Details

Time bar (total: 54.1s)

sample23.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
1.0ms6×body320valid
0.0ms3×body640valid
0.0ms2×body160valid
0.0ms1×body1280valid

simplify76.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0548
11467
23377
310177
436597
550017

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(tanh (/ x y))
0.2b
(- (tanh (/ t y)) (tanh (/ x y)))
0.3b
(* z (- (tanh (/ t y)) (tanh (/ x y))))
1.3b
(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
29×*-un-lft-identity
27×prod-diff
25×add-cube-cbrt
18×frac-sub
13×tanh-def
11×distribute-rgt-in distribute-lft-in associate-*r/
6×pow1 add-exp-log add-cbrt-cube add-log-exp
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u
3×sub-neg fma-neg associate-*l*
2×flip3-- flip-- distribute-lft-out-- difference-of-squares
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 114
Calls
4 calls:
1.0ms
(tanh (/ x y))
7.0ms
(- (tanh (/ t y)) (tanh (/ x y)))
27.0ms
(* z (- (tanh (/ t y)) (tanh (/ x y))))
0.0ms
(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)

series758.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(tanh (/ x y))
217.0ms
(- (tanh (/ t y)) (tanh (/ x y)))
216.0ms
(* z (- (tanh (/ t y)) (tanh (/ x y))))
245.0ms
(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)

simplify68.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05601798
122571400
250011397

prune370.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize21.0ms

Local error

Found 4 expressions with local error:

1.3b
(fma y (+ (* z (fma (* (cbrt (tanh (/ t y))) (cbrt (tanh (/ t y)))) (cbrt (tanh (/ t y))) (- (* (tanh (/ x y)) 1)))) (* z (* (tanh (/ x y)) (+ (- 1) 1)))) x)
6.6b
(cbrt (tanh (/ t y)))
6.6b
(cbrt (tanh (/ t y)))
6.6b
(cbrt (tanh (/ t y)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod cbrt-div
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 tanh-def
1×fma-udef
Counts
4 → 58
Calls
4 calls:
0.0ms
(fma y (+ (* z (fma (* (cbrt (tanh (/ t y))) (cbrt (tanh (/ t y)))) (cbrt (tanh (/ t y))) (- (* (tanh (/ x y)) 1)))) (* z (* (tanh (/ x y)) (+ (- 1) 1)))) x)
1.0ms
(cbrt (tanh (/ t y)))
1.0ms
(cbrt (tanh (/ t y)))
2.0ms
(cbrt (tanh (/ t y)))

series854.0ms

Counts
4 → 12
Calls
4 calls:
339.0ms
(fma y (+ (* z (fma (* (cbrt (tanh (/ t y))) (cbrt (tanh (/ t y)))) (cbrt (tanh (/ t y))) (- (* (tanh (/ x y)) 1)))) (* z (* (tanh (/ x y)) (+ (- 1) 1)))) x)
170.0ms
(cbrt (tanh (/ t y)))
171.0ms
(cbrt (tanh (/ t y)))
173.0ms
(cbrt (tanh (/ t y)))

simplify114.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
0299814
1876730
24297696
35001678

prune404.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))
1.0b
(* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))
1.3b
(fma y (/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y)))))) x)
9.7b
(/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
6780×frac-add
6093×frac-times
5434×tanh-def
3407×associate-/r/
2053×associate-*r/
2031×associate-*l/
432×prod-diff
277×add-sqr-sqrt
247×*-un-lft-identity
243×unpow-prod-down cube-prod
227×add-cube-cbrt
146×distribute-rgt-in distribute-lft-in
89×sqr-pow
73×cube-mult unpow3
54×cube-div
32×difference-of-squares
27×frac-sub
25×associate-*r*
16×flip3-+ flip-+
12×fma-neg
11×add-exp-log add-cbrt-cube associate-/l/
10×distribute-lft-out--
6×pow1 add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×sub-neg flip3-- times-frac associate-*l* associate-/r* flip--
2×difference-cubes cbrt-undiv div-exp prod-exp cbrt-unprod
1×frac-2neg diff-log pow-prod-down clear-num *-commutative fma-udef div-inv associate-/l* unswap-sqr
Counts
4 → 3997
Calls
4 calls:
27.0ms
(- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))
92.0ms
(* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))
0.0ms
(fma y (/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y)))))) x)
361.0ms
(/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))

series7.9s

Counts
4 → 12
Calls
4 calls:
995.0ms
(- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))
887.0ms
(* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))
2.6s
(fma y (/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y)))))) x)
3.4s
(/ (* z (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))

simplify2.6s

Algorithm
egg-herbie
Counts
4009 → 4009
Iterations

Useful iterations: 0 (240.0ms)

IterNodesCost
013731305438

prune38.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize6.0ms

Local error

Found 2 expressions with local error:

2.5b
(/ (* t z) y)
5.9b
(fma y (/ (* t z) y) x)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
7×add-exp-log add-cbrt-cube
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
3×times-frac associate-/r*
2×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
1×frac-2neg prod-exp clear-num cbrt-unprod fma-udef div-inv associate-/l*
Counts
2 → 33
Calls
2 calls:
3.0ms
(/ (* t z) y)
0.0ms
(fma y (/ (* t z) y) x)

series64.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(/ (* t z) y)
42.0ms
(fma y (/ (* t z) y) x)

simplify70.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0133144
1573122
22685122
35001122

prune79.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

regimes147.0ms

Accuracy

0% (2.0b remaining)

Error of 2.2b against oracle of 0.1b and baseline of 2.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03224
14124
24124

end0.0ms

sample591.0ms

Algorithm
intervals
Results
331.0ms8316×body80valid
16.0ms90×body640valid
10.0ms47×body1280valid
6.0ms56×body320valid
4.0ms45×body160valid