Details

Time bar (total: 16.8s)

sample64.0ms

Algorithm
intervals
Results
34.0ms269×body80valid
1.0ms2×body1280valid
1.0ms3×body320valid
0.0ms1×body640valid
0.0ms1×body160valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
01215
15415
214714
333414
499614
5330514
done500014

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(tanh (/ t y))
0.7b
(* z (- (tanh (/ t y)) (tanh (/ x y))))
0.9b
(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×*-un-lft-identity
18×prod-diff
17×add-cube-cbrt
11×distribute-rgt-in distribute-lft-in associate-*r/
9×frac-sub
7×tanh-def
5×pow1 add-exp-log associate-*r* add-cbrt-cube
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×sub-neg
1×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod fma-udef distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 77
Calls
3 calls:
4.0ms
(tanh (/ t y))
61.0ms
(* z (- (tanh (/ t y)) (tanh (/ x y))))
0.0ms
(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)

series885.0ms

Counts
3 → 9
Calls
3 calls:
145.0ms
(tanh (/ t y))
379.0ms
(* z (- (tanh (/ t y)) (tanh (/ x y))))
361.0ms
(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)

simplify904.0ms

Counts
86 → 86
Iterations

Useful iterations: done (899.0ms)

IterNodesCost
01962041
14581690
214521438
done50001286

prune333.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(tanh (/ t y))
0.7b
(* z (- (pow (tanh (/ t y)) 1) (tanh (/ x y))))
0.9b
(fma y (* z (- (pow (tanh (/ t y)) 1) (tanh (/ x y)))) x)

rewrite413.0ms

Algorithm
rewrite-expression-head
Rules
42×prod-diff
38×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
23×distribute-rgt-in distribute-lft-in
19×unpow-prod-down
7×associate-*r* sqr-pow
5×pow1 add-exp-log add-cbrt-cube
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp difference-of-squares
2×sub-neg associate-*r/
1×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod fma-udef tanh-def distribute-lft-out-- unswap-sqr
Counts
3 → 94
Calls
3 calls:
2.0ms
(tanh (/ t y))
69.0ms
(* z (- (pow (tanh (/ t y)) 1) (tanh (/ x y))))
0.0ms
(fma y (* z (- (pow (tanh (/ t y)) 1) (tanh (/ x y)))) x)

series830.0ms

Counts
3 → 9
Calls
3 calls:
108.0ms
(tanh (/ t y))
323.0ms
(* z (- (pow (tanh (/ t y)) 1) (tanh (/ x y))))
398.0ms
(fma y (* z (- (pow (tanh (/ t y)) 1) (tanh (/ x y)))) x)

simplify841.0ms

Counts
103 → 103
Iterations

Useful iterations: done (836.0ms)

IterNodesCost
01983217
13862127
29991602
done50001314

prune371.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(tanh (/ t y))
0.0b
(+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
5.6b
(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
36×prod-diff
31×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
22×distribute-rgt-in associate-+r+ distribute-lft-in
11×associate-*r/
9×frac-sub
8×pow1 add-exp-log add-cbrt-cube
7×tanh-def
5×associate-*r* add-log-exp
4×sub-neg
3×expm1-log1p-u fma-def pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
1×+-commutative flip3-- flip3-+ associate-*l* sum-log *-commutative flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
3 → 105
Calls
3 calls:
4.0ms
(tanh (/ t y))
23.0ms
(+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
73.0ms
(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

series1.0s

Counts
3 → 9
Calls
3 calls:
144.0ms
(tanh (/ t y))
600.0ms
(+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
266.0ms
(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

simplify2.0s

Counts
114 → 114
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02372937
16502426
224152058
done50001846

prune467.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (* 2 (/ t y)))
0.3b
(/ (expm1 (* 2 (/ t y))) (+ (exp (* 2 (/ t y))) 1))
0.7b
(* z (- (pow (/ (expm1 (* 2 (/ t y))) (+ (exp (* 2 (/ t y))) 1)) 1) (tanh (/ x y))))
0.9b
(fma y (* z (- (pow (/ (expm1 (* 2 (/ t y))) (+ (exp (* 2 (/ t y))) 1)) 1) (tanh (/ x y)))) x)

rewrite656.0ms

Algorithm
rewrite-expression-head
Rules
159×*-un-lft-identity
132×prod-diff
123×add-sqr-sqrt
113×add-cube-cbrt
110×unpow-prod-down
85×times-frac
68×distribute-rgt-in distribute-lft-in
22×distribute-lft-out
14×associate-/r/
8×add-exp-log associate-*r* add-cbrt-cube
7×flip3-+ flip-+ div-inv sqr-pow
6×pow1
5×log1p-expm1-u
4×expm1-log1p-u associate-/r* add-log-exp difference-of-squares
3×associate-*l* associate-/l*
2×sub-neg associate-*r/ expm1-udef
1×cbrt-undiv expm1-log1p flip3-- frac-2neg div-sub div-exp pow-prod-down prod-exp clear-num *-commutative flip-- cbrt-unprod fma-udef distribute-lft-out-- unswap-sqr
Counts
4 → 220
Calls
4 calls:
0.0ms
(expm1 (* 2 (/ t y)))
26.0ms
(/ (expm1 (* 2 (/ t y))) (+ (exp (* 2 (/ t y))) 1))
612.0ms
(* z (- (pow (/ (expm1 (* 2 (/ t y))) (+ (exp (* 2 (/ t y))) 1)) 1) (tanh (/ x y))))
0.0ms
(fma y (* z (- (pow (/ (expm1 (* 2 (/ t y))) (+ (exp (* 2 (/ t y))) 1)) 1) (tanh (/ x y)))) x)

series744.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(expm1 (* 2 (/ t y)))
72.0ms
(/ (expm1 (* 2 (/ t y))) (+ (exp (* 2 (/ t y))) 1))
287.0ms
(* z (- (pow (/ (expm1 (* 2 (/ t y))) (+ (exp (* 2 (/ t y))) 1)) 1) (tanh (/ x y))))
356.0ms
(fma y (* z (- (pow (/ (expm1 (* 2 (/ t y))) (+ (exp (* 2 (/ t y))) 1)) 1) (tanh (/ x y)))) x)

simplify1.5s

Counts
232 → 232
Iterations

Useful iterations: done (1.5s)

IterNodesCost
038212519
17309178
219277112
done50015875

prune661.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes218.0ms

Accuracy

0% (1.6b remaining)

Error of 2.0b against oracle of 0.4b and baseline of 2.0b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01316
11614
done1614

end0.0ms

sample1.5s

Algorithm
intervals
Results
911.0ms8336×body80valid
33.0ms108×body640valid
18.0ms45×body1280valid
14.0ms50×body320valid
6.0ms35×body160valid