Details

sample55.0ms

Algorithm

intervals

Results

29.0ms	270×	body	80	valid
2.0ms	4×	body	640	valid
1.0ms	2×	body	1280	valid
0.0ms	1×	body	320	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	12	15
1	54	15
2	147	14
3	334	14
4	996	14
5	3305	14
done	5000	14

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(tanh (/ t y))
0.0b	(tanh (/ x y))
1.0b	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
1.0b	(* z (- (tanh (/ t y)) (tanh (/ x y))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
9×	`frac-sub`
8×	`tanh-def`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
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

4 → 89

Calls

4 calls:

3.0ms	(tanh (/ t y))
2.0ms	(tanh (/ x y))
0.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
61.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

series1.1s

Counts

4 → 12

Calls

4 calls:

140.0ms	(tanh (/ t y))
124.0ms	(tanh (/ x y))
426.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
408.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

simplify985.0ms

Counts

101 → 101

Iterations

Useful iterations: done (981.0ms)

Iter	Nodes	Cost
0	205	2180
1	476	1819
2	1553	1567
done	5000	1413

prune485.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(tanh (/ t y))
0.0b	(- (tanh (/ t y)) (tanh (/ x y)))
0.0b	(tanh (/ x y))
5.2b	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
24×	`add-cube-cbrt`
18×	`frac-sub`
14×	`tanh-def`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `associate-l` `*-commutative`

Counts

4 → 116

Calls

4 calls:

2.0ms	(tanh (/ t y))
17.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
2.0ms	(tanh (/ x y))
102.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

series1.4s

Counts

4 → 12

Calls

4 calls:

113.0ms	(tanh (/ t y))
390.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
132.0ms	(tanh (/ x y))
724.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

simplify1.8s

Counts

128 → 128

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	217	3360
1	634	2813
2	2434	2449
done	5000	2218

prune474.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(tanh (/ x y))
0.3b	(+ (* (tanh (/ t y)) (* y z)) (* (- (tanh (/ x y))) (* y z)))
5.7b	(* (- (tanh (/ x y))) (* y z))
5.9b	(* (tanh (/ t y)) (* y z))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-*l/`
14×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`associate-l`
12×	`distribute-neg-frac`
9×	`frac-add` `tanh-def`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-out` `distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `neg-mul-1` `distribute-rgt-out` `fma-def` `flip3-+` `unsub-neg` `sum-log` `flip-+`

Counts

4 → 92

Calls

4 calls:

4.0ms	(tanh (/ x y))
61.0ms	(+ (* (tanh (/ t y)) (* y z)) (* (- (tanh (/ x y))) (* y z)))
43.0ms	(* (- (tanh (/ x y))) (* y z))
45.0ms	(* (tanh (/ t y)) (* y z))

series1.3s

Counts

4 → 12

Calls

4 calls:

125.0ms	(tanh (/ x y))
721.0ms	(+ (* (tanh (/ t y)) (* y z)) (* (- (tanh (/ x y))) (* y z)))
215.0ms	(* (- (tanh (/ x y))) (* y z))
201.0ms	(* (tanh (/ t y)) (* y z))

simplify2.1s

Counts

104 → 104

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	197	1850
1	645	1683
2	2722	1578
done	5001	1571

prune532.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (exp (* 2 (/ t y))))
0.7b	(/ (expm1 (* 2 (/ t y))) (+ 1 (exp (* 2 (/ t y)))))
1.0b	(fma y (* z (- (/ (expm1 (* 2 (/ t y))) (+ 1 (exp (* 2 (/ t y))))) (tanh (/ x y)))) x)
1.0b	(* z (- (/ (expm1 (* 2 (/ t y))) (+ 1 (exp (* 2 (/ t y))))) (tanh (/ x y))))

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`distribute-rgt-in` `distribute-lft-in`
23×	`distribute-lft-out`
14×	`associate-/r/`
8×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
7×	`div-inv`
6×	`pow1` `associate-r` `add-log-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `associate-l` `frac-sub` `associate-/l*`
2×	`sub-neg` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `flip3--` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `tanh-def` `distribute-lft-out--` `expm1-udef` `unswap-sqr`

Counts

4 → 203

Calls

4 calls:

9.0ms	(+ 1 (exp (* 2 (/ t y))))
15.0ms	(/ (expm1 (* 2 (/ t y))) (+ 1 (exp (* 2 (/ t y)))))
0.0ms	(fma y (* z (- (/ (expm1 (* 2 (/ t y))) (+ 1 (exp (* 2 (/ t y))))) (tanh (/ x y)))) x)
287.0ms	(* z (- (/ (expm1 (* 2 (/ t y))) (+ 1 (exp (* 2 (/ t y))))) (tanh (/ x y))))

series922.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ 1 (exp (* 2 (/ t y))))
105.0ms	(/ (expm1 (* 2 (/ t y))) (+ 1 (exp (* 2 (/ t y)))))
433.0ms	(fma y (* z (- (/ (expm1 (* 2 (/ t y))) (+ 1 (exp (* 2 (/ t y))))) (tanh (/ x y)))) x)
348.0ms	(* z (- (/ (expm1 (* 2 (/ t y))) (+ 1 (exp (* 2 (/ t y))))) (tanh (/ x y))))

simplify1.3s

Counts

215 → 215

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	336	10266
1	658	8084
2	1586	6908
done	5000	5690

prune723.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes156.0ms

Accuracy

16% (3.4b remaining)

Error of 3.6b against oracle of 0.2b and baseline of 4.2b

bsearch152.0ms

Steps

Iters	Range		Point
9	7.084463501826363e+102	4.7146917033201894e+110	4.864775668665886e+109
11	-1.1597648106180424e+207	-1.5360852676117261e+181	-1.3195084377482854e+194

simplify17.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	58
1	46	58
2	50	58
3	57	58
done	57	58

end0.0ms

sample1.3s

Algorithm

intervals

Results

919.0ms	8329×	body	80	valid
25.0ms	81×	body	640	valid
18.0ms	41×	body	1280	valid
17.0ms	74×	body	320	valid
6.0ms	39×	body	160	valid