ms (0.9%)

Algorithm
1×intervals
Results
27.0ms256×body80valid
18.0ms183×body80nan
Compiler

Compiled 67 to 66 computations (1.5% saved)

simplify88.0ms (1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
0498144
1498144

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 2.7b

Counts
2 → 1
Compiler

Compiled 58 to 50 computations (13.8% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 z (sqrt.f64 (+.f64 t a)))
0.4b
(/.f64 2/3 t)
1.6b
(-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
5.8b
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite45.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
20×frac-sub_binary64
19×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
13×add-exp-log_binary64 add-cbrt-cube_binary64
12×times-frac_binary64
9×flip3--_binary64 flip--_binary64
8×associate-*r/_binary64 frac-times_binary64
7×associate-*r*_binary64
6×associate-/r*_binary64 add-log-exp_binary64 pow1_binary64
5×flip3-+_binary64 sqrt-prod_binary64 flip-+_binary64
4×associate--r+_binary64 associate-/l*_binary64 insert-posit16 sqrt-div_binary64
3×sub-neg_binary64 cbrt-undiv_binary64 associate-*l*_binary64 div-exp_binary64
2×associate-/l/_binary64 cbrt-unprod_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-inv_binary64 associate--l+_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 diff-log_binary64 distribute-lft-out_binary64 *-commutative_binary64
Counts
4 → 108
Calls

4 calls:

17.0ms
(-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
10.0ms
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
9.0ms
(*.f64 z (sqrt.f64 (+.f64 t a)))
4.0ms
(/.f64 2/3 t)

series620.0ms (7.3%)

Counts
4 → 12
Calls

4 calls:

363.0ms
(-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
131.0ms
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
100.0ms
(*.f64 z (sqrt.f64 (+.f64 t a)))
25.0ms
(/.f64 2/3 t)

simplify102.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049603055
149603055

prune224.0ms (2.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1164120
Fresh000
Picked101
Done000
Total1174121

Merged error: 0.0b

Counts
121 → 4
Compiler

Compiled 4823 to 2416 computations (49.9% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 t)
0.6b
(cbrt.f64 t)
1.6b
(-.f64 (*.f64 (/.f64 z (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
1.9b
(*.f64 (/.f64 z (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))

rewrite73.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
63×add-sqr-sqrt_binary64
60×frac-sub_binary64
58×times-frac_binary64
47×*-un-lft-identity_binary64
46×associate-*r*_binary64
39×frac-times_binary64
35×add-cube-cbrt_binary64
31×cbrt-prod_binary64
28×sqrt-prod_binary64
27×associate-*r/_binary64
25×flip3--_binary64 add-exp-log_binary64 flip--_binary64
21×associate-*l/_binary64
18×add-cbrt-cube_binary64
10×unswap-sqr_binary64
9×flip3-+_binary64 flip-+_binary64
8×cbrt-unprod_binary64 prod-exp_binary64
7×cbrt-undiv_binary64 associate-*l*_binary64 div-exp_binary64
6×add-log-exp_binary64 pow1_binary64 distribute-lft-out_binary64
4×associate--r+_binary64 insert-posit16
3×sub-neg_binary64
2×pow1/3_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 div-inv_binary64 associate--l+_binary64
1×pow-prod-down_binary64 diff-log_binary64 *-commutative_binary64
Counts
4 → 170
Calls

4 calls:

30.0ms
(*.f64 (/.f64 z (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
27.0ms
(-.f64 (*.f64 (/.f64 z (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
1.0ms
(cbrt.f64 t)
1.0ms
(cbrt.f64 t)

series863.0ms (10.1%)

Counts
4 → 12
Calls

4 calls:

398.0ms
(-.f64 (*.f64 (/.f64 z (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
157.0ms
(*.f64 (/.f64 z (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (sqrt.f64 (+.f64 t a)) (cbrt.f64 t)))
155.0ms
(cbrt.f64 t)
153.0ms
(cbrt.f64 t)

simplify110.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
049787384
149787384

prune438.0ms (5.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1820182
Fresh033
Picked011
Done000
Total1824186

Merged error: 0.0b

Counts
186 → 4
Compiler

Compiled 9148 to 4487 computations (51% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 2/3 t)
1.6b
(-.f64 (/.f64 (posit16->binary64 (binary64->posit16 (*.f64 z (sqrt.f64 (+.f64 t a))))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
5.8b
(/.f64 (posit16->binary64 (binary64->posit16 (*.f64 z (sqrt.f64 (+.f64 t a))))) t)
55.7b
(posit16->binary64 (binary64->posit16 (*.f64 z (sqrt.f64 (+.f64 t a)))))

rewrite26.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
20×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 frac-sub_binary64
18×times-frac_binary64
9×flip3--_binary64 flip--_binary64
8×add-exp-log_binary64 add-cbrt-cube_binary64 frac-times_binary64
6×associate-/r*_binary64 add-log-exp_binary64 associate-/l*_binary64
4×pow1_binary64 associate--r+_binary64 associate-*r/_binary64 insert-posit16
3×flip3-+_binary64 sub-neg_binary64 flip-+_binary64
2×cbrt-undiv_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 associate--l+_binary64 associate-*l/_binary64
1×diff-log_binary64 remove-posit16
Counts
4 → 95
Calls

4 calls:

14.0ms
(-.f64 (/.f64 (posit16->binary64 (binary64->posit16 (*.f64 z (sqrt.f64 (+.f64 t a))))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
4.0ms
(/.f64 2/3 t)
4.0ms
(/.f64 (posit16->binary64 (binary64->posit16 (*.f64 z (sqrt.f64 (+.f64 t a))))) t)
1.0ms
(posit16->binary64 (binary64->posit16 (*.f64 z (sqrt.f64 (+.f64 t a)))))

series379.0ms (4.4%)

Counts
4 → 12
Calls

4 calls:

274.0ms
(-.f64 (/.f64 (posit16->binary64 (binary64->posit16 (*.f64 z (sqrt.f64 (+.f64 t a))))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (/.f64 2/3 t))))
54.0ms
(/.f64 (posit16->binary64 (binary64->posit16 (*.f64 z (sqrt.f64 (+.f64 t a))))) t)
26.0ms
(/.f64 2/3 t)
25.0ms
(posit16->binary64 (binary64->posit16 (*.f64 z (sqrt.f64 (+.f64 t a)))))

simplify89.0ms (1%)

Algorithm
1×egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
051022838

prune173.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1070107
Fresh022
Picked011
Done011
Total1074111

Merged error: 0.0b

Counts
111 → 4
Compiler

Compiled 4325 to 2033 computations (53% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 2/3 t)
3.3b
(-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
3.6b
(log.f64 (exp.f64 (/.f64 2/3 t)))
5.8b
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)

rewrite44.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
22×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
21×times-frac_binary64
14×log-pow_binary64
13×exp-prod_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
8×frac-sub_binary64
7×flip3--_binary64 flip--_binary64
6×associate-/r*_binary64 add-log-exp_binary64
5×pow1_binary64
4×associate--r+_binary64 associate-*r/_binary64 associate-/l*_binary64 insert-posit16 frac-times_binary64
3×sub-neg_binary64 log-prod_binary64 cbrt-undiv_binary64 div-inv_binary64 div-exp_binary64
2×associate-/l/_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 sqrt-div_binary64 associate--l+_binary64 associate-*l/_binary64
1×flip3-+_binary64 diff-log_binary64 cbrt-unprod_binary64 rem-log-exp_binary64 prod-exp_binary64 flip-+_binary64
Counts
4 → 102
Calls

4 calls:

19.0ms
(-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
10.0ms
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
6.0ms
(log.f64 (exp.f64 (/.f64 2/3 t)))
5.0ms
(/.f64 2/3 t)

series540.0ms (6.3%)

Counts
4 → 12
Calls

4 calls:

359.0ms
(-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a 5/6) (log.f64 (exp.f64 (/.f64 2/3 t))))))
135.0ms
(/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)
24.0ms
(/.f64 2/3 t)
23.0ms
(log.f64 (exp.f64 (/.f64 2/3 t)))

simplify127.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (91.0ms)

IterNodesCost
049492336
149492336

prune199.0ms (2.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1140114
Fresh011
Picked011
Done022
Total1144118

Merged error: 0.0b

Counts
118 → 4
Compiler

Compiled 4368 to 2233 computations (48.9% saved)

regimes132.0ms (1.5%)

Compiler

Compiled 1052 to 986 computations (6.3% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
021756
121756

end0.0ms (0%)

sample2.2s (26%)

Algorithm
1×intervals
Results
846.0ms8000×body80valid
505.0ms5050×body80nan
Compiler

Compiled 321 to 261 computations (18.7% saved)

Profiling

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